A Railway Track Geometry Measuring Trolley System Based on Aided INS

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Article A Railway Track Geometry Measuring Trolley System Based on Aided INS

Qijin Chen 1, Xiaoji Niu 1,2, Lili Zuo 3, Tisheng Zhang 1,*, Fuqin Xiao 3, Yi Liu 4 and Jingnan Liu 1,2

1 GNSS Research Center, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China; [email protected] (Q.C.); [email protected] (X.N.); [email protected] (J.L.) 2 Collaborative Innovation Center of Geospatial Technology, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China 3 Wuhan Municipal Construction Group Co., Ltd., Wuhan 430023, China; [email protected] (L.Z.); [email protected] (F.X.) 4 Shenzhen Datie Detecting and Surveying Inc., Shenzhen 518109, China; [email protected] * Correspondence: [email protected]

Received: 8 January 2018; Accepted: 7 February 2018; Published: 10 February 2018

Abstract: Accurate measurement of the railway track geometry is a task of fundamental importance to ensure the track quality in both the construction phase and the regular maintenance stage. Conventional track geometry measuring trolleys (TGMTs) in combination with classical geodetic surveying apparatus such as total stations alone cannot meet the requirements of measurement accuracy and surveying efficiency at the same time. Accurate and fast track geometry surveying applications call for an innovative surveying method that can measure all or most of the track geometric parameters in short time without interrupting the railway traffic. We provide a novel solution to this problem by integrating an inertial navigation system (INS) with a geodetic surveying apparatus, and design a modular TGMT system based on aided INS, which can be configured according to different surveying tasks including precise adjustment of slab track, providing tamping measurements, measuring track deformation and irregularities, and determination of the track axis. TGMT based on aided INS can operate in mobile surveying mode to significantly improve the surveying efficiency. Key points in the design of the TGMT’s architecture and the data processing concept and workflow are introduced in details, which should benefit subsequent research and provide a reference for the implementation of this kind of TGMT. The surveying performance of proposed TGMT with different configurations is assessed in the track geometry surveying experiments and actual projects.

Keywords: railway; track geometry surveying; aided INS; track trolley; inertial surveying; mobile surveying

1. Introduction Railway track geometry quality has a decisive inﬂuence on the dynamic performance of the vehicle [1], and railway operating safety and passenger comfort depend to a large extent on the smoothness of the railway track, especially for high-speed railways. The track condition tends to deteriorate due to external factors, such as the frequent passage of heavy trains and deformation of the track bed. These factors make the railway track drift away from its designed geometric position and result in track irregularities. Track irregularity, i.e., track deformation, is one of the most important factors that cause safety problems and further track deterioration, so accurate measurement of the track geometry is a task of fundamental importance for adjusting deformed tracks and ensuing high operational safety.

Sensors 2018, 18, 538; doi:10.3390/s18020538 www.mdpi.com/journal/sensors Sensors 2018, 18, 538 2 of 26

Railway track geometry is characterized by its external and internal geometric parameters. The external track geometry is defined by the absolute position of the track axis/centerline in 3D space, and the internal geometry is determined with five types of principal parameters, including alignment, longitudinal level, gauge, cross level and twist [2]. There are different accuracy requirements concerning the track smoothness and the absolute position of the track in the geodetic reference frame [3]: (a) For example, the high speed railway track must be maintained with an absolute position accuracy of 1 cm relative to the track geodetic control network and sub-millimeter relative accuracy to control the short wavelength track irregularity and ensure track smoothness and inner geometry consistency; (b) The requirements in terms of track correction values to guide tamping machines or precise adjustment of slab track are about 1 mm; (c) For the norm speed ballasted railway, it is practically required to survey the track axis with 1–5 cm accuracy for redesign, building an adjacent new line or reconstructing the geometric parameters to improve the operating speed of an existing line. Besides these accuracy requirements, time efficiency is another critical issue for track surveying, because the time slots or skylight time permitted for railway surveying each day for an existing line is typically limited due to the high traffic volumes. The overall railway track geometry condition of the existing line is inspected regularly by dedicated track inspection trains or track recording vehicles [4] owned by the railway management department. Dedicated track inspection trains can survey at high speed, but provide only relative information which hardly conforms to the accuracy requirements in the determination of the track geometric deformation and their related localization for tasks such as precise track adjustment applications. In addition, it is too expensive and inflexible to use heavy dedicated track inspection trains for geometry surveying on short track sections or on construction sites. Lightweight and flexible track geometry measuring trolleys (TGMTs) in combination with high precision geodetic surveying apparatus were developed for geometry measurements of unloaded tracks, and provide follow-up accurate measurements after the dedicated track inspection train for regular maintenance of existing lines and accurate measurement for alignment, precise adjustment or tamping applications during the railway construction stage [5]. There are a variety of TGMTs with different functionalities, handling different tasks and using different surveying technology, which can be roughly classified into two typical categories: the relative measuring trolley/relative TGMTs and absolute measuring trolley/absolute TGMTs, but sometimes it is not easy to distinguish between them. The relative TGMTs mainly measure part or all of the internal geometric parameters and provide relative measurement information by using some relative measuring techniques such as the Hallade/versine method [1,3,6], inertial sensors, and laser alignment methods [7]. The classical chord method or Hallade surveying originally used in dedicated track inspection trains are adopted in the relative TGMTs to measure the versine of a predefined chord to evaluate the inner geometric consistency of the track. The inertial surveying method typically uses inertial sensors such as gyroscopes or inertial measurement units (IMUs) to measure the track attitude angles, including roll, pitch and azimuth, then the IMU trajectory is derived by integration of the pitch and azimuth angle measurements along the covered distance provided by distance sensors such as odometers. The measurement accuracy of the inertial surveying method degrades as the covered distance increases. Absolute TGMTs measure the absolute external geometric parameters together with part or all of the internal geometric parameters. Absolute track axis/centerline position coordinates are determined instantly by such absolute geodetic surveying apparatuses as total stations or global navigation satellite system (GNSS) receivers. A number of previous research works on TGMTs in combination with classical geodetic apparatuses can be found, for example the Rhomberg track surveying trolley originally developed by the University of Stuttgart, the SURVER trolley developed by German Railway DB, and the Geo++ trolley of Garbsen. More details on these trolleys can be found in [3]. Galus [3] at ETH Zurich designed a modular multisensory track surveying trolley system, the Swiss trolley, which integrates a total station, laser scanner, cameras and GNSS to determine the track geometric Sensors 2018, 18, 538 3 of 26 parameters instantly while measuring. Details on the design and functionalities of the TGMTs are introduced thoroughly and comprehensively in his Ph.D. thesis. Akpinar [8] designed a multisensory railway track geometry surveying system based on GNSS, total station, linear variable differential transformers and inclinometer which is used as an alternative to classical geodetic measurement methods to control the railway track geometry. The adaptive Kalman filtering algorithm is adapted for instant determination of the track geometric parameters including track gauge, cross level, gradient and track axis coordinates [9]. More similar literatures can be found in [5,10]. TGMTs using these classical geodetic apparatuses such as total station and GNSS in combination with gauge and cross level measuring sensors are a proven technology for precise railway track geometry surveying, and it is now the instrument manufacturing companies’ business to customize and produce such kind of TGMTs. The most well-known product using this technology is the Amberg GRP surveying system series by Amberg Technologies (Regensdorf-Wattcity, Switzerland), and the Trimble GEDO system by Trimble Inc. (Sunnyvale, CA, USA). Typical absolute TGMTs, such as the Amberg GRP1000, use an autonomous motorized total station to measure the 3D coordinates of the trolley-borne prism relative to the geodetic control network, in which case the total station is typically placed near the track axis and the TGMT stops at the sleeper/fastening system point or at pre-determined distance intervals and remains stationary for static measurements. The TGMT combined with a high precision total station is able to achieve about 1 mm accuracy in this stop-and-go surveying mode when the line of sight is shorter than 70 m. Obviously absolute TGMTs are accurate enough for railway track geometry surveying, but the speed is fair low due to the stop-and-go surveying mode, and only about 150-m track per hour can be surveyed by this method. GNSS is also widely used for absolute geo-referencing to achieve 2–5 cm measurement accuracy in the post-processing kinematic mode. Is it possible to measure the track geometry with 1 mm absolute accuracy in real mobile surveying mode and significantly improve the speed, for example to 2.5 km/h, compared to the conventional stop-and-go mode (0.15 km/h). It is obvious that both the conventional absolute and relative TGMTs each have their own shortcomings and neither of them can address this problem, so clients have to compromise between the measurement accuracy and surveying speed when choosing a method. Actually, achieving 1 mm absolute accuracy in mobile surveying mode is a big challenge for the whole geodesy and surveying discipline. There is little previous research work attempting to address this problem from different aspects. The authors of this work proposed in 2013 a novel method of measuring the railway track irregularity based on INS/GNSS integrated system, which is capable of measuring the track irregularity with 1 mm relative accuracy and significantly improve the surveying efficiency, and is the primary prototype of the TGMT based on aided INS introduced in this paper [11,12]. Since then there has been some follow-up research on TGMTs that use the inertial navigation technique to improve the surveying speed. Li [13] used the laser-aided INS/odometer integrated system to measure the subway track irregularity where the geo-reference absolute position relative to the geodetic control network is determined by the laser scanner to estimate the INS drift. Jiang [14,15] introduced a data processing algorithm for TGMTs based on IMUs/odometers and analyzed the theoretical error propagation of the INS/odometer integration updated by landmark and zero velocity. Since 2015, Amberg Technologies has updated their Amberg GRP system by integrating an IMU to improve the surveying efficiency of models such as the Amberg IMS 3000, and Leica Geosystems and Trimble Inc. claim they will offer similar TGMT products in the coming future, but insight into the technical details of these commercial products is limited. Further studies are need to comprehensively address the related technique problems on the TGMTs based on aided INS which aim at achieving 1 mm accuracy in mobile surveying mode. The contribution of this paper is to provide a comprehensive solution to the challenges mentioned above by integrating INS with a precise geodetic surveying method such as total station and GNSS to provide accurate measurement of the track geometry aiming at different task in mobile surveying modes with a modular system design. Since TGMTs based on aided INS for fast and accurate Sensors 2018, 18, 538 4 of 26

Sensors 2018, 18, x 4 of 26 track geometry surveying are a newly emerging technology, key points of the design of the TGMT’s whicharchitecture should and benefit the data subsequent processing research concept and and provide workflow a reference are introduced for the thoroughly, implementation which shouldof this kindbenefit of subsequentTGMTs based research on aided and INS. provide This paper a reference is organized for the implementationas follows: Section of this2 presents kind of the TGMTs basic measuringbased on aided principle INS. This of th papere TGMT is organized based on as aided follows: INS. Section Section2 presents 3 is devoted the basic to the measuring concept principle and key pointsof the TGMTof designing based onthe aided track INS.geometry Section measuring3 is devoted trolley to the system. concept The and concept key points and ofworkflow designing of thethe datatrack post geometry processing measuring is introduced trolley system. in Section The concept 4. Field and test workflow and result of the analysis data post is preseprocessingnted in is Sectionintroduced 5. in Section4. Field test and result analysis is presented in Section5.

2. Measuring Principle of TGMT Based on Aided INS The r railail or track axis is a three dimensional curve by nature and there are different accuracy requirements concerning the rail smoothness and its absolute position in the reference geod geodeticetic frame. The railway track geometry can be uniquely determined with the 3D position coordinates of the track axis or referencereference rail rail together together with with gauge gauge and and cross cross level. level. Once Once the the track track position, position, gauge gauge and crossand cross level levelare measured are measured accurately, accurately, the actual the track actual geometry track geometry can be reconstructed, can be reconstructed, track geometric track parameters geometric parametersand deformation and deformation can be identified, can be and identified, track geometric and track quality geometric can bequality evaluated. can be The evaluated. definition The of definitionthe principal of track the principal geometric track parameters geometric including parameters gauge, including cross level, gauge, alignment, cross longitudinal level, alignment, level, longitudinaltwist, together level, with twist, versines together with respectwith versines to a chord with of respect given length,to a chord and of track given irregularities length, and in track both irregularitiesthe horizontal in and both vertical the horizontal directions and can vertical be found directions in [2,11 ,can12]. be found in [2,11,12]. TThehe TGMT based on aided INS integrates an IMU, gauge measuring sensor, odometer and absolute positioning sensor on on a specific specific lightweight tra trackck trolley to survey the track geometry in kinematic/mobile surveying surveying mode. mode. The The track track trolley trolley without without suspension suspension connection maintains continuous contact with the railway track in both the across across-track-track and vertical directions. The The trolley trolley wheels are used to link the aided INS and the rails mechanically mechanically,, which allowsallows the inertial sensors to “sense”“sense” thethe tracktrack geometrygeometry andand deformation.deformation. Railway track irregularity inspection is based on the response ofof thethe tracktrack trolleytrolley toto thethe track track irregularities, irregularities which, which would would cause cause a motiona motion state state fluctuation fluctuation of ofthe the trolley trolley moving moving on on the the rails. rails. These These response response signal signal can can be be captured captured by by the the aided aided INS. INS. INS is is well well known known to beto capable be capable of providing of providing position position and attitude and attitudemeasurements measurements with extremely with extremelyhigh relative high accuracy relative inaccuracy a short in time a short range. time Aided range. INS Aided can INS take can advantage take advantage of external of external update updateinformation, information, such as GNSS such or as total GNSS station or total position, station to correct position, the navigationto correct error the navigation accumulation error of accumulationthe INS so as of to the maintain INS so itsas to relative maintain measurement its relative measurement accuracy over accuracy a longer over time a longer range andtime attachrange andthe measurements attach the measurements to an absolute to geo-reference.an absolute geo Figure-reference.1 illustrates Figure the 1 measuring illustrates principle the measuring of the principleTGMT based of the on TGMT aided based INS: the on TGMTaided INS: captures the TGMT the 3D captures position, the attitude 3D position, angles, attitude gauge accurately angles, gauge and accuratelysimultaneously, and simultaneously, based on which base thed track on which geometry the istrack determined geometry and is determined all principal and track all geometric principal trackparameters geometric can beparameters derived. can be derived.

Figure 1.1. Illustration of the TGMT based on GNSS/INS system system..

3. Concept of A-INS Railway Track Measuring System 3. Concept of A-INS Railway Track Measuring System The TGMT based on aided INS is designed to capture accurate 3D position coordinates, gauge, The TGMT based on aided INS is designed to capture accurate 3D position coordinates, gauge, and event signals simultaneously, based on which all railway track geometric parameters can be and event signals simultaneously, based on which all railway track geometric parameters can be derived and track quality can be evaluated and associate the precise localization information to the derived and track quality can be evaluated and associate the precise localization information to the measured data. The TGMT based on aided INS is a multisensory surveying system which integrates measured data. The TGMT based on aided INS is a multisensory surveying system which integrates several units including track trolley platform, inertial measurement unit, absolute positioning module such as total station or GNSS, gauge measuring sensor, odometer, sleeper recognizer, data recording system. A modular design is adopted for the system’s structure implementation as

Sensors 2018, 18, 538 5 of 26 several units including track trolley platform, inertial measurement unit, absolute positioning module suchSensors as 2018 total, 18, stationx or GNSS, gauge measuring sensor, odometer, sleeper recognizer, data recording5 of 26 system. A modular design is adopted for the system’s structure implementation as depicted in Figure2. Thedepicted basic in and Figure common 2. The module basic containsand common track module trolley platform contains ontrack which trolle ally sensors platform are on ﬁtted: which IMU, all twosensors odometers, are fitted and: IMU, gauge two measuring odometers, sensor. and The gauge absolute measuring positioning sensor. module The absoluteprovides positioningan absolute geo-referencemodule provides for thean absolute multi-sensor geo- datareference fusion for and the can multi be- conﬁguredsensor data as fusion a GNSS and or can total be station configured module as accordinga GNSS or tototal different station surveying module accordin tasks. Eventg to different signals surveying are recorded task simultaneouslys. Event signals to are label recorded some importantsimultaneously information, to label suchsome as important tagging the information, position of such a tie/sleeper. as tagging All the data position from different of a tie/sleeper. sensors All are centrallydata from synchronized different sensors in time are and centrally recorded synchronized in the data recording in time and system. recorded Key points in the of data the surveyingrecording systemsystem. andKey sensors points of are the introduced surveying in system the following and sensors subsections. are introduced in the following subsections.

Track geometry measuring trolley based on aided INS

Basic module Abs.position module 1 PPS IMU GNSS

Raw observations Basi Basi Odometers Total Station Pos. & raw meas.

Gauge Data recording System Synchronize & record Events

Figure 2 2.. Modular design of the TGMT based on aided INS.INS.

3.1. Track Trolley 3.1. Track Trolley The rigid and accurate trolley is the platform on which all measuring systems and sensors are The rigid and accurate trolley is the platform on which all measuring systems and sensors fitted. Conforming to the normative railway standards, the trolley is designed as a portable T-shaped are fitted. Conforming to the normative railway standards, the trolley is designed as a portable structure which does not load the track and can readily be placed on or off the track by two operating T-shaped structure which does not load the track and can readily be placed on or off the track by two surveyors as shown in Figure 3 and Figure 4. The trolley consists of two beams with one along the operating surveyors as shown in Figures3 and4. The trolley consists of two beams with one along the x-direction and the other along the y-direction. An adapter is designed available for different track x-direction and the other along the y-direction. An adapter is designed available for different track gauges. The trolley can be pushed or hauled by human force with a pushing rod and is capable of gauges. The trolley can be pushed or hauled by human force with a pushing rod and is capable of measuring from standstill to the maximum permissible speed of 5 m/s. A handbrake is adopted to measuring from standstill to the maximum permissible speed of 5 m/s. A handbrake is adopted to prevent unintentional motion when the trolley must stay at rest for static measuring, such as the static prevent unintentional motion when the trolley must stay at rest for static measuring, such as the static alignment process of the INS and free stationing of the total station. The trolley has three wheels fixed alignment process of the INS and free stationing of the total station. The trolley has three wheels fixed to the platform that contact the rails on the upper surface of the head of the rail, i.e., running table, to the platform that contact the rails on the upper surface of the head of the rail, i.e., running table, the axles of which are coplanar and all perpendicular to the x-direction. A lateral roller is mounted the axles of which are coplanar and all perpendicular to the x-direction. A lateral roller is mounted under each wheel with its axle coplanar with those of the related wheels. The rollers contact the inner under each wheel with its axle coplanar with those of the related wheels. The rollers contact the inner surface of the rails at the gauge measuring point specified by the normative standards. Two rollers surface of the rails at the gauge measuring point specified by the normative standards. Two rollers on the left hand side, i.e., along the x-axis direction under wheel A1 and wheel A2 as depicted in on the left hand side, i.e., along the x-axis direction under wheel A1 and wheel A2 as depicted in Figure 3, are fixed with trolley platform guiding the motion of the trolley, and the third one is fixed Figure3, are fixed with trolley platform guiding the motion of the trolley, and the third one is fixed with a gauge measuring spring to form a free expansion end. The acting force of the gauge measuring with a gauge measuring spring to form a free expansion end. The acting force of the gauge measuring spring along the y-direction presses the rollers against the inner surface of the rails to ensure rigid spring along the y-direction presses the rollers against the inner surface of the rails to ensure rigid and reliable contact is maintained. Adopting the lateral rollers architecture design has advantages and reliable contact is maintained. Adopting the lateral rollers architecture design has advantages over the wheel flange for its longer life span and reduced necessity for maintenance when working over the wheel flange for its longer life span and reduced necessity for maintenance when working in in kinematic/mobile surveying mode. The response of the platform to rails’ geometric deformation is kinematic/mobile surveying mode. The response of the platform to rails’ geometric deformation is the premise of track geometry survey, thus the wheels of the trolley should be able to keep reliable the premise of track geometry survey, thus the wheels of the trolley should be able to keep reliable and continuous rigid contact with the rails when moving on rails. This requires that the trolley does and continuous rigid contact with the rails when moving on rails. This requires that the trolley does not jump off with respect to the rails in the vertical direction and not slide laterally, in which case the not jump off with respect to the rails in the vertical direction and not slide laterally, in which case track geometry can be derived from the trajectory of the trolley. Special attention should be paid to the magnitude of the acting force of the loaded spring to guarantee the continuous and rigid contact, especially in the case when the wheel A3 is put on the lower rail on the curved track section. A universal pedestal adapter in the center of trolley structure is designed as a holder of a total station, GNSS antenna or prism.

Sensors 2018, 18, x 6 of 26

A Wheel (A1, A2, A3) E Pushing rod B Gauge sensor (B1, B2) F Battery holder C IMU G Data recording system A3 G D Gauge adapter

B1 C F v Sensors 2018, 18, 538 xv y 6 of 26 D the track geometry can be derived from the trajectory of the trolley. Special attention should be A1 paid to the magnitude of the acting forcezv of the loaded spring to guarantee the continuous and rigid contact, especially in the case when the wheel A3 is put on the lower rail onE the curved track section. A universal pedestal adapter inB the2 center of trolley structure is designed as a holder of a total station, GNSSSensors antenna 2018, 18, x or prism. 6 of 26 A2 A Wheel (A1, A2, A3) E Pushing rod Figure 3. TGMT based on aided INS design (lateral view). B Gauge sensor (B1, B2) F Battery holder C IMU G Data recording system A3 G As a multisensoryD Gauge system, adapter different sensors cannot be physically co-located on the host trolley platform, and their mounting positions are distinct, which is known as the lever arm. The lever arm is a three dimensional vector defining the displacement from the origin of theB1 reference frame, to the F measurement point of different sensorsC and usually revolved in the reference frame. All lever arms v yv for different sensors should x be measured and calibrated accurately in the identical reference D coordinate frame. Within this work, we choose the host vehicle frame as the reference frame. The vehicle frame (v-frame) is rigidly attached to and defined with the host trolley carrying the measuring system and sensorsA1 with its origin centeredv at the IMU center as depicted in Figure 3. The x-axis z points forward along the vehicle longitudinal direction parallel to the straightE line formed by the two contact points of the left rollersB2 with the inner rail surface, the z-axis is perpendicular to the plane formed by the contact points of the three wheels and points downward, and the y-axis point outward, completing the right-hand set. There areA2 different lever arms those should be accurately measured include the positioning sensor (GNSS, or total station), odometer contact points of the wheels and FigureFigure 3. 3TGMT. TGMT based based on on aided aided INS INS design design (lateral (lateral view). view). rollers, the IMU and so on. As a multisensory system, different sensors cannot be physically co-located on the host trolley A Brake platform, and their mounting positions are distinct, whichD is known as the lever arm. The lever arm B Lateral roller is a three dimensional vector defining the displacement from the origin of the reference frame, to the C Pedestal adapter measurement pointD GNSS of different antenna sensors and usually revolved in the reference frame. All lever arms for different sensorsE Odometer should sensors be measured and calibrated accurately in the identical reference coordinate frame.F SleeperWithin recognizer this work, we choose the host vehicle frame as the reference frame. The vehicle frame (v-frame) is rigidly attached to and defined with the host trolley carrying the measuring C system and sensors with its origin centered at the IMU center as depicted in Figure 3. The x-axis points forward along the vehicle longitudinal direction parallel to the straight line formed by the two contact points of the left rollers with the inner rail surface, the z-axis is perpendicular to the plane formed by the contactA points of the three wheels and points downward, and the y-axis point outward, completing the right-handF set. There are different lever arms those shouldE be accurately measured include the positioningB sensor (GNSS, or totald1 station), odometer contactd2 points of the wheels and rollers, the IMU and so on. FigureFigure 4. 4.TGMT TGMT basedbased onon aided aided INS INS design design (front (front view). view). A Brake D 3.2. IMU B Lateral roller As a multisensoryC Pedestal system, adapter different sensors cannot be physically co-located on the host trolley platform,Inertial and measurement theirD mounting GNSS antenna unit positions (IMU) areis the distinct, core sensor which of is knownthe TGMT as the based lever on arm. aided The INS, lever which arm isis aused three to dimensional bridge theE Odometer positioningvector deﬁning sensors gap the between displacement two external from theabsolu originte position of the reference from a GNSS frame, or to total the measurementstation. The measurement pointF ofSleeper different recognizeraccuracy sensors differs and usuallyfor different revolved type ins of the IMU, reference and the frame. choice All of lever IMU armsdepends for differenton the accuracysensors should requirement, be measured surveying and calibrated task and accurately how frequent in the identicalthe external reference absolute coordinate update C frame. Within this work, we choose the host vehicle frame as the reference frame. The vehicle frame

(v-frame) is rigidly attached to and deﬁned with the host trolley carrying the measuring system and sensors with its origin centered at the IMU center as depicted in Figure3. The x-axis points forward along the vehicle longitudinalA direction parallel to the straight line formed by the two contact points of the left rollers with theF inner rail surface, the z-axis is perpendicular to theE plane formed by the contact points of the threeB wheels and pointsd1 downward, and the y-axisd2 point outward, completing the right-hand set. There are different lever arms those should be accurately measured include the Figure 4. TGMT based on aided INS design (front view).

Sensors 2018, 18, 538 7 of 26 positioning sensor (GNSS, or total station), odometer contact points of the wheels and rollers, the IMU and so on.

3.2. IMU Inertial measurement unit (IMU) is the core sensor of the TGMT based on aided INS, which is used to bridge the positioning gap between two external absolute position from a GNSS or total station. The measurement accuracy differs for different types of IMU, and the choice of IMU depends on the accuracy requirement, surveying task and how frequent the external absolute update information is available. The longer the inertial navigation system is required to work alone the higher the grade of IMU that should be chosen. Since the IMU is mounted on the trolley without any suspension, the IMU is required to be able to withstand some shock and vibration, especially when the trolley is moving at high speed over welded joints. The operating temperature range should also be taken into account since the IMU may be used in a wide temperature range in real railway track surveying. In our design, a navigation grade IMU POS830 manufactured by Wuhan MAP Space Time Navigation Technology Co., Ltd. (shortened as MAP Inc., Wuhan, China) is integrated. It contains a linear quartz accelerometers triad and a ring laser (RLG) gyros triad, and measures acceleration and angular velocity in three mutually orthogonal direction centered at the IMU measuring center, and outputs datasets as incremental velocity and angles. A NovAtel OEMV-2 receiver is built in this system to provide raw GNSS observations at 1 Hz sampling rate. The IMU and GNSS receiver is enclosed in a fully sealed housing designed to withstand water, oil and gas spray. The IMU performance speciﬁcations are listed in Table1.

Table 1. Speciﬁcation of the IMU in POS830.

Physical Weight 8.5 kg Size 190 cm × 190 cm × 183 cm height Temperature range (operating) −40 ◦C~+71 ◦C Power 18–32 V DC, <60 w IMU Parameter Gyroscope Accelerometers Range ±300 deg/s ±10 g Bias 0.01 deg/h 25 mGal Scale factor 10 ppm 10 ppm Sampling rate 200 Hz Shock 40 g GNSS Dual frequency, Sampling rate: 1 Hz, Position accuracy: 2 cm + 1 ppm (RMS) in RT-2 LITE mode

The coordinates of the IMU measurement center, nominally defined as the intersection point of the built-in accelerometer trials, in the v-frame should be calibrated accurately. In practice a chosen reference point rather than the actual measurement center of the IMU are referred to since the actual measurement center is not easy to measure. The aided INS can provide the attitude measurement of itself including roll, pitch and heading angle, while in the coordinate transformation from the measuring sensor to the reference coordinated frame we need the attitude of the trolley platform. Thus the mounting angles or attitude misalignment of the IMU, i.e., the physical angular offset of the IMU body frame with respect to the vehicle body frame (v-frame), should be measured and calibrated accurately which effects the following coordinate transformation. Uncompensated roll and pitch misalignment will result in constant roll and pitch measurement errors, and consequently will produce constant slope and cross level measurement error. For example, to achieve 0.1 mm accuracy in cross Sensors 2018, 18, 538 8 of 26 level measurement, the residual misalignment around roll axis after calibration should be smaller than 0.005 deg. In addition, the mounting angles also effect the performance of the non-holonomic constraint (NHC) of the rails on the motion of the trolley in the aided INS algorithm [11,16]. Therefore, it is critical to estimate and calibrate the mounting angles as accurately as possible, and at least as accurate as the attitude measurement of the aided INS. The mounting angles can be estimated through several approaches. The misalignment around the roll and pitch axes can be easily estimated to a relatively high accuracy by comparing the static attitude measurement from the TGMT in the forward-orientated and reverse-orientated at the same mileage point. The misalignment around the heading axis can be computed by differencing the heading measurements and the reference truth in the calibration lab, or by differencing the heading measurements and the nominal track azimuth series derived from the design file of the railway track. Though the IMU does not need to be mounted in particular orientation, in our TGMT the IMU is mounted with the IMU body frame approximately coinciding with the v-frame. Three specific alignment pins are fixed on the trolley platform to ensure the mounting repeatability of the IMU. The misalignment angles around the heading and pitch axis can also be estimated and calibrated in the data processing algorithm with odometer speed and NHC aiding [16,17].

3.3. Absolute Positioning Unit Absolute positioning module in the TGMT based on aided INS is designed to provide absolute geo-reference data such as the absolute position coordinates to estimate and correct the inertial sensor errors, ensure the absolute measurement accuracy, and attach precise localization information to all measurement results. The requirement for absolute measurement accuracy differs for different surveying tasks which will be discussed in Section5, thus two absolute positioning modules are optional, including a GNSS and total station. The GNSS conﬁguration is designed to provide centimeter level coordinates and a total station is available to achieve an absolute measurement accuracy of 1~2 mm relative to the geodetic control network.

3.3.1. GNSS GNSS is an important method for providing absolute positions in the global coordinate frame with different accuracy levels in geodetic surveying applications. A post processed carrier-phase-dominated differential GNSS is adapted by the TGMT to provide centimeter level positions. The build-in GNSS receiver in the POS830 works as the rover, and the master GNSS receiver locates at a known position, such as the geodetic control network points of the railway. The rover and master receivers record raw GNSS observations at 1 Hz sampling rate simultaneously, and the baseline length usually does not exceed 15 km to ensure centimeter accuracy. A GNSS would always be a good option for the measuring trolley system to provide absolute geo-reference data and integrate with INS whenever GNSS signals are available. The benefits and drawbacks of INS and GNSS are complementary, so by integrating them, the advantages of both technologies are combined to give a continuous, high-bandwidth, complete navigation solution with high long- and short-term accuracy. In the GNSS/INS integrated system GNSS measurements prevent the inertial solution from drifting, while the INS smooths the GNSS solution and bridges signal outages [18]. A loosely coupled GNSS/INS integration algorithm that uses the GNSS position and/or velocity solutes as the measurement inputs to the Kalman filter is adapted for the data processing for its simplicity. Carrier-phase-dominated DGNSS/INS provide high frequency positioning solution with centimeter accuracy and much higher relative measurement accuracy. The TGMT with GNSS/INS module can realize submillimeter relative accuracy in inner track geometric parameter measurement including the track deformation/displacement or track irregularity measurement, however this is not sufficiently accurate for determining the absolute position of the track when millimeter absolute positioning accuracy is required. Therefore, the available application Sensors 2018, 18, 538 9 of 26 scenario of the TGMT with GNSS/INS module is restricted which will be discussed in details in Section5.

3.3.2. Total Station A high precision total station is an important engineering surveying apparatus that provides absolute geo-reference data with submillimeter accuracy relative to the track geodetic control network. The total station is designed to be fixed on the host trolley and moves with the TGMT. The advantage of mounting the total station on the moving host trolley platform rather than on an outside tripod near the track axis is the improvement of stationing efficiency, since the total station can be transferred to next stationing site and set up quickly and the total station does not need leveling before stationing. TheSensors TGMT 2018, stops18, x and keeps in rest at each point where a total station measurement should9 beof 26 carried out. The location of the total station in the reference coordinate system of the control network is bearings and distances of the total station to 5~8 known back-sight points of the railway geodetic determinedcontrol network by a freesurrounding stationing themethod, stationing i.e., site resection. are measur Duringed, as illustrated the free stationing in Figure process,5. The local bearings andpolar distances coordinates of theof the total back station-sight points to 5~8 defined known by back-sight the horizontal points circle of of the the railway total station geodetic can be control networkreadily calculated. surrounding With the a similarity stationing transformation, site are measured, these local as po illustratedlar coordinates in Figure are transformed5. The local to polar coordinatesthe coordinates of the system back-sight of the points track defined control network, by the horizontal and errors circle are distributed of the total by station least can squares be readily calculated.adjustment. With The position a similarity and attitude transformation, angles of the these total local station polar in relation coordinates to the control are transformed network is to the coordinatesdetermined. system of the track control network, and errors are distributed by least squares adjustment. The positionMeasurem andent attitude accuracy angles is the of first the considerationtotal station ininrelation choosing to a the total control station. network Special is attention determined. shouldMeasurement be paid to accuracy protect the is the total first station consideration from mechanical in choosing shock a total when station. experiencing Special large attention shouldacceleration be paids while to protect moving the over total features station fromsuch as mechanical weld joint shocks. For the when TGMT experiencing based on largeaided accelerationsINS, a Leica Nova TS50 optical tracking total station is integrated. The Leica Nova TS50 (Leica Geosystem while moving over features such as weld joints. For the TGMT based on aided INS, a Leica Nova TS50 AG, Heerbrugg, Switzerland), shown in Figure 6, is the latest generation of autonomous tracking optical tracking total station is integrated. The Leica Nova TS50 (Leica Geosystem AG, Heerbrugg, total station with 0.5 automatic aiming accuracy, and 0.6 mm + 1 ppm to prism electronic distance Switzerland),measurement shown accuracy. in Figure By measuring6, is the latest5–8 redundant generation back of- autonomoussight control tracking points, submillimeter total station with 0.5stationing automatic accuracy aiming can accuracy, be ensured. and The 0.6 free mm stationing + 1 ppm provides to prism subm electronicillimeter position distance to integrate measurement accuracy.with the ByINS measuring to give a high 5–8 frequency redundant coordinate back-sight measurement. control points, For accurate submillimeter integration, stationing the lever accuracy canarm be of ensured. the total Thestation free measurement stationing provides center in submillimeterthe host vehicle positionframe, and to the integrate mounting with angles the INS of the to give a hightotal frequency station relative coordinate to the IMU measurement. should be measured For accurate and calibrated. integration, The the total lever station arm measurements of the total station measurementare synchronized center and in recorded the host centrally vehicle frame,in the data and recording the mounting system. angles of the total station relative to the IMUAbout should 1.4 mm be positioning measured andaccuracy calibrated. of the TGMT The total with stationTS/INS module measurements can be achieved are synchronized when the and recordedfree stationing centrally of t inhe thetotal data station recording is carried system. out every 120 m which will be validated in Section 6.2, and longer distance interval between two adjacent stations will lead to an accuracy degradation.

Figure 5. Free stationing procedure. Figure 5. Free stationing procedure.

Figure 6. Leica TS16 total station.

3.4. Gauge Measuring Sensor

Sensors 2018, 18, x 9 of 26 bearings and distances of the total station to 5~8 known back-sight points of the railway geodetic control network surrounding the stationing site are measured, as illustrated in Figure 5. The local polar coordinates of the back-sight points defined by the horizontal circle of the total station can be readily calculated. With a similarity transformation, these local polar coordinates are transformed to the coordinates system of the track control network, and errors are distributed by least squares adjustment. The position and attitude angles of the total station in relation to the control network is determined. Measurement accuracy is the first consideration in choosing a total station. Special attention should be paid to protect the total station from mechanical shock when experiencing large accelerations while moving over features such as weld joints. For the TGMT based on aided INS, a Leica Nova TS50 optical tracking total station is integrated. The Leica Nova TS50 (Leica Geosystem AG, Heerbrugg, Switzerland), shown in Figure 6, is the latest generation of autonomous tracking total station with 0.5 automatic aiming accuracy, and 0.6 mm + 1 ppm to prism electronic distance measurement accuracy. By measuring 5–8 redundant back-sight control points, submillimeter stationing accuracy can be ensured. The free stationing provides submillimeter position to integrate with the INS to give a high frequency coordinate measurement. For accurate integration, the lever arm of the total station measurement center in the host vehicle frame, and the mounting angles of the total station relative to the IMU should be measured and calibrated. The total station measurements are synchronized and recorded centrally in the data recording system. About 1.4 mm positioning accuracy of the TGMT with TS/INS module can be achieved when the free stationing of the total station is carried out every 120 m which will be validated in Section 6.2, and longer distance interval between two adjacent stations will lead to an accuracy degradation.

Sensors 2018, 18, 538 10 of 26 Figure 5. Free stationing procedure.

Figure 6. Leica TS16 total station. Figure 6. Leica TS16 total station.

3.4. Gauge Measuring Sensor About 1.4 mm positioning accuracy of the TGMT with TS/INS module can be achieved when the free stationing of the total station is carried out every 120 m which will be validated in Section 6.2, and longer distance interval between two adjacent stations will lead to an accuracy degradation.

3.4. Gauge Measuring Sensor Track gauge is measured using a high-precision contact mechanical distance measuring system. The gauge measuring sensor is by nature a distance measurement sensor ﬁxed on the beam of the trolley which is perpendicular to the x-axis of the vehicle frame, and measures the length variation of the loaded spring. During the surveying process the spring is under compression, thus the spring presses the three rollers to the inner surface of both rails to keep reliable and continuous contact with rails. The gauge measurement as depicted in Figure7 can be represented as:

d = d1 + d2 + ∆d + KT T (1) where d is the gauge measurement, d1 is a constant offset, d2 represents the varying part of the gauge, KTT is the correction term induced by temperature variation, the related coefﬁcient KT can be calibrated and T is the temperature value measured by thermometer. ∆d is the gauge correction term induced in the curved track section; its theoretical value is computed as: q 2 2 |∆d| = R − R − dw/4 (2) where R is the radius of curvature of the nominal track axis, dw is the distance between the axles of wheel A1 and A2 as illustrated in Figure3. The sign of ∆d is determined by the turn direction of the curve and the orientation of the trolley set on the rails. It is obvious that ∆d shall be zero in a straight line section. The larger the radii of curvature is the smaller the ∆d would be. For example the high speed railway track is usually designed with large radii, in which case the ∆d is small, while for the rails with small radii such as subway and tramway lines this correction term cannot be ignored. It should be pointed out that ∆d is just the nominal correction, while the actual value of this term may be slightly different from the nominal value due to the short wavelength track deformation. Thus it is optimal choice to add another gauge measuring sensor between the two wheels along the x-axis of the trolley to give the complete measurement of the gauge as depicted in Figure3. The gauge sensor shall sample at a sufﬁciently high data rate when the TGMT based on A-INS is working in kinematic/mobile mode. For example, if the trolley moves at a speed of 5 m/s, and the gauge sensor samples at 20 Hz, then the distance interval of the gauge measuring samples would be 0.25 m. In addition, gauge measurement should be synchronized with IMU data. TGMT based on aided INS is able to measure the absolute track gauge with 0.1 mm accuracy after calibration. Sensors 2018, 18, x 10 of 26

Track gauge is measured using a high-precision contact mechanical distance measuring system. The gauge measuring sensor is by nature a distance measurement sensor fixed on the beam of the trolley which is perpendicular to the x-axis of the vehicle frame, and measures the length variation of the loaded spring. During the surveying process the spring is under compression, thus the spring presses the three rollers to the inner surface of both rails to keep reliable and continuous contact with rails. The gauge measurement as depicted in Figure 7 can be represented as:

d d  d Δd  K T (1) 12 T where d is the gauge measurement, d1 is a constant offset, d2 represents the varying part of the gauge, KTT is the correction term induced by temperature variation, the related coefficient KT can be calibrated and T is the temperature value measured by thermometer. Δd is the gauge correction term induced in the curved track section; its theoretical value is computed as:

Δd R  R22  d 4 (2) w where R is the radius of curvature of the nominal track axis, dw is the distance between the axles of wheel A1 and A2 as illustrated in Figure 3. The sign of Δd is determined by the turn direction of the curve and the orientation of the trolley set on the rails. It is obvious that Δd shall be zero in a straight line section. The larger the radii of curvature is the smaller the Δd would be. For example the high speed railway track is usually designed with large radii, in which case the Δd is small, while for the rails with small radii such as subway and tramway lines this correction term cannot be ignored. It should be pointed out that Δd is just the nominal correction, while the actual value of this term may be slightly different from the nominal value due to the short wavelength track deformation. Thus it is optimal choice to add another gauge measuring sensor between the two wheels along the x-axis of the trolley to give the complete measurement of the gauge as depicted in Figure 3. The gauge sensor shall sample at a sufficiently high data rate when the TGMT based on A-INS is working in kinematic/mobile mode. For example, if the trolley moves at a speed of 5 m/s, and the gauge sensor samples at 20 Hz, then the distance interval of the gauge measuring samples would be 0.2Sensors5 m2018. In, addition,18, 538 gauge measurement should be synchronized with IMU data. TGMT based11 ofon 26 aided INS is able to measure the absolute track gauge with 0.1 mm accuracy after calibration.

Δd d1 d2

Δdˆ

Actual position Nominal position

FigureFigure 7 7.. GaugeGauge measurement measurement compensation compensation in in the the curved curved track track section. section.

3.5. Odometer 3.5. Odometer The Hall-effect wheel transducer is chosen as the odometer sensor in the TGMT to measure the The Hall-effect wheel transducer is chosen as the odometer sensor in the TGMT to measure longitudinal distance travelled by the trolley along rails by counting the number of rotations of the the longitudinal distance travelled by the trolley along rails by counting the number of rotations of wheels. The distance measured by the odometer sensor contains a cumulative error which is the wheels. The distance measured by the odometer sensor contains a cumulative error which is proportional to the longitudinal travel distance due to the uncertainty in wheel radius, resolution of proportional to the longitudinal travel distance due to the uncertainty in wheel radius, resolution the odometer, dirt adhered to the wheels, and possible slippage. To obtain more reliable travel of the odometer, dirt adhered to the wheels, and possible slippage. To obtain more reliable travel distance recordings, we mount odometer sensor on both wheel #A1 and #A3 as shown in Figure3. Odometer measurements from the wheel #A1 and #A3 is combined to give a more robust odometer measurement whose cumulative error versus the travel distance is controlled to be smaller than 0.05%. Two Hall-effect transducers are installed on both wheel #A1 and #A3 in a speciﬁc manner, as an effect of the phase shifted signals, the moving directions of the trolley could be derived. Velocity derived from longitudinal distance measurement is an important auxiliary information and constraint for the inertial navigation, which can effectively improve the accuracy of the integrated navigation solution especially when GNSS measurement is unavailable. Complementary to the non-holonomic constraint, the odometer signal can be regarded as the velocity update along the forward (along-track) direction. Therefore, the non-holonomic constraint and the odometer speed compose a complete three dimensional velocity constraint in the vehicle frame [11,16]. In the aided INS algorithm, the scale factor error of the odometer measurement should be taken into account and augmented into the state vector of the Kalman ﬁlter for data fusion, which would be observable when external positioning aiding such as GNSS or position from total station is available. In practice, the lever arm from the IMU measurement center to the contact point of the wheels where odometer sensors are mounted with the rails should be accurately measured and taken into account in the data fusion. Time tags are attached to the odometer sensor recordings so as to synchronize with the IMU raw data. Odometer measurement is also used to aid the zero velocity detection of the TGMT.

3.6. Sleeper Detector Since the correction or precise adjustment of track slabs can be only carried out through the adjustable fastening system, the surveying trolley should output measurements data at the localization of each sleeper or fastening system point. The TGMT based on aided INS is designed for kinematic surveying, which means the trolley does not stop at each sleeper point to measure as the conventional track trolley based on total station such as the Amberg GRP1000 does. Therefore, a TGMT for kinematic surveying should detect and measure the localization of the sleepers, which is implemented by recording the time pulse when the TGMT passes over the sleeper or fastening system. Sensors 2018, 18, 538 12 of 26

A reflective ultrasonic sensor is integrated under the trolley beam to detect the sleepers as illustrated in Figure4. The ultrasonic sensor sends ultrasonic waves from the emitter on the trolley toward the track slab, then receives the reflected waves with a detector. It measures distance between the sensor and the sensing objective, i.e., track slab. The distance between the sensor and the track slab varies significantly when passing over a sleeper, and this event indicating a sleeper would be recorded and synchronized with other sensors. The sleeper detector has the probability of missed and false detection, but this can be identified and corrected easily with the aiding from odometer measurements. Finally, the sleeper localizations are determined by reading the positioning solution through time synchronization information.

3.7. Time Synchronization A kinematic/mobile multisensory system requires accurate time synchronization between the measurements from different sensors. The faster the TGMT moves the more accurate the time synchronization that should be carried out. Since the multiple sensors on the TGMT have different data sampling rates, the event-driven method [3] is adopted for time synchronization: all sensor measurements are recorded in a same data recording system, and tagged by the local clock inside the recording system in the identical time frame. Whenever the recording system receives a measurement signal from sensors, the local time tag is insert into the data package and then stored in the system. The local time provided by the data recording system may drift due to the frequency instability but does not effects the mutual time synchronization between sensors. When GNSS is available the local clock drift can be checked and corrected by introducing the 1 PPS signal (pulse per second) from the GNSS receiver, and the identical local time system can be transformed to the more accurate and uniform GNSS time system. The time synchronization for aided INS integration is critical. When the GNSS/INS module Sensors 2018, 18, x 12 of 26 is adopted as shown in Figure8a, the accurate time synchronization can be ensured from the high precision GNSS time. In In the the case case when when total total station station is is configured conﬁgured as an external absolute positioning sensorsensor as as shown in in Figure 88b,b, thethe timetime synchronizationsynchronization betweenbetween IMUIMU andand totaltotal stationstation isis easyeasy sincesince thethe TGMT is keep static when total station measurement measurementss are carried out. The time synchronization between the positioning sensor and the gauge, sleeper recognizer measurement only only effects the localizationlocalization accuracy accuracy along along the the mileage mileage direction direction where centimeter ssynchronizationynchronization accuracy in distance is is sufficient sufﬁcient and and can can be be easily easily realized. realized. For For example, example, when when the the TGMT TGMT moves moves at a at speed a speed of 5of m/s, 5 m/s, 5 cm 5 cm synchronization synchronization accuracy accuracy in in mileage mileage can can be be guaranteed guaranteed with with time time synchronization accuracy of 10 ms ms..

(a) (b)

FigureFigure 8. Modular 8. Modular design design of of the the TGMT TGMT based based on on aided aided INS. INS. (a ) ( TGMTa) TGMT with with TS/INS TS/INS conﬁguration; configuration; (b) TGMT(b) TGMT with GNSS/INS with GNSS/INS configuration. conﬁguration.

4. Data Data Processing Processing Concepts Concepts TThehe s synchronizedynchronized datasets datasets from from multi multipleple sensors sensors will will be dealt be dealt with with centrally centrally with awith post a- processingpost-processing software software to produce to produce the thefinal ﬁnal solutions. solutions. In Inthis this section section the the concept concept and and workflow workﬂow of of the the data processing is introduced, and key points of the algorithm are emphasized, while the details will be given in a future companion paper. The post-processing software adopts a cascading design which means measurements from different sensors will be preprocessed prior to being fed into the data fusion Kalman filter as shown in Figure 9. This loosely coupled architecture allows for a flexible and modular processing. The data post-processing software contains five modules including: (1) pre-processing, include data integrity check, detection and exclusion. (2) positioning process of the GNSS or the total station. (3) aided INS processing, which includes Kalman filtering and smoothing. (4) mileage/spatial synchronization of all measurements from different sensors; (5) track geometric parameter calculation and track quality assessment. Finally, the implementation of the data post processing software will be introduced.

GNSS or TS Aided INS Integration Odometer Track (Filtering geometric and parameters IMU check integrity smoothing)

& & calculation & track Gauge sensor quality evaluation

Events Faultdetection Design Geometry

Figure 9. Concept of data post processing.

4.1. Data Fault Detection and Integrity Check Like any technology or system, the TGMT based on aided INS are subject to hardware or software failures, and can occasionally outputs outliers much larger than the uncertainty bounds. Integrity checking module detects and isolate these faults in each channel and protect the final

Sensors 2018, 18, x 12 of 26 precision GNSS time. In the case when total station is configured as an external absolute positioning sensor as shown in Figure 8b, the time synchronization between IMU and total station is easy since the TGMT is keep static when total station measurements are carried out. The time synchronization between the positioning sensor and the gauge, sleeper recognizer measurement only effects the localization accuracy along the mileage direction where centimeter synchronization accuracy in distance is sufficient and can be easily realized. For example, when the TGMT moves at a speed of 5 m/s, 5 cm synchronization accuracy in mileage can be guaranteed with time synchronization accuracy of 10 ms.

(a) (b)

Figure 8. Modular design of the TGMT based on aided INS. (a) TGMT with TS/INS configuration; (b) TGMT with GNSS/INS configuration.

4. Data Processing Concepts Sensors 2018, 18, 538 13 of 26 The synchronized datasets from multiple sensors will be dealt with centrally with a post- processing software to produce the final solutions. In this section the concept and workflow of the data processing is introduced, and key points of the algorithm are emphasized emphasized,, while the details will be given given in in a a future future companion companion paper. paper. The The post post-processing-processing software software adopts a cascading cascading design design which which means measurementsmeasurements fromfrom different different sensors sensors will will be preprocessedbe preprocessed prior prior to being to being fed into fed the into data the fusion data fusionKalman Kalman filter as filter shown as shown in Figure in9 Figure. This loosely 9. This coupledloosely coup architectureled architecture allows for allows a flexible for a and flexible modular and modularprocessing. processing. The data post-processing The data post software-processing contains software five modules contains including: five modules (1) pre-processing, including: (include1) pre-processing, data integrity include check, data detection integrity and check, exclusion. detection (2) positioning and exclusion. process (2) of positioning the GNSS orprocess the total of thestation. GNSS (3) aided or the INS total processing, station. ( which3) aided includes INS processing,Kalman filtering which and includes smoothing. Kalman (4) mileage/spatial filtering and smoothing.synchronization (4) mileage/spatial of all measurements synchronization from different of all sensors; measurements (5) track geometricfrom different parameter sensors; calculation (5) track geometricand track quality parameter assessment. calculation Finally, and track the implementation quality assessment. of the Finally, data post the processing implementa softwaretion of will the databe introduced. post processing software will be introduced.

GNSS or TS Aided INS Integration Odometer Track (Filtering geometric and parameters IMU check integrity smoothing)

& & calculation & track Gauge sensor quality evaluation

Events Faultdetection Design Geometry

FigureFigure 9 9.. ConceptConcept of of data data post post processing processing..

4.1. Data Data Fault Fault Detection Detection and and Integrity Integrity Check Like any technology or or systemsystem,, the the TGMT TGMT based based on on ai aidedded INS INS are are subject subject to to hardware hardware or or softwaresoftware failure failures,s, and and can can occasionally occasionally outputs outputs outliers outliers much much larger larger than than the the uncertainty uncertainty bounds. bounds. IntegrityIntegrity checking checking module module detects detects and and isolate isolate these these faults faults in in each each channel channel and and protect protect the the final final measurement solution from being contaminated [18]. Data integrity checks are carried out mostly in the pre-processing phase for each sensor prior to being sent to the data fusion filter. IMU measurement integrity should be checked including the IMU measurement failures, sampling gaps and the sensor measurement errors such as those due to shock and variation, and sensor biases. Individual inertial sensor faults are due to hardware failures and can manifest as no outputs at all, null readings, repeated readings, or simply much larger errors than specified [18]. Small sampling gaps arising in the raw data can be accepted and recovered by interpolation to fill in the sampling gap. However, once a large gap has been detected, such as more than three successive missed epochs, the data after the large gap should be discarded. Special attention should be paid to the time synchronization between the ring laser gyro IMU and the GNSS when the inner FIR filter is implemented for the raw gyros’ measurements which may introduce uncompensated time latency and degrade the navigation accuracy of the GNSS/INS integrated system. Outliers or unexpected signals manifesting as isolated impulsive spike signals can occasionally be present in the gauge, odometer, attitude angle measurements and positioning solutions, especially when the trolley passes over a weld joint or experiences some unexpected large acceleration or vibration. These impulsive spike signals should be detected and filtered to prevent them from being fed into the following data processing. The measurement of the gauge, attitude angle measurement can be treated as one dimensional signal, the impulsive spike signals can be detected simply with a median filter [3]. The outliers in GNSS or total station positioning solutions can be detected dealt with through the innovation filtering in the data fusion Kalman filtering which will be discussed later. Sensors 2018, 18, 538 14 of 26

4.2. Positioning Process If GNSS is adopted as the absolute positioning sensor, the post processed carrier-phase-dominated differential GNSS will be applied to provide centimeter-level accuracy position. The GNSS positioning engine is developed by the navigation group at GNSS Research Center at Wuhan University cooperated with MAP Inc. The GNSS positioning modular supports standard positioning processing (SPP), differential GNSS, and carrier-phase based differential positioning processing. Attention should be paid to the fact that incorrect determination of carrier phase ambiguity happens in the complicated railway surveying environment which may result in a several decimeter or several meter errors in GNSS positioning solutions. The total station positioning is also subject to the phase ambiguity resolution problem. Innovation filtering, which also known as spike filtering, measurement gating, is applied in the data fusion Kalman filtering phase prior to the computation of the Kalman gain to detect the outlier from the positioning sensors including GNSS or total station by comparing the magnitude of each normalized measurement innovation with a threshold and rejects the measurement for that iteration where threshold is exceeded. Sensors 2018, 18, x 14 of 26 4.3. Aided INS Processing station.Fusion The of navigation the external system’s auxiliary initial information attitudes and are the established IMU raw through measurement the ground is implemented alignment inprocedure a loosely includes coupled two architecture stages for the due high to grade the simplicity IMU. The of initial its algorithm phase, coarse structure. alignment As of the leveling, basis ofprovides the aided an estimate INS processing of initial module, attitude. the In extendedthe final phase, Kalman fin filtere-alignment, with 22-dimensional a Kalman filter error is used states to vectorsrefine the including alignment 3-position and estimate errors, 3-velocity inertial sensor errors, errors 3-attitude prior errors, to kinematic residual biasessurveying and scale[19]. factor While errorscoarseof and the fine gyroscopes alignment and requires accelerometers, the IMU be and of sufficient odometer accuracy scale factor to yield error a isreasonable adopted. estimate Moreover, of ainitial Rauch-Tung-Striebel attitude. If conditions (RTS) backward for ground smoothing self-alignment algorithm does is not applied exist, in for the example software when to achieve low grade high accuracyIMU is used in the or finalwithout solutions. sufficient The stationary flowchart time of the range, aided the INS initial integration attitudes is depictedincludingin bank Figure angle, 10 includinggradient of three slope, main and sub-modules: azimuth angles INS can processing, be derived Kalman from the filtering, nominal RTS railway smoothing. track geometry file.

Biases and scale factors ˆ δrvINS,,δ INS  INS

f b , b ib INS IMU Compensation Initialization Mechanization

rvnn,  rvˆ ,,ˆ Cˆ n  RTS INS INS b Measurements nn EKF rv, smoothing

Figure 10. Diagram of the aided INS algorithm in loosely coupled manner. Figure 10. Diagram of the aided INS algorithm in loosely coupled manner.

INS mechanization refers to the procedure of updating the navigation results through integratingOutputs the of IMU the inertial measurements, sensors, i.e., where gyroscopes the compensated and accelerometers, accelerometer should outputs be corrected are rotated with and the sensorintegrated errors toincluding update th biasese INS andvelocity scale and factors position, before beingand the fed compensated to the navigation gyro algorithm. measurements The raw are IMUintegrated measurements to obtain isthe compensated attitudes [20 online]. The aided with theINS optimally system combines estimated navigation biases and state scale data factors from from INS themechanization integrated Kalman with independent filter. redundant external auxiliary data in an extended Kalman filter algorithm,Navigation and followed initialization by a refers RTS smoothing to the procedure for the of post determining processing system’s mode to initial benefit position, from velocitythe past andand attitude future atcorrections the beginning of adjacent of INS processing measurement. prior Deadto the kinematicreckoning surveying. based on The the initial aided position attitude andsolutions velocity and of odometer the INS measurements is obtained from can the also external be adopted positioning to provide sensors, the accurate such as 3D the coordinates GNSS or totalmeasurements station. The [14 navigation]. The estimated system’s gyros initial and attitudes accelerometers are established biases and through residual the scale ground factors alignment are fed procedureback to compensate includes two the stages raw IMU for the measurements, high grade IMU. meanwhile The initial the phase, estimated coarse position, alignment velocity of leveling, and providesattitude errorsan estimate are fed of initialback to attitude. correct In the the INS final-indicated phase, fine-alignment, navigation state a Kalman data. The filter final is used optimal to refineestimation the alignment of the total and navigation estimate inertial states sensor of the errors aided prior INS tois kinematicproduced surveyingand stored. [19 ].The While aided coarse INS andalgorithm fine alignment also supports requires other the auxiliary IMU be of information sufficient accuracy for INS tosuch yield asa zero reasonable velocity estimate update of(ZUPT), initial attitude.odometer If measurements, conditions for groundheading self-alignment measurements, does non not-holonomic exist, for exampleconstraints when to improve low grade the IMU aided is INS performance. The related algorithm details can be found in [11,20,21]. Since the auxiliary measurement for the aided INS system can occasionally output errors larger than the uncertainty bounds, such as the wrong ambiguity fixing of the GNSS RTK processing may cause a position jump. To protect the overall navigation solutions from contamination of the outliers, fault detection and integrity monitoring strategy based on innovation filtering is adopted in the integration algorithm. The measurement innovations provide an indication of whether the measurements and state estimates are consistent. Innovation filtering may be used to detect large discrepancies immediately, while innovation sequence monitoring enables smaller discrepancies to be detected over time. Details on this algorithm can be found in literature [18]. The integrated algorithm of the aided INS for loosely coupled architecture is introduced briefly below.

4.3.1. System Model of aided INS A state propagation model is developed here for a Kalman filter estimating attitude, velocity, and position error referenced to earth frame and resolved in local navigation frame (ref to [19]), together with the biases and scale factor of the accelerometers and gyros, and odometer scale factor. The error state vector is written as:

Sensors 2018, 18, 538 15 of 26 used or without sufficient stationary time range, the initial attitudes including bank angle, gradient of slope, and azimuth angles can be derived from the nominal railway track geometry file. INS mechanization refers to the procedure of updating the navigation results through integrating the IMU measurements, where the compensated accelerometer outputs are rotated and integrated to update the INS velocity and position, and the compensated gyro measurements are integrated to obtain the attitudes [20]. The aided INS system combines navigation state data from INS mechanization with independent redundant external auxiliary data in an extended Kalman filter algorithm, and followed by a RTS smoothing for the post processing mode to benefit from the past and future corrections of adjacent measurement. Dead reckoning based on the aided attitude solutions and odometer measurements can also be adopted to provide the accurate 3D coordinates measurements [14]. The estimated gyros and accelerometers biases and residual scale factors are fed back to compensate the raw IMU measurements, meanwhile the estimated position, velocity and attitude errors are fed back to correct the INS-indicated navigation state data. The final optimal estimation of the total navigation states of the aided INS is produced and stored. The aided INS algorithm also supports other auxiliary information for INS such as zero velocity update (ZUPT), odometer measurements, heading measurements, non-holonomic constraints to improve the aided INS performance. The related algorithm details can be found in [11,20,21]. Since the auxiliary measurement for the aided INS system can occasionally output errors larger than the uncertainty bounds, such as the wrong ambiguity fixing of the GNSS RTK processing may cause a position jump. To protect the overall navigation solutions from contamination of the outliers, fault detection and integrity monitoring strategy based on innovation filtering is adopted in the integration algorithm. The measurement innovations provide an indication of whether the measurements and state estimates are consistent. Innovation filtering may be used to detect large discrepancies immediately, while innovation sequence monitoring enables smaller discrepancies to be detected over time. Details on this algorithm can be found in literature [18]. The integrated algorithm of the aided INS for loosely coupled architecture is introduced briefly below.

4.3.1. System Model of aided INS A state propagation model is developed here for a Kalman ﬁlter estimating attitude, velocity, and position error referenced to earth frame and resolved in local navigation frame (ref to [19]), together with the biases and scale factor of the accelerometers and gyros, and odometer scale factor. The error state vector is written as:

h iT n T n T T T T T T x(t) = (δr ) (δv ) φ bg ba sg sa sodo (3)

n T where operator δ denotes the error of a variable, δr = [δrN δrE δrD] is the INS-indicated position error n T resolved in n-frame. δν = [δνN δνE δνD] is the INS-indicated velocity error resolved in the n-frame. T φ = [φroll φpitch φyaw] , the elements φroll, φpitch correspond to the attitude errors with respect to the vertical, the level or tilt errors, while φyaw represents the error about vertical, the heading or azimuth error; bg, ba, sg, sa are dominant inertial sensor residual errors which will be discussed later, sodo is the odometer scale factor error. The system model in continuous time form is expressed as:

. x(t) = F(t)x(t) + G(t)w(t) (4)

To obtain the aided INS system model, time derivative of each state variable must be calculated. The position, velocity and attitude error differential equations is [22]:

. n n n δr = Frrδr + Frvδv . n δv = Cnδfb + fn × φ − 2ωn + ωn × δvn + vn × 2δωn + δωn + δgn (5) . b ie en ie en l n n n n b φ = Fφrδr + Fφvδv − ωin × φ − Cb δωib Sensors 2018, 18, 538 16 of 26

n T Symbols in above equations are defined as follows: ν = [νN νE νD] is the velocity in the n-frame, φ and h not in equations are latitude and ellipsoidal height position component, respectively. The radii of curvature along lines of constant longitude and latitude are defined as RM and RN, respectively. b ωe is the magnitude of the rotation rate of the Earth. δf refers to the accelerometer measurement b n errors, δωib is the gyros measurement errors; Cb represents the b-frame to n-frame transformation n n matrix. f is the specific force resolved in n-frame. ωie is the angular rate of the Earth frame relative n to the inertial frame in n-frame. ωen is the angular rate of n-frame with respect to the Earth frame n n n resolved in n-frame. δgl is the local gravity error in n-frame. The error rotation vectors δωie and δωen are functions of velocity and position perturbations, respectively, and are required to complete the expression for the velocity error equation. The detailed expression of Equation (5) can be found in a number of references [19,20,22,23].

4.3.2. Measurement Model The navigation aids include GNSS position solutions and vehicle frame velocity (e.g., non-holonomic constraint and odometer) will be considered. • GNSS Position update The position of GNSS antenna is related to the INS position by taking into account the lever arm as follows: n n −1 n b rGNSS = rIMU + DR Cb lGNSS (6) h iT D−1 = diag 1 1 − 1 (7) R RM + h (RN + h) cos ϕ

n n where rGNSS and rIMU are the positions of the GNSS antenna phase center and the IMU measurement b center, respectively; and lGNSS is the lever arm from the IMU to GNSS antenna resolved about the IMU −1 b-frame (ref to [11]) which is assumed here to be well known. DR refers to the Cartesian-to-curvilinear position change transformation matrix. For the loosely-coupled integration, the measurement innovation vector comprises the difference between the GNSS and the corrected inertial position, accounting for the lever-arm effect from the INS to the GNSS antenna. The measurement equation can be derived by perturbation, as:

ˆ n n zrGNSS = DR rˆGNSS −erGNSS n n b (8) ≈ δr + Cb lGNSS× φ + nrG

n n where rˆGNSS is the estimated position of the GNSS antenna center. erGNSS is the position provided by GNSS receiver. nrG represents the GNSS position error in meter modeled as Gaussian white noise, which is adequate if the GNSS sampling rate is below 1 Hz [23]. • Velocity update in vehicle frame The aided INS is mounted on a speciﬁc track geometry surveying trolley for the railway track surveying applications [11], and the relationship between the trolley wheel velocity and the IMU velocity can be expressed as:

v v b n v b b vwheel = CbCnv + Cb ωnb× lwheel (9)

b where lwheel is the lever-arm vector from IMU measurement center to the wheel sensor, resolved in the v b-frame. The estimated velocity at the wheel point is denoted asv ˆ wheel. For the railway track surveying application, the wheels of the track trolley carrying the aided INS are designed able to keep reliable and continuous rigid contact with the rails when moving on rails. Thus the motion of the track trolley on the rails is governed by two non-holonomic constraints (NHC), since the trolley does not jump off and sideslip on the rails. In this case, the trolley has only an Sensors 2018, 18, 538 17 of 26 along-track speed, and velocities in both cross-track directions are zero. Non-holonomic constraint is considered as navigation aid for the aided INS. The v-frame velocity measurement can also be expressed as: v v vewheel = vwheel − nvW (10) T v h i vewheel = vodo 0 0 (11) v where vewheel is the velocity measurement vector resolved in v-frame, νodo represents the along-track velocity derived from the odometer output, nνW is the velocity measurement noise, modeled as Gaussian white noise. The noise strength of the last component of nνW is different from that for the ﬁrst component and should be set according to the NHC condition. Therefore, the v-frame velocity error measurement equation can be expressed as:

v v zvW = vˆ wheel − vewheel v b n v b n v b b (12) = CbCnδv − CbCn(v ×)φ − Cb lwheel× δωib + nvW

v The direction cosine matrix Cb is assumed to contain no error, since the three misalignment angles between b-frame and v-frame can be well calibrated or measured. • Smoothing algorithm A smoothing algorithm is applied to obtain an optimal estimation utilizing all the past, current and future measurements, since the data is allowed to post-processed for accuracy improvement. In this paper, the well-known Rauch-Tung-Striebel (RTS) algorithm is implemented as follows [22]: = + − − xˆk/N xˆk Ak xˆk+1/N xˆk+1 = + − − T Pk/N Pk Ak Pk/N Pk+1 Ak (13) −1 = T − Ak PkΦk Pk+1 where, Ak is the smoothing gain, Φ is the state transition matrix. P is the state error covariance, and subscript N is the total number of measurements.

4.4. Mileage Synchronization and Resampling In practice, the aided INS outputs the positioning solutions as the geodetic coordinates, i.e., latitude, longitude, and ellipsoid height, in the Earth-Centered Earth-Fixed frame, while the railway track position is defined in a specific mapping projection coordinate frame. The projected coordinates can be calculated through the Gauss-Kruger projection [24,25], which is an ellipsoid form of the transverse Mercator projection in the first phase. Then the projected coordinates in the Gauss-Kruge plane are transformed to the specific local mapping coordinate frame for the railway track construction through a similarity transformation with a rotation and scale factor estimation, such as the Helmert transformation, with at least two common control points with known coordinates in these two coordinate system [26]. The difference in the height datum between the INS-indicated ellipsoid height and the orthometric height can be determined from the common height control points with height values in these two height datums. The localization of the measurement, i.e., mileage along the track, can be determined based on the projected coordinates by deriving the projection of the projected coordinates to the nominal track axis as depicted in Figure 11. All sensors’ measurement can be synchronized with the aided INS positioning solutions through the identical time tagging information. The IMU, gauge sensors record the raw measurement at high frequency, such as the aided INS provides position solutions at 200 Hz and gauge sensors sample at 20 Hz, which results in a large amount of redundant measurement information. For example, if the trolley surveys at a constant speed Sensors 2018, 18, 538 18 of 26 of 5 m/s, the aided INS outputs navigation solutions with about 2.5 m distance intervals. For practical railway surveying and precise track adjustment, such dense measurement points are not necessary. Thus the multi sensor measurement should be resampled with identical specific distance interval. A simple moving average is applied to the measurements series of gauge, height, attitude angles Sensorsto resample 2018, 18, themx at a fixed distance interval and smooth out the short-term fluctuation or18 highof 26 frequency noise. The subset size for the moving average is fixed and there is overlapping between measuredadjacent subsets. with a real Robust chord moving method/versine least square system. fitting Track is used irregularity with the projected indicates coordinateswhether and series where to thekeep track the should inherent be relationship adjusted, more between details the can coordinates be found inin easting[11]. and northing [27].

Nominal reference rail

Pm,i

Pnom,i optimal track axis

Paxis,i

y o FigureFigure 11 11.. DeviationDeviation of of alignment alignment..

4.64.5.. Implementation Calculating the Trackof the GeometricData Post Processing Parameters Software TAllhe principaldata post trackprocessing geometric software parameters, InsRail, canis developed be calculated by the with author the 3Dat the position Navigation coordinates, group ofgauge, GNSS and Research cross level Center measurements. at Wuhan University The deviation in C++of gauge programming and cross level language is readily for the computed Windows by operatingsubtracting system the designed and later nominal customized value fromin cooperat the correspondingion with MAP measurements. Inc. as shown For in the Figure TGMT 12 based. The wholeon aided data INS, processing the cross can level be is completed determined with by the InsRail roll angle in several measurement minutes fromimmediately the aided alongside INS. Twist the is trackcomputed on the as surveying the algebraic worksite. difference InsRail between is designed two cross able level to: (1) taken create at 3D a defined position distance coordinates apart along [2,11]. rails andTrack track deviation/deformation axis/centerlines, attitude in angle across-track measurements and vertical including directions, roll, pitch i.e., and alignment azimuth, and and mileagelongitudinal measurement; level directions, (2) referscalculate to the all displacement kinds of track of the geometric actual rails pa fromrameters their nominal including position rail deformationas shown in Figure magnitude 11. It is in obtained both horizontal by calculating and vertical the distance directions, from the alignment measuring and point longitudinal on rails to irregularities,the nominal axis cross of thelevel, track gauge and subtractingand twist et the al.; nominal (3) associate value. precise Figure localization11 depicts the information calculation to of the the measuredalignment, data i.e., across-track/horizontaland track geometric parameters; track deformation. (4) produce If no graphical nominal geometrydrawings isof defined, the surveying such as solutions.the case for The the surveying old existing reports line, the exported track deviation from the can InsRail be expressed can be used as the for excursion track geometry of measurement quality monitoring,point on rails precise from an track optimal adjustment, axis. The and optimal be sent axis to thecan tampingbe found machines with a total in leastindustry square standard fitting foformats. 3D position coordinates of the actual rails [2,11,27], or by fitting a curve in the path-tangent angle chart. The principle of the total least square fitting is finding a new optimum trajectory graphically by minimizing the deviation from the fitting curve. The track deviation/displacement in lateral and vertical direction is used for precise track adjustment of the slab track and tamping of the ballast track. Track irregularity in both the lateral (alignment direction) and vertical direction is defined as the algebraic difference in versines deviations of two measurement points with a defined distance apart. The versine magnitude is distance from the rails to the prescribed moving chord with given length, usually 30 m for the short wavelength, and 300 m for the long wavelength track irregularity [11]. The versines for a prescribed chord is calculated based on the 3D position measurements rather than measured with a real chord method/versine system. Track irregularity indicates whether and where the track should be adjusted, more details can be found in [11].

Figure 12. Graphical user interface of the post processing software—InsRail.

Sensors 2018, 18, x 18 of 26 measured with a real chord method/versine system. Track irregularity indicates whether and where the track should be adjusted, more details can be found in [11].

Nominal reference rail

Pm,i

Pnom,i optimal track axis

Paxis,i

y o

Sensors 2018, 18, 538 Figure 11. Deviation of alignment. 19 of 26

4.6. Implementation of the Data Post Processing Software 4.6. Implementation of the Data Post Processing Software The data post processing software, InsRail, is developed by the author at the Navigation group of GNSSThe data Research post processing Center at software, Wuhan University InsRail, is developedin C++ programming by the author language at the Navigation for the Windows group of operatingGNSS Research system Center and atlater Wuhan customized University in incooperat C++ programmingion with MAP language Inc. as forshown the Windows in Figure operating 12. The wholesystem data and processing later customized can be incompleted cooperation with with InsRail MAP in Inc.several as shown minutes in immediately Figure 12. The alongside whole data the trackprocessing on thecan surveying be completed worksite. with InsRail InsRail is designed in several able minutes to: (1) create immediately 3D position alongside coordinates the track along on railsthe surveying and track worksite.axis/centerline InsRails, attitude is designed angle ablemeasurements to: (1) create including 3D position roll, pitch coordinates and azimuth, along railsand mileageand track measurement; axis/centerlines, (2) attitude calculate angle all kinds measurements of track including geometric roll, parameters pitch and including azimuth, and rail deformationmileage measurement; magnitude (2) in calculate both horizontal all kinds of and track vertical geometric directions, parameters alignment including and rail longitudinal deformation irregularities,magnitude in bothcross horizontallevel, gauge and and vertical twist directions,et al.; (3) associate alignment precise and longitudinal localization irregularities,information to cross the measuredlevel, gauge data and and twist track et al.; geometri (3) associatec parameters; precise localization(4) produce informationgraphical drawings to the measured of the surveying data and solutions.track geometric The surveying parameters; reports (4) produce exported graphical from the drawings InsRail of can the be surveying used for solutions. track geometry The surveying quality monitoring,reports exported precise from track the adjustment, InsRail can be and used be sentfor track to the geometry tamping quality machines monitoring, in industry precise standard track fadjustment,ormats. and be sent to the tamping machines in industry standard formats.

Figure 12. Graphical user interface of the post processing software—InsRail. Figure 12. Graphical user interface of the post processing software—InsRail.

5. Application Scenario The TGMT based on aided INS is designed for precise measurement of the internal or/and external track geometry in mobile surveying mode, and can be adjusted for a variety of surveying tasks for different type of tracks with different optional configurations including basic configuration, GNSS/INS configuration, and TS/INS configuration. TGMT based on aided INS with any configuration can measure the gauge, cross level and twist with 0.3 mm accuracy. The differences between these three configurations and their possible application scenarios are discussed below. TGMT based on aided INS with basic configuration is mainly designed for relative surveying scenarios, such as measuring part or all of the internal track geometric parameters, inspecting track geometric quality for different kinds of rails including high speed railway slab track, norm speed line ballast track, metro track, and tramway track in both the track construction and maintenance phase. TGMT with basic configuration is not able to provide precise 3D position coordinates of the track axis/centerline. This configuration can be operated at a very high speed up to 18 km/h. TGMT with GNSS/INS configuration is an enhanced version of basic configuration and provides global position coordinates with centimeter absolute accuracy and submillimeter relative accuracy in measuring internal track geometric parameters including the track deformation, track irregularities together with gauge, cross level and twist. TGMT with this configuration can also be used for track geographic information system (GIS), redesign of the track, recovering the geometry axis of the existing Sensors 2018, 18, 538 20 of 26 line, documentation of GIS for building a new line besides the existing line. TGMT based on aided INS with GNSS/INS configuration can be operated at a very high speed up to 18 km/h. Introducing the carrier-phase-dominated differential GNSS combined with INS restricts its application scenario to: absolute surveying requires centimeter level 3D position, or the case which focuses on relative measurement accuracy such as track irregularity measurement which can be derived from the accurate attitude angle measurements. Attention should be paid to the GNSS signal interference and availability in the complicated railway track surveying environment especially in the tunnel. TGMT with TS/INS configuration is designed for absolute mobile/kinematic track geometry surveying and measuring all kind of internal and external track geometric parameters for different type of track. It is able to provide 1.4 mm absolute positioning accuracy relative to the track geodetic control network together with other geometric parameters, and can be applied for railway track construction, precise adjustment, track geometric quality inspection, precise track geometry surveying and produce the adjustment data needed by the tamping machine. TGMT with TS/INS configuration can be operated at a speed of 2~3 km/h currently when the total station measurement is carried out about every 120 m, which is much slower than other two configurations due to the free stationing of the total station. Nevertheless, it is about 20 times faster than the conventional TGMTs combined with total station alone surveying in the stop-and-go mode.

6. Field Tests and Performance Analysis

6.1. GNSS/INS Conﬁguration

6.1.1. Experiment Description The TGMT based on GNSS/INS configuration for railway track irregularities measurement was evaluated for the first time in November 2013 on the newly built Lanzhou-Urumqi high speed railway line. Experiments were conducted to assess its performance and track irregularity surveying accuracy, i.e., relative measurement accuracy. The Lanzhou-Urumqi high speed line adopting the slab track system is a high speed passenger railway in northwestern China running from Lanzhou to Urumqi with a designed operation speed of 250 km/h. The slab track was under the precise adjustment phase for the second time when the experiment was conducted. About a 1000-m-length track section was surveyed using the TGMT based on aided INS with GNSS/INS configuration as shown in Figure 13. The trolley system depicted in the figure is the first version prototype of the TGMT based on aided INS presented in this paper. A navigation grade INS/GNSS integrated system, integrating high precision ring laser gyros (RLG) and high stability quartz accelerometers based IMU with a professional NovAtel GNSS OEM6 card. The INS/GNSS system has almost the same performance and accuracy as the POS830 mentioned before, whose specifications are listed in Table1. A GNSS base station sampling simultaneously was set nearby for post positioning processing in the carrier phase differential GNSS mode to provide accurate update to the inertial navigation system. The master station and rover GNSS receivers are under favorable observation conditions and sampled at 1 Hz. In this experiment, we surveyed the same track section three times with the TGMT pushed by human force in both forward and backward directions for repeatability analysis [28]. To quantitatively assess the surveying accuracy of the TGMT, we surveyed the same track section using high precision digital level and conventional TGMT based on total station only to create the surveying references. A Trimble DiNi digital level was used to measure the heights of both rails at each sleeper point with a 0.625 distance interval. The height measurement sequences by the accurate digital level is known to have a relative accuracy of 0.3 mm after errors adjustment, which is accurate enough to characterize the vertical profile of the rails and to be used as reference to evaluate the surveying accuracy of the aided INS in vertical direction. Mileage information is attached to the leveling measurement. A conventional Ambeg GRP1000 system was used as the reference system to provide desired solutions in horizontal or alignment direction. The Amberg GRP1000 system combined Sensors 2018, 18, x 20 of 26

A navigation grade INS/GNSS integrated system, integrating high precision ring laser gyros (RLG) and high stability quartz accelerometers based IMU with a professional NovAtel GNSS OEM6 card. The INS/GNSS system has almost the same performance and accuracy as the POS830 mentioned before, whose specifications are listed in Table 1. A GNSS base station sampling simultaneously was set nearby for post positioning processing in the carrier phase differential GNSS mode to provide accurate update to the inertial navigation system. The master station and rover GNSS receivers are under favorable observation conditions and sampled at 1 Hz. In this experiment, we surveyed the same track section three times with the TGMT pushed by human force in both forward and backward directions for repeatability analysis [28]. To quantitatively assess the surveying accuracy of the TGMT, we surveyed the same track section using high precision digital level and conventional TGMT based on total station only to create the surveying references. A Trimble DiNi digital level was used to measure the heights of both rails at each sleeper point with a 0.625 distance interval. The height measurement sequences by the accurate digital level is known to have a relative accuracy of 0.3 mm after errors adjustment, which is accurate enough to characterize the vertical profile of the rails and to be used as reference to evaluateSensors 2018 the, 18, 538 surveying accuracy of the aided INS in vertical direction. Mileage information21 of 26is attached to the leveling measurement. A conventional Ambeg GRP1000 system was used as the reference system to provide desired solutions in horizontal or alignment direction. The Amberg withGRP1000 high system precision combined Leica TCA with 2003 high total precision station, Leica is able TCA to provide2003 total the station track position, is able to determination provide the withtrack theposition accuracy determination of 1.4 mm inwith the the stop-and-go accuracy of mode. 1.4 mm in the stop-and-go mode.

Figure 13. Experimental setups. Figure 13. Experimental setups. 6.1.2. Results Analysis 6.1.2. Results Analysis The performance of the TGMT based on A-INS is assessed through both the repeatability The performance of the TGMT based on A-INS is assessed through both the repeatability analysis analysis and evaluating its measurement consistency with the reference system. As mentioned above, and evaluating its measurement consistency with the reference system. As mentioned above, the the TGMT with GNSS/INS configuration has high relative accuracy in measuring the inner geometric TGMT with GNSS/INS configuration has high relative accuracy in measuring the inner geometric parameters. The inner consistency in track geometry or track irregularity is indicated as a series of parameters. The inner consistency in track geometry or track irregularity is indicated as a series versine difference of two measurement points with specific distance interval. The parameters of versine difference of two measurement points with specific distance interval. The parameters representing horizontal and vertical track irregularity are obtained by calculating the difference in representing horizontal and vertical track irregularity are obtained by calculating the difference in versince of any two measurement points with a specific distance interval along the track for a chord versince of any two measurement points with a specific distance interval along the track for a chord with given length (30 m chord is predefined for the short wavelength track irregularity, and 300 m with given length (30 m chord is predefined for the short wavelength track irregularity, and 300 m for for the long wavelength) and then subtracting the related nominal value of the difference [11]. the long wavelength) and then subtracting the related nominal value of the difference [11]. Figures 14 and 15 depict the short wavelength lateral/horizontal and vertical track irregularity Figures 14 and 15 depict the short wavelength lateral/horizontal and vertical track irregularity measurements and the difference in measurement between multiple runs over the same track section, measurements and the difference in measurement between multiple runs over the same track section, where the subplot (a) in each figure shows the measurement of related track geometric parameter in where the subplot (a) in each figure shows the measurement of related track geometric parameter in the 1st run and the subplot (b) shows the difference of the related measurement of the 2nd and the the 1st run and the subplot (b) shows the difference of the related measurement of the 2nd and the 3rd 3rd runs with respect to the 1st run to indicate the measurement repeatability. Comparisons show runs with respect to the 1st run to indicate the measurement repeatability. Comparisons show that that the track irregularity measurement repeatability of the TGMT based on aided INS with the track irregularity measurement repeatability of the TGMT based on aided INS with GNSS/INS GNSS/INS configuration in both horizontal and vertical direction is smaller than 0.3 mm. configurationSensors 2018,in 18,both x horizontal and vertical direction is smaller than 0.3 mm. 21 of 26

6 run1 3

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Difference Difference (mm) -0.4 0 100 200 300 400 500 600 700 800 900 1000 Mileage - 1653120 (m) Figure 14. Short wavelength lateral irregularity measurement repeatability of reference rail: Figure(a) 14.measurementShort wavelengthof the 1st run; ( lateralb) difference irregularity of measurement measurement of the 2ndrepeatability and the 3rd runs of with reference respect rail: (a) measurementto the 1st run. of the 1st run; (b) difference of measurement of the 2nd and the 3rd runs with respect to the 1st run. 4 run1 2

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Figure 16 depicts the comparison of short wavelength track irregularity measurement between the TGMT with GNSS/INS configuration and the reference system in both horizontal and vertical directions. The statistical values of the difference with respect to the reference mearing system is depicted in Figure 17, which shows the difference is smaller than 1 mm in vertical direction with respect to the leveling elevations and mostly smaller than 1 mm in horizontal direction with respect to the conventional TGMT measurement. The difference in horizontal direction is slightly larger than that in vertical direction, which can be explained as the reference measurement by conventional TGMT is not as accurate as the leveling and on the other hand our result has slightly lower precision in horizontal direction due to the larger heading angle measurement uncertainty. The results indicate that proposed method can achieve millimeter and even submillimeter relative accuracy in the railway track inner geometry survey and comply with the accuracy requirements specified by the normative standard for TGMT [11,28]. The proposed TGMT based on aided INS with GNSS/INS configuration has been successfully applied in several real projects, including the track precision adjustment in the new Lanzhou-Urumqi high speed railway in 2013 and the track geometric quality inspection for the Wuhan modern tramway in 2016.

Sensors 2018, 18, x 21 of 26

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Difference Difference (mm) -0.4 0 100 200 300 400 500 600 700 800 900 1000 Mileage - 1653120 (m) Figure 14. Short wavelength lateral irregularity measurement repeatability of reference rail: Sensors 2018(,a18) measurement, 538 of the 1st run; (b) difference of measurement of the 2nd and the 3rd runs with respect 22 of 26 to the 1st run.

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Difference Difference (mm) -0.4 0 100 200 300 400 500 600 700 800 900 1000 Mileage - 1653120 (m) Figure 15. Short wavelength vertical irregularity measurement repeatability of reference rail: Figure 15. Short wavelength vertical irregularity measurement repeatability of reference rail: (a) measurement of the 1st run; (b) difference of measurement of the 2nd and the 3rd runs with respect (a) measurement of the 1st run; (b) difference of measurement of the 2nd and the 3rd runs with to the 1st run. respect to the 1st run. Figure 16 depicts the comparison of short wavelength track irregularity measurement between theFigure TGMT 16 depictswith GNSS/INS the comparison configuration of short and wavelengththe reference tracksystem irregularity in both horizontal measurement and vertical between the TGMTdirections. with The GNSS/INS statistical values configuration of the difference and the with reference respect system to the inreference both horizontal mearing system and verticalis depicted in Figure 17, which shows the difference is smaller than 1 mm in vertical direction with directions. The statistical values of the difference with respect to the reference mearing system is respect to the leveling elevations and mostly smaller than 1 mm in horizontal direction with respect depicted in Figure 17, which shows the difference is smaller than 1 mm in vertical direction with to the conventional TGMT measurement. The difference in horizontal direction is slightly larger than respectthat to in the vertical leveling direction, elevations which and can mostly be explained smaller as than the 1 reference mm in horizontal measurement direction by conventional with respect to the conventionalTGMT is not as TGMT accurate measurement. as the leveling Theand on difference the other inhand horizontal our result direction has slightly is slightlylower precision larger than that inin verticalhorizontal direction, direction which due to canthe larger be explained heading asangle the measurement reference measurement uncertainty. The by conventional results indicate TGMT is notthat as proposed accurate method as the can leveling achieve and millimeter on the and other even hand submillimeter our result relative has slightly accuracy lower in the railway precision in horizontaltrack inner direction geometry due survey to the and larger comply heading with the angle accuracy measurement requirements uncertainty. specified by The the results normative indicate that proposedstandard for method TGMT can[11,28 achieve]. The proposed millimeter TGMT and based even submillimeteron aided INS with relative GNSS/INS accuracy configuration in the railway trackhas inner been geometry successfully survey applied and in complyseveral real with projects, the accuracy including requirements the track precision specified adjustment by the in normative the new Lanzhou-Urumqi high speed railway in 2013 and the track geometric quality inspection for the standard for TGMT [11,28]. The proposed TGMT based on aided INS with GNSS/INS configuration Wuhan modern tramway in 2016. has been successfully applied in several real projects, including the track precision adjustment in the new Lanzhou-Urumqi high speed railway in 2013 and the track geometric quality inspection for the

WuhanSensors modern 2018, 18 tramway, x in 2016. 22 of 26

6 AINS Total Station 3

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Align. IrregAlign. (mm) -6 0 100 200 300 400 500 600 700 800 900

4 AINS Leveling 2

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Vertical IrregVertical (mm) -4 0 100 200 300 400 500 600 Mileage - 1653120 (m)

FigureFigure 16. Comparison 16. Comparison of of short short wavelength wavelength alignment (a ()a )and and longitudinal longitudinal (b) (trackb) track irregularity irregularity parameters (i.e., differential ver-sines) over 30 m distance measured by aided INS and reference parameters (i.e., differential ver-sines) over 30 m distance measured by aided INS and reference system; system; the tolerance for short wavelength longitudinal track irregularity is 2 mm. the tolerance for short wavelength longitudinal track irregularity is 2 mm. 20 20

15 15

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6.2. Total Station/INS Configuration

6.2.1. Experiment Description Here we present some results of the TGMT with TS/INS configuration from a real surveying project which was carried out in October 2017 to survey the railway track geometry of the existing Beijing-Shanghai high speed railway to illustrate the measurement accuracy of the TGMT. The Beijing-Shanghai high speed railway adopting ballastless slab track system is the first one in China designed for a maximum speed of 380 km/h in commercial operations, and opened for commercial service in June, 2011. This project is to survey the absolute/external geometric parameters of the track for regular maintenance. It is required to achieve 1~2 mm position accuracy relative to the track control network so to evaluate the deterioration of the track relative to its designed position and geometry. On the other hand, it requires to survey as fast as possible since the time range permitted for surveying is limited to only about 3–4 h every day. In this project the TGMT with TS/INS configuration is adopted for measuring the absolute 3D position and other track geometric parameters. Prior to real surveying application, experiments have been carried out to assess the measurement accuracy and performance of our TGMT by comparing

Sensors 2018, 18, x 22 of 26

6 AINS Total Station 3

0 (a)

-3

Align. IrregAlign. (mm) -6 0 100 200 300 400 500 600 700 800 900

4 AINS Leveling 2

0 (b)

-2

Vertical IrregVertical (mm) -4 0 100 200 300 400 500 600 Mileage - 1653120 (m) Figure 16. Comparison of short wavelength alignment (a) and longitudinal (b) track irregularity Sensors 2018parameters, 18, 538 (i.e., differential ver-sines) over 30 m distance measured by aided INS and reference 23 of 26 system; the tolerance for short wavelength longitudinal track irregularity is 2 mm.

20 20

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0 0 -2 -1 0 1 2 -2 -1 0 1 2 (a) Diffrence of Alignment Irreg. (mm) (b) Diffrence of Vertical Irreg. (mm) Figure 17. Histogram of difference of the irregularity measurements from the TGMT based on TS/INS Figure 17. Histogram of difference of the irregularity measurements from the TGMT based on TS/INS and the reference system in horizontal (a) and vertical (b) direction, respectively. and the reference system in horizontal (a) and vertical (b) direction, respectively. 6.2. Total Station/INS Configuration 6.2. Total Station/INS Configuration 6.2.1. Experiment Description 6.2.1. Experiment Description Here we present some results of the TGMT with TS/INS configuration from a real surveying Hereproject we which present was ca somerried resultsout in October of the TGMT2017 to withsurvey TS/INS the railway configuration track geometry from of a the real existing surveying projectBeijing which-Shanghai was carried high speed out railway in October to illustrate 2017 theto survey measurement the railway accuracy track of the geometry TGMT. The of the existingBeijing Beijing-Shanghai-Shanghai high speed high railway speed railwayadopting to ballastless illustrate slab the track measurement system is the accuracy first one ofin theChina TGMT. designed for a maximum speed of 380 km/h in commercial operations, and opened for commercial The Beijing-Shanghai high speed railway adopting ballastless slab track system is the first one in China service in June, 2011. This project is to survey the absolute/external geometric parameters of the track designedfor regular for a maximum maintenance. speed It is of required 380 km/h to achieve in commercial 1~2 mm position operations, accuracy and openedrelative to for the commercial track servicecontrol in June, network 2011. so This to evaluate project isthe to deterioration survey the absolute/external of the track relative geometric to its designed parameters position of theand track for regulargeometry. maintenance. On the other It hand, is required it requires to achieve to survey 1~2 as mm fast position as possible accuracy since the relative time range to the permitte track controld networkfor surveying so to evaluate is limited the to deterioration only about 3–4 of h theevery track day. relative to its designed position and geometry. On the otherIn this hand, project it requires the TGMT tosurvey with TS/INS as fast configuration as possible sinceis adopted the time for measuring range permitted the absolute for surveying 3D is limitedposition to onlyand other about track 3–4 geometric h every day.parameters. Prior to real surveying application, experiments have Inbeen this carried project out the to assess TGMT the with measurement TS/INS configuration accuracy and performance is adopted forof our measuring TGMT by the comparing absolute 3D position and other track geometric parameters. Prior to real surveying application, experiments have been carried out to assess the measurement accuracy and performance of our TGMT by comparing with the result from an Amberg GRP1000 system. In this experiment, about 1000-m-length track was surveyed by both our trolley and the Amberg GRP1000 which is used as the reference system. The TGMT with TS/INS configuration and the reference trolley stopped about every 120 m to free stationing to obtain the absolute 3D position coordinates in the control network frame, and surveyed in kinematic mode between every two stationing points.

6.2.2. Results Analysis Figure 18 depicts the comparison of the lateral and vertical displacement measurements, i.e., the absolute deviation of the track with respect to its designed positing in horizontal and vertical direction respectively, from the TGMT with TS/INS conﬁguration and the reference system. The difference between the measurements from these two system is calculated, and a representation of whose distribution is plotted in Figure 19. Statistics shows the difference is smaller than 2 mm in both the horizontal and vertical directions. Analogous analysis is carried out for the gauge and cross level measurements and shown in Figures 20 and 21. Taking into account the measuring uncertainty of the reference TGMT we can conclude that the proposed TGMT based on TS/INS can achieve about 1.4 mm accuracy in absolute 3D position coordinates surveying and 0.3 mm for the gauge and cross level measurement when involving a free stationing every 120 m. Sensors 2018, 18, x 23 of 26 Sensors 2018, 18, x 23 of 26 with the result from an Amberg GRP1000 system. In this experiment, about 1000-m-length track was with the result from an Amberg GRP1000 system. In this experiment, about 1000-m-length track was surveyed by both our trolley and the Amberg GRP1000 which is used as the reference system. The surveyed by both our trolley and the Amberg GRP1000 which is used as the reference system. The TGMT with TS/INS configuration and the reference trolley stopped about every 120 m to free TGMT with TS/INS configuration and the reference trolley stopped about every 120 m to free stationing to obtain the absolute 3D position coordinates in the control network frame, and surveyed stationing to obtain the absolute 3D position coordinates in the control network frame, and surveyed in kinematic mode between every two stationing points. in kinematic mode between every two stationing points. 6.2.2. Results Analysis 6.2.2. Results Analysis Figure 18 depicts the comparison of the lateral and vertical displacement measurements, i.e., the Figure 18 depicts the comparison of the lateral and vertical displacement measurements, i.e., the absolute deviation of the track with respect to its designed positing in horizontal and vertical absolute deviation of the track with respect to its designed positing in horizontal and vertical direction respectively, from the TGMT with TS/INS configuration and the reference system. The direction respectively, from the TGMT with TS/INS configuration and the reference system. The difference between the measurements from these two system is calculated, and a representation of difference between the measurements from these two system is calculated, and a representation of whose distribution is plotted in Figure 19. Statistics shows the difference is smaller than 2 mm in both whose distribution is plotted in Figure 19. Statistics shows the difference is smaller than 2 mm in both the horizontal and vertical directions. Analogous analysis is carried out for the gauge and cross level the horizontal and vertical directions. Analogous analysis is carried out for the gauge and cross level measurements and shown in Figures 20 and 21. Taking into account the measuring uncertainty of the measurements and shown in Figures 20 and 21. Taking into account the measuring uncertainty of the reference TGMT we can conclude that the proposed TGMT based on TS/INS can achieve about reference TGMT we can conclude that the proposed TGMT based on TS/INS can achieve about 1.4 mm accuracy in absolute 3D position coordinates surveying and 0.3 mm for the gauge and cross Sensors1.4 mm2018 accuracy, 18, 538 in absolute 3D position coordinates surveying and 0.3 mm for the gauge and 24cross of 26 level measurement when involving a free stationing every 120 m. level measurement when involving a free stationing every 120 m.

8 8 Amberg GRP1000 A-INS trolley Amberg GRP1000 A-INS trolley 4 4 (a) 0 (a) 0

Lateral Lateral Dev.(mm) -4 Lateral Lateral Dev.(mm) -4 500 600 700 800 900 1000 1100 1200 1300 1400 500 600 700 800 900 1000 1100 1200 1300 1400 8 8 Amberg GRP1000 A-INS trolley 4 Amberg GRP1000 A-INS trolley 4 0 (b) 0 (b) -4 -4

Vertical Dev.(mm)Vertical -8 Vertical Dev.(mm)Vertical -8 500 600 700 800 900 1000 1100 1200 1300 1400 500 600 700 800 Mileage900 - 1480001000 (m) 1100 1200 1300 1400 Mileage - 148000 (m) Figure 18. Comparison of the displacement measurements from the TGMT based on TS/INS and the FigureFigure 18. 18.Comparison Comparison of of the the displacement displacement measurementsmeasurements fromfrom thethe TGMTTGMT basedbased onon TS/INSTS/INS and and the the reference system. (a) lateral displacement measurement; (b) vertical displacement measurement. referencereference system. system. ( a(a)) lateral lateral displacement displacement measurement; measurement; ((bb)) verticalvertical displacementdisplacement measurement.measurement.

15 15 15 15

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Frequency Frequency

Frequency 5 Frequency 5 5 5

0 0 0-3 -2 -1 0 1 2 3 0-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (a) Difference of lateral displacement (mm) (b) Difference of vertical displacement (mm) (a) Difference of lateral displacement (mm) (b) Difference of vertical displacement (mm) Figure 19. Histogram of difference of the lateral (a) and vertical (b) displacement measurements from Figure 19. Histogram of difference of the lateral (a) and vertical (b) displacement measurements from Figurethe TGMT 19. Histogram based on TS/INS of difference and the of reference the lateral system (a) and. vertical (b) displacement measurements from the TGMT based on TS/INS and the reference system. the TGMT based on TS/INS and the reference system. Sensors 2018, 18, x 24 of 26

4 Amberg GRP1000 A-INS trolley 2 (a) 0

Cant Cant Dev.(mm) -2

500 600 700 800 900 1000 1100 1200 1300 1400

4 Amberg GRP1000 A-INS trolley 2 (b) 0

-2 Gauge Gauge Dev.(mm) 500 600 700 800 900 1000 1100 1200 1300 1400 Mileage - 148000 (m) Figure 20. Comparison of the cross level (a) and gauge (b) measurements from the TGMT based on Figure 20. Comparison of the cross level (a) and gauge (b) measurements from the TGMT based on TS/INS and the reference system. TS/INS and the reference system.

15 15

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7. Conclusions We propose a modular railway track geometry measuring trolley system based on aided INS. Concepts and key points on the design and implementation of the TGMT’s architecture and the data processing of the TGTM based on aided INS with different configurations are presented in great details, which would benefit researchers in this field and those who want to implement this kind of TGMT. The surveying performance of our TGMT based on aided INS with different configurations was assessed in the real track geometry surveying experiments and projects. Results show the measurement accuracy conforms to the requirement of the normative standard. In addition, the new method proposed in this paper improves the surveying efficiency by orders of magnitude, e.g., at least 20-times faster, compared to conventional methods and TGMTs. The TGMT based on aided INS can indeed realize precise mobile/kinematic surveying of railway track geometry.

Acknowledgments: This work is funded partly by the National Key Research and Development Program of China (No. 2016YFB0501803) and the National Natural Science Foundation of China (No. 41674038, and No. 41404029). The development of the TGMT based on aided INS is funded by Wuhan Municipal Construction Group Co., Ltd., Tisheng Zhang is funded in part by the National High Technology Research and Develop Program of China (No. 2015AA124002). The authors would like to thank Wuhan MAP Space Time Navigation Technology Co., LTD and Shenzhen Datie Detecting and Surveying Inc. for their efforts in customizing and bringing this technology from lab to a commercial product.

Sensors 2018, 18, x 24 of 26

4 Amberg GRP1000 A-INS trolley 2 (a) 0

Cant Cant Dev.(mm) -2

500 600 700 800 900 1000 1100 1200 1300 1400

4 Amberg GRP1000 A-INS trolley 2 (b) 0

-2 Gauge Gauge Dev.(mm) 500 600 700 800 900 1000 1100 1200 1300 1400 Mileage - 148000 (m) Figure 20. Comparison of the cross level (a) and gauge (b) measurements from the TGMT based on Sensors 2018, 18, 538 25 of 26 TS/INS and the reference system.

15 15

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Frequency 5 Frequency 5

0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 (a) Difference of gauge displacement (mm) (b) Difference of cant displacement (mm) Figure 21. Histogram of difference of the cross level (a) and gauge (b) measurements from the TGMT Figure 21. Histogram of difference of the cross level (a) and gauge (b) measurements from the TGMT based on TS/INS and the reference system. based on TS/INS and the reference system.

7. Conclusions 7. Conclusions We propose a modular railway track geometry measuring trolley system based on aided INS. We propose a modular railway track geometry measuring trolley system based on aided INS. Concepts and key points on the design and implementation of the TGMT’s architecture and the data Concepts and key points on the design and implementation of the TGMT’s architecture and the data processing of the TGTM based on aided INS with different configurations are presented in great processing of the TGTM based on aided INS with different configurations are presented in great details, which would benefit researchers in this field and those who want to implement this kind of details, which would benefit researchers in this field and those who want to implement this kind of TGMT. The surveying performance of our TGMT based on aided INS with different configurations TGMT. The surveying performance of our TGMT based on aided INS with different configurations was assessed in the real track geometry surveying experiments and projects. Results show the was assessed in the real track geometry surveying experiments and projects. Results show the measurement accuracy conforms to the requirement of the normative standard. In addition, the new measurement accuracy conforms to the requirement of the normative standard. In addition, the new method proposed in this paper improves the surveying efficiency by orders of magnitude, e.g., at method proposed in this paper improves the surveying efficiency by orders of magnitude, e.g., at least least 20-times faster, compared to conventional methods and TGMTs. The TGMT based on aided INS 20-times faster, compared to conventional methods and TGMTs. The TGMT based on aided INS can can indeed realize precise mobile/kinematic surveying of railway track geometry. indeed realize precise mobile/kinematic surveying of railway track geometry. Acknowledgments: This work is funded partly by the National Key Research and Development Program of Acknowledgments: This work is funded partly by the National Key Research and Development Program of China (No.China 2016YFB0501803) (No. 2016YFB0501803) and the National and the Natural National Science Natural Foundation Science Foundation of China (No. of 41674038,China (N ando. 41674038, No. 41404029). and TheNo. 41404029 development). The of development the TGMTbased of the onTGMT aided based INS on is fundedaided INS by is Wuhan funded Municipal by Wuhan Construction Municipal Construction Group Co., Ltd.,Group Tisheng Co., Ltd. Zhang, Tisheng is funded Zhang in part is funded by the National in part by High the Technology National High Research Technology and Develop Research Program and ofDevelop China (No.Program 2015AA124002). of China (No. The 20 authors15AA124002). would The like toauthors thank would Wuhan like MAP to Spacethank TimeWuhan Navigation MAP Space Technology Time Navigation Co., Ltd., and Shenzhen Datie Detecting and Surveying Inc. for their efforts in customizing and bringing this technology Technology Co., LTD and Shenzhen Datie Detecting and Surveying Inc. for their efforts in customizing and from lab to a commercial product. bringing this technology from lab to a commercial product. Author Contributions: Qijin Chen, Xiaoji Niu proposed the track surveying method based on aided INS, conceived and designed the data processing algorithm. Tisheng Zhang designed the architecture of the system and the data recording system. Lili Zuo and Fuqin Xiao arranged several railway track surveying experiments. Yi Liu performed the railway track surveying experiments. Jingnan Liu guided the whole work related to the TGMTs based on aided INS. Qijin Chen wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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