MEMS and FOG Technologies for Tactical and Navigation Grade Inertial Sensors—Recent Improvements and Comparison

sensors

Article MEMS and FOG Technologies for Tactical and Navigation Grade Inertial Sensors—Recent Improvements and Comparison

Olaf Deppe, Georg Dorner, Stefan König, Tim Martin, Sven Voigt and Steffen Zimmermann *

Northrop Grumman LITEF GmbH, 79115 Freiburg, Germany; [email protected] (O.D.); [email protected] (G.D.); [email protected] (S.K.); [email protected] (T.M.); [email protected] (S.V.) * Correspondence: [email protected], Tel.: +49-761-4901-483

Academic Editor: Jörg F. Wagner Received: 26 January 2017; Accepted: 7 March 2017; Published: 11 March 2017

Abstract: In the following paper, we present an industry perspective of inertial sensors for navigation purposes driven by applications and customer needs. Microelectromechanical system (MEMS) inertial sensors have revolutionized consumer, automotive, and industrial applications and they have started to fulfill the high end tactical grade performance requirements of hybrid navigation systems on a series production scale. The Fiber Optic Gyroscope (FOG) technology, on the other hand, is further pushed into the near navigation grade performance region and beyond. Each technology has its special pros and cons making it more or less suitable for specific applications. In our overview paper, we present latest improvements at NG LITEF in tactical and navigation grade MEMS accelerometers, MEMS gyroscopes, and Fiber Optic Gyroscopes, based on our long-term experience in the field. We demonstrate how accelerometer performance has improved by switching from wet etching to deep reactive ion etching (DRIE) technology. For MEMS gyroscopes, we show that better than 1◦/h series production devices are within reach, and for FOGs we present how limitations in noise performance were overcome by signal processing. The paper also intends a comparison of the different technologies, emphasizing suitability for different navigation applications, thus providing guidance to system engineers.

Keywords: MEMS accelerometer; MEMS gyroscope; coriolis vibratory gyroscope; ﬁber optic gyroscope; multifunction integrated optics chip; angle random walk

1. Introduction As an industry provider of navigation systems, gyrocompasses and attitude and heading reference systems (AHRS), we start our discussion driven by industry practice and long term experience by introducing the basic inertial building blocks, then turn to specific inertial system level requirements driven by customers and, at the end of this section, introduce the inertial sensor technologies we provide for our series products based on several decades of experience in the field. For our most recent improvements we have dedicated sections to each type of inertial sensor. The terminology of inertial systems can be summarized as follows [1,2]: An Inertial Sensor Assembly (ISA) is obtained through the combination of accelerometers and gyroscopes in defined orientations. An Inertial Measurement Unit (IMU) uses an ISA in order to measure the movement of its body in three-dimensional space without external reference. An inertial system uses an IMU and external aids could be employed, such as a magnetic compass, airspeed data, barometric altitude, star tracker, satellite navigation systems (GNSS), etc.

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Some typical links between sensor performance and system functionality are: An Inertial Reference System (IRS) for aviation estimates an aircraft’s position, velocity, and attitude with respect to the earth. An IRS requires an ‘inertial navigation quality’ IMU with a gyroscope performance of 0.01◦/h and better. IMUs with a gyroscope performance between 0.01◦/h to 5◦/h are used in attitude and heading reference systems (AHRSs). An AHRS primarily estimates the attitude angles of an aircraft. Gyroscopes with 0.1◦/h and better enable the capability to perform coarse navigation and to gyrocompass. AHRS with 1◦/h gyroscopes need external references, such as magnetic compass, to find the north direction. Although the integration of IMU and Global Navigation Satellite Systems (GNSS) has a lot of advantages, a benefit for air navigation can be generated with a gyro performance of 0.1◦/h or better. More about the role of inertial systems in the environment of GNSS is described in [3]. Inertial systems in GNSS-denied environments and areas where GNSS are simply not available are receiving more and more attention again. For example, the main accuracy requirement of the NG LITEF Drill Pilot used in drilling and mining is defined in terms of the position error relative to the respective bore distance, i.e., position error (1σ) ≤ 0.5%. In addition, the continuous rotation around the longitudinal axis with a high angular rate (up to 700◦/s) during drilling operations represents a major challenge with respect to the sensors and their processing [4]. For the design of inertial systems, sensor performance data and error models are crucial, and numerical system simulations are an appropriate tool to support the design and evaluation phases. Reliable simulation tools are more than helpful during the validation and verification process for complex integrated systems intended to be certified. A suitable tool chain, developed by NG LITEF, is presented in [5]. Manufacturers that have a deep understanding about the inertial sensors and their performance characteristics are in a good positon to design optimized inertial systems, namely the effectiveness in terms of performance and cost. During the last decades, sensor types without moving parts such as Sagnac effect-based gyroscopes have replaced mechanical gyroscopes which require rather short maintenance intervals. For instance, the Fiber Optic Gyroscope (FOG) [6] allows for performance scaling through the fiber coil length and navigation grade performance has been reported for FOGs. However, mechanical inertial sensors have reentered the arena due to the progress in microelectronics and associated silicon processing in the form of MEMS devices. MEMS-based sensors do not require maintenance of bearings, are suitable to be manufactured in mass production, and were first introduced for accelerometers, and a little later also for gyroscopes. Silicon is a very robust material with advantageous properties borrowed from metals, including low electrical resistivity, but with practically no wear-out when moved or bent within elastic region. On the other hand, silicon dioxide is an excellent insulator, easy to process and perfectly matches the mechanical and thermal properties of silicon. Layers of silicon separated by silicon dioxide are called Silicon-On-Insulator (SOI) wafers and can be purchased as raw material. Among technologies adopted for MEMS fabrication, two main Si-based branches have evolved: (i) Si-bulk technology with KOH wet etching and (ii) Deep Reactive Ion Etching (DRIE) and its various derivatives originating from the classic Bosch process [7]. The chip assembly relies on wafer bonding in both cases. While Si-bulk technology is still widely used for MEMS accelerometers, for MEMS gyroscopes—apart from a few early exceptions [8]—nowadays Deep Reactive Ion Etching is applied, owing to structural complexity of the devices [9]. Having introduced the available sensor technologies and the requirements flow-down from the system level to inertial sensor performance characteristics, we provide an overview of recent improvements in NG LITEF MEMS accelerometers in Section2. We demonstrate that the introduction of the proof mass as a laterally moving structure along with an optimized DRIE bridge technology has greatly improved sensor performance at a higher efficiency. Latest developments in MEMS gyroscopes are addressed in Section3, where we emphasize the suitability of an optimized dual-mass Lin-Lin-design in harsh environments including vibration and acoustic noise. NG LITEF’s Fiber Optic Sensors 2017, 17, 567 3 of 22

Gyroscopes have been optimized over more than two decades [10–14], nevertheless some parasitic effectsSensors 2017 of, the17, 5 Multifunction67 Integrated Optics Chip (MIOC) have so far limited the overall3 high of 21 end FOG performance. In Section4, we present solutions to signiﬁcantly reduce these limitations. Wetechnologies complement and the their discussion suitability with for a different brief comparison applications of FOG in Section and MEMS 5, assuming technologies that thisand addstheir suitabilityvalue to the for paper different for readers applications with a in system Section engineering5, assuming background that this adds who value are to searching the paper for for selection readers withcriteria. a system engineering background who are searching for selection criteria.

2. MEMS Accelerometers 2.1. Background 2.1. Background For micromechanical ‘pendulum-type’ accelerometers with capacitive readout and torqueing, For micromechanical ‘pendulum-type’ accelerometers with capacitive readout and torqueing, designs with vertical (out-of-plane) or lateral (in-plane) displacements are commonly used. Throughout designs with vertical (out-of-plane) or lateral (in-plane) displacements are commonly used. Section2 these are referred to as vertical and lateral designs. Throughout Section 2 these are referred to as vertical and lateral designs. In the accelerometer products of NG LITEF, both design concepts are realized. The vertical design In the accelerometer products of NG LITEF, both design concepts are realized. The vertical as used in [15] was developed in the 1990s, whereas the lateral design was introduced in the past few design as used in [15] was developed in the 1990s, whereas the lateral design was introduced in the years. In the following, the two concepts are analyzed theoretically. The results of the analysis are then past few years. In the following, the two concepts are analyzed theoretically. The results of the supported by production data of the two different accelerometer types. At the end of Section2, a short analysis are then supported by production data of the two different accelerometer types. At the end outlook into the near future is given. of Section 2, a short outlook into the near future is given. 2.2. Theoretical Analysis 2.2. Theoretical Analysis The capacity C0 of a parallel plate capacitor is given by The capacity C0 of a parallel plate capacitor is given by εε0·ε∙εR·∙AA ε ε∙ε0·ε∙L∙hR·L·h C0 C= =N N∙· 0 R == N∙N·0 R , ,(1) (1) 0 dd d d where L and h areare dimensionsdimensions of thethe plateplate andand dd isis thethe gapgap betweenbetween thethe twotwo plates.plates. N is the total number of electrodes.

2.2.1.2.2.1. Electrode Design:Design: Geometrical Sensitivity The geometrical sensitivitysensitivity γγof of an an accelerometer accelerometer to to displacements displacements x isx is given given by by the the derivative derivative of theof the capacity capacity by displacement.by displacement. In designsIn designs with with vertical vertical sensing, sensing the, sensitivethe sensitive direction direction (input (input axis x)axis of thex) of single the single (N = 1)(N accelerometer = 1) accelerometer electrode electrode is in directionis in direction of d, asof shownd, as shown in Figure in Figure1. 1.

(a) (b)

Figure 1. Accelerometer Vertical Design: ( a) SEM image without top electrode; ( b) Electrode scheme, including top electrode.

Hence the sensitivity of the vertical design is Hence the sensitivity of the vertical design is ε ∙ε ∙A ε ∙ε ∙A 0 R 0 R γ ≈ε ·ε2 · ≈ ε ·2ε · . (2) V 0d R-xA2 d0 R A γV ≈ ≈ . (2) d2−x2 d2 For vertical designs, wet etching processes can be used. Large pendulum sizes A of e.g., 1 × 1 mm2 can be structured within a wafer, whereas the gap d between the parallel plates is adjusted by removing specific silicon oxides from top and bottom electrodes. Thus, tiny gaps of the order of a few microns are easily attainable. Vertical designs, processed with KOH, were the first MEMS accelerometer designs, not only at NG LITEF. With the rough numbers given above, geometrical sensitivities of the order >10−6 F/m = 1 pF/µm can be realized.

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For vertical designs, wet etching processes can be used. Large pendulum sizes A of e.g., 1 × 1 mm2 can be structured within a wafer, whereas the gap d between the parallel plates is adjusted by removing speciﬁc silicon oxides from top and bottom electrodes. Thus, tiny gaps of the order of a few microns are easily attainable. Vertical designs, processed with KOH, were the ﬁrst MEMS accelerometer designs, notSensors only 2017 at, 17 NG, 567 LITEF. With the rough numbers given above, geometrical sensitivities of the4 orderof 21 >10−6 F/m = 1 pF/µm can be realized. WithWith wet wet etching etching processes,processes, high aspect ratios ratios (the (the ratio ratio of of the the size size to to the the height height of of structures, structures, suchsuch as as gaps gaps or or trenches) trenches) areare notnot achievable,achievable, since different crystal crystal lattice lattice orientations orientations show show largely largely differentdifferent etching etching rates. rates. Thus, Thus, wet-etched wet-etched accelerometer accelerometer designs designs most most likely likely show show features features with angleswith ofangles 54.74 ◦ofas 54.74° can also as can be seenalso be in seen Figure in1 Figure. 1. Later,Later, Deep Deep Reactive Reactive IonIon EtchingEtching (DRIE)(DRIE) was developed, in in particular particular with with the the development development of of the Bosch process [7]. Although the 54.74° limitation of wet etching processes does not exist for the Bosch process [7]. Although the 54.74◦ limitation of wet etching processes does not exist for DRIE, DRIE, there is still a limit for the maximum aspect ratio that must be obeyed. The actual limit there is still a limit for the maximum aspect ratio that must be obeyed. The actual limit depends on the depends on the etching machines and the level of experience of the MEMS technologists operating etching machines and the level of experience of the MEMS technologists operating them. In order to them. In order to allow for gap sizes of a few microns, the active layer thickness is of the order of 100 allow for gap sizes of a few microns, the active layer thickness is of the order of 100 µm maximum at µm maximum at present. For newer designs, DRIE processes are utilized to structure the wafer. present. For newer designs, DRIE processes are utilized to structure the wafer. In vertical DRIE designs, the pendulum size is smaller. It is given by the product of the In vertical DRIE designs, the pendulum size is smaller. It is given by the product of the thickness thickness of the active layer times the electrode length. This results in an electrode area of the order of the active layer times the electrode length. This results in an electrode area of the order of 0.05 mm2 of 0.05 mm2 maximum. Thus, in vertical DRIE designs between 10 and 50 electrodes are required to maximum. Thus, in vertical DRIE designs between 10 and 50 electrodes are required to produce a produce a similar geometrical sensitivity as a vertical wet-etched design with a single pendulum similarelectrode. geometrical sensitivity as a vertical wet-etched design with a single pendulum electrode. ± InIn lateral lateral DRIEDRIE designs, the the length length L L is is changed changed through through external external accelerations accelerations by ± byΔx. Her∆x.e, Here,the thesymbol symbol h refers h refers either either to the to thethickness thickness of the of thedevice device wafer wafer (the (thependulum pendulum height), height), as in asFigure in Figure 2. 2.

(a) (b)

FigureFigure 2. 2.Accelerometer Accelerometer Lateral Lateral Design: Design: (a ) ( SEMa) SEM image image showing showing the large the large number number of electrodes of electrodes needed toneeded achieve to reasonableachieve reasonable sensitivity; sensitivity; (b) Electrode (b) Electrode scheme. scheme.

In lateral designs, the sensitivity is In lateral designs, the sensitivity is ε ∙ε ∙h γ = 2∙N∙ 0 R . (3) L ε0d·εR·h γL = 2·N· . (3) The aspect ratio (h/d) puts a universal limit on the dsensitivity of a single electrode. For an aspect −10 ratioThe of aspect h/d ≈ ratio18, one (h/d) finds puts a a geometric universal limit sensitivity on the of sensitivity only 3 × of 10 a single F/m electrode. = 0.3 fF/µm. For an Newer aspect ratiodevelopments of h/d ≈ [16]18, oneutilize ﬁnds a gap a geometricreduction a sensitivityfter DRIE. ofThis only method 3 × 10allows−10 F/m increasing = 0.3 fF/the µmaximumm. Newer developmentsaspect ratio by [ 16a factor] utilize of a5 gapto 10 reduction. Nevertheless, after the DRIE. relationship This method between allows the increasingsensitivity theof vertical maximum to aspectlateral ratio designs by aisfactor at least of of 5 the to10. order Nevertheless, of several hundreds the relationship to a thousand between for a the single sensitivity electrod ofe. verticalThus, the number of electrodes must be increased in lateral design in order to compensate the lack of to lateral designs is at least of the order of several hundreds to a thousand for a single electrode. sensitivity, as shown in Figure 2. Thus, the number of electrodes must be increased in lateral design in order to compensate the lack of sensitivity, as shown in Figure2. 2.2.2. Spring Design and Displacement vs. Acceleration At low frequencies, the displacement x of the pendulum is proportional to the acceleration by a x = 2 , (4) ω0

where ω0 is the undamped resonant frequency of the pendulum, determined by the ratio of the spring constant k and the mass m of the pendulum. In order to obtain a high sensitivity to acceleration, the resonant frequency must be low. This can be obtained with a spring design that

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2.2.2. Spring Design and Displacement vs. Acceleration At low frequencies, the displacement x of the pendulum is proportional to the acceleration by a = x 2 , (4) ω0 where ω0 is the undamped resonant frequency of the pendulum, determined by the ratio of the spring constant k and the mass m of the pendulum. In order to obtain a high sensitivity to acceleration, the resonant frequency must be low. This can be obtained with a spring design that provides a small spring constant in the sensitive direction, but has a high stiffness in the perpendicular directions (in order to suppress cross-axis sensitivities). Alternatively, the spring constant in the sensitive direction can be adjusted electrostatically [17]. The product of geometrical sensitivity and the displacement/acceleration relationship yields the capacitive sensitivity of the MEMS chip to accelerations. If a high bias stability of the accelerometer is desired, it is important to have a high capacitive sensitivity to accelerations, so that parasitic capacitive impacts are suppressed effectively. For designs with a lower acceleration sensitivity, as for example in lateral designs, special care must be taken in the packaging, MEMS die attachment, layout, and bonding of the sensitive lines to the front-end electronics.

2.2.3. Forces: Linearity The force F in a parallel plate capacitor with constant voltage U is

U2 F = γ · . (5) max V/L 2 For vertical designs, the force depends on the pendulum position (the sensitivity depends on the displacement x), whereas in lateral designs the maximum acceleration is independent from the pendulum position. This means that torque and pickoff signals do depend on the pendulum position in a non-linear way in vertical designs. Consequently, a linearization procedure has to be performed in accelerometers operating with vertical displacement if good performance is required. In contrast, accelerometers with lateral displacement do not require such additional linearization procedure. When the feedback force is largely independent from the pendulum displacement, an excellent behavior of the accelerometer, even under high vibration levels, can be expected. Since the force determines the accelerometer scale factor, a positive impact on its progression over temperature should be observable. This statement is true in particular for lateral designs, where a position independent force is reached by design. A further impact on the accelerometer scale factor is given by the fact that in vertical designs processed with wet etching, the top and bottom electrodes are subject to the outside air pressure. Changes in the pressure can alter the electrode distances and thus the scale factor. This impact is particularly visible in non-hermetic accelerometer packages for obvious reason, in non-evacuated hermetic packages the impact can be seen as a progression with temperature. In lateral designs and in vertical design processed with DRIE, the electrode distance is normally not in a pressure sensitive direction.

2.2.4. Damping, Noise, and Bandwidth In vertical designs, squeeze film damping is dominant between the two parallel plates moving on each other. Even with a low pressure in the MEMS device, a high damping coefficient can be obtained. In contrast, the squeeze film effect does not play an important role in lateral designs, since the electrodes do not move over each other. Thus, special damping electrodes are required if large displacements shall be avoided. In addition, the gas pressure must be significantly higher in Sensors 2017, 17, 567 6 of 22 comparison to vertical designs. Unfortunately, this causes a higher thermomechanical noise from the Brownian motion of the fill gas. Damping very often is a tradeoff between thermomechanical noise and vibration rectification error (VRE). The latter can be partly compensated even with a lower damping coefficient if the accelerometer is operated closed-loop and the bandwidth is sufficiently high. In NG LITEF’s current accelerometer products, the vibration rectification error of lateral designs is kept low by both maximum damping and a very fast dead-beat controller [18] loop with a bandwidth of well above 2 kHz. The drawback is higher thermomechanical noise.

2.3. Production Data For the evaluation of production data, the following two settings representing two different accelerometer products of NG LITEF were evaluated (see Table1).

Table 1. Details of two different accelerometer products of NG LITEF with different design concepts.

Accelerometer Design Vertical Lateral Structuring KOH—Wet etching DRIE Controller PI Dead-beat Bandwidth >400 Hz >2 kHz Damping Torquer/Pickoff electrodes Damping electrodes Gas pressure 13 mbar 200 mbar

It is important to mention that the following results and the conclusion are speciﬁc for the two MEMS accelerometers from NG LITEF. They are calibrated in a temperature range from −40 ◦C to 85 ◦C. The parameters scale factor, bias, and misalignment are determined with a static multi position test [19] at various temperatures during heating and cooling. Effectively, a progression of these parameters with temperature is obtained and loaded into the accelerometer’s digital signal processor (DSP) as compensation models. The following residual errors over temperature are measured and verify the compensation in a ﬁnal acceptance test.

2.3.1. Scalefactor Residual Error According to the theory presented above, the accelerometer scale factor of lateral designs should have a smoother progression over temperature for two reasons: First, it is independent from the actual pendulum position, and secondly the electrode distance is not sensitive to changes of the outside pressure. Looking at data obtained with the two different designs, one ﬁnds an improvement in scale factor residuals over temperature by more than a factor of two for the lateral design with currently 50 ppm in average.

2.3.2. Bias and Bias Residual Error The raw bias of lateral designs should be higher due to their lower sensitivity to acceleration. Effectively, tiny asymmetries in the MEMS chip or stray capacities in any place lead to a high bias. The comparison of production data from vertical and lateral design indeed reveals a raw absolute bias value that is a factor 3.5 higher for the lateral design with about 300 mg average. Nevertheless, the bias variation over temperature is about 30% smaller for the lateral design which shows a temperature sensitivity of the bias of about 20 µg/K. This positive result is mainly due to the fact that, during the development of the lateral design for series production, packaging topics and layout issues were improved signiﬁcantly. Consequently, the bias residual error over temperature was also improved by about 30% to 65 µg on average. Sensors 2017, 17, 567 7 of 22

2.3.3. Vibration Rectification Error The vibration rectification error of NG LITEF’s AHRS product LCR-100 [20] is monitored regularly in production in a vibration performance test. This test allows for comparison of accelerometers with the two different design approaches. As expected, it turns out that the lateral design is superior to the vertical design. This statement is true for all vibration levels. While the improvement in vibration rectification error is only about 20% at highest vibration levels (above 10 grms at sensor level), the impact of displacement independent forces can be seen even more at the lowest vibration levels where highest performance is required. At these vibration levels, the lateral design outperforms the vertical design by more than a factor of five.

2.4. Summary and Outlook Two different designs of MEMS accelerometers were compared on a theoretical level and by analyzing data collected during series production of both designs at NG LITEF. In summary, the newer design operating with lateral displacement shows an improved performance in comparison to the older design with vertical displacement. Some of the performance improvements were expected per design, such as scale factor and vibration performance at low vibration levels. Others were reached by carefully adapting the overall accelerometer concept to the special weaknesses of lateral designs, such as low damping and lower sensitivity. The impressive results for the lateral design are partly due to the fact that wet etching technology is applied for the vertical design. A comparison with a vertical design, processed with DRIE, would probably come out more balanced. In the future, two aspects of high performance MEMS accelerometers will be improved:

1. The excellent behavior of the current lateral design in heavy vibration environments will be improved by further increasing the bandwidth of the accelerometer while the force independency of the design will be maintained. 2. The acceleration sensitivity of the MEMS chip shall be increased to improve the bias stability of the system. This can be achieved by either a chip redesign or by electrostatic manipulation of the accelerometer’s spring constant. While the former concept is a more general task to be performed as an iteration of the current MEMS chip design, the latter can be applied already on existing chip designs.

However, we recognize there is a trade-off between the two aspects.

3. MEMS Gyroscopes

3.1. Technology The technological processes are identical for our MEMS accelerometers and gyroscopes and are based on DRIE and Silicon Fusion Bonding as already explained in Sections1 and 2.1. However, recent major improvements have been achieved by the insertion of an additional routing layer through wafer-bonding of conductive silicon on silicon in addition to silicon on insulating silicon dioxide [21] as depicted in Figure3. Research groups have reported similar approaches [ 22]. A a major step forward this, MEMS-bridging technology provides conductive access to inner MEMS electrodes without sacriﬁcing valuable degrees of freedom in micro-mechanical design. Open C-frame shaped Coriolis-sensitive masses can be circumvented and thus the associated parasitic effects of pincer movements. With the bridging technology, we manage to achieve quality factors above 0.1 Mio. without a getter and measure the quality factor with a precision of better than 0.25% with relative measurements before and after aging stress and monitoring storage. This is accomplished on a series production scale for every single MEMS gyroscope and can thus conﬁrm long-term stability over product lifetime. Sensors 2017, 17, 567 7 of 21 expected per design, such as scale factor and vibration performance at low vibration levels. Others were reached by carefully adapting the overall accelerometer concept to the special weaknesses of lateral designs, such as low damping and lower sensitivity. The impressive results for the lateral design are partly due to the fact that wet etching technology is applied for the vertical design. A comparison with a vertical design, processed with DRIE, would probably come out more balanced. In the future, two aspects of high performance MEMS accelerometers will be improved: 1. The excellent behavior of the current lateral design in heavy vibration environments will be improved by further increasing the bandwidth of the accelerometer while the force independency of the design will be maintained. 2. The acceleration sensitivity of the MEMS chip shall be increased to improve the bias stability of the system. This can be achieved by either a chip redesign or by electrostatic manipulation of the accelerometer’s spring constant. While the former concept is a more general task to be performed as an iteration of the current MEMS chip design, the latter can be applied already on existing chip designs. However, we recognize there is a trade-off between the two aspects.

3. MEMS Gyroscopes

(a) (b)

Figure 3. Gyroscope Chip Technology:Technology: (a)) ClassicalClassical 3-layer3-layer SOI;SOI; ((bb)) ImprovedImproved BridgeBridge Technology.Technology.

With the bridging technology, we manage to achieve quality factors above 0.1 Mio. without a 3.2. Gyroscope Chip Design getter and measure the quality factor with a precision of better than 0.25% with relative measuForrements our latest before MEMS and after gyroscope aging stress design, and the monitoring main focus storage. was This on robustness is accomplished with respecton a series to environmentalproduction scale conditions for every for single which MEMS MEMS gyroscope are known and to can be inherentlythus confirm susceptible. long-term Manystability MEMS over manufacturers have reported excellent results for bias under benign conditions. However, under real Sensorsproduct 2017 lifetime., 17, 567 8 of 21 operating conditions over temperature, vibration, acoustic noise, cross-axis coupling, and aging, the availabilitydual3.2. Gyroscope-mass gyroscopeof Chip performant Design with devices dedicated quickly rotational narrows. coupling We have addressedand intentiona the abovel decoupling by a dual-mass of the gyroscope with dedicated rotational coupling and intentional decoupling of the Coriolis-sensitive parts CoriolisFor- sensitive our latest parts MEMS from g yroscopethe excitation design oscillation, the main [23] focus. We was found on that robustness by using with special respect linear to from the excitation oscillation [23]. We found that by using special linear acceleration control loops accelerationenvironmental control conditions loops operatedfor which in MEMS the DC are-frequency known -toband be forinherently each of thesusceptible. two Coriolis Many-sensitive MEMS operated in the DC-frequency-band for each of the two Coriolis-sensitive masses, only an approximate massesmanufacturers, only an have approximate reported 8 excellent–10 factor results of reduction for bias of under vibration benign rectification conditions coefficient. However could, under be 8–10 factor of reduction of vibration rectiﬁcation coefﬁcient could be achieved. While by strong achievedreal operating. While conditions by strong over rotational temperature, spring vibration,coupling inacoustic the gyro noise,-chip cross, a reduction-axis coupling of two, and orders aging, of rotational spring coupling in the gyro-chip, a reduction of two orders of magnitude has been achieved. magnitudethe availability has been of performantachieved. Figure devices 4 depicts quickly the narrows. micromechanical We have structure addressed (a) and the the above strongly by a Figurecoupling4 depicts rotational the micromechanicalspring (b). structure (a) and the strongly coupling rotational spring (b).

(a) (b)

Figure 4.4. Gyroscope Design: ( a) SEM image showing the dual mass Lin-Lin-structureLin-Lin-structure with rotational spring; ((b)) Mass-suspensionMass-suspension scheme.scheme.

Acoustic sensitivity is strongly related to vibration sensitivity however, the predominant parts Acoustic sensitivity is strongly related to vibration sensitivity however, the predominant parts of of vibration spectra typically range from 0 Hz to about 1 kHz, while the predominant acoustic vibration spectra typically range from 0 Hz to about 1 kHz, while the predominant acoustic spectra spectra range from 0 Hz to about 8 kHz and can therefore directly influence the MEMS-oscillations. range from 0 Hz to about 8 kHz and can therefore directly inﬂuence the MEMS-oscillations. The strong The strong rotational spring coupling also reduces the acoustic sensitivity, and a simple measure is rotational spring coupling also reduces the acoustic sensitivity, and a simple measure is to keep the to keep the resonant frequency out of the acoustic spectrum. Additionally, a carefully chosen chip resonant frequency out of the acoustic spectrum. Additionally, a carefully chosen chip mounting on the mounting on the module assembly level further mitigates acoustic noise susceptibility. For the module assembly level further mitigates acoustic noise susceptibility. For the targeted tactical-grade targeted tactical-grade performance, we found the measures to be by far sufficient, however it is performance, we found the measures to be by far sufﬁcient, however it is evident that a quad mass evident that a quad mass design could be superior for higher-precision MEMS gyros as they are not design could be superior for higher-precision MEMS gyros as they are not only force balanced, but only force balanced, but also torque balanced with respect to an outer frame [24]. also torque balanced with respect to an outer frame [24]. Aging effects are very hard to model. With class II gyros such as quad mass gyros, methods for Aging effects are very hard to model. With class II gyros such as quad mass gyros, methods dynamic self-calibration have been proposed [25] and promise a new revolutionary MEMS gyro for dynamic self-calibration have been proposed [25] and promise a new revolutionary MEMS gyro performance range. However, there are also drawbacks in terms of complexity and redundancy and the alternative is to reserve aging margins in the specification and to monitor key characteristics during the manufacturing process. This is especially true for the enclosed vacuum, as it can be seen from the error model in [26] that the stability of the resonator quality factors directly affects the long-term stability of the instrument bias.

3.3. Operating Principles Various MEMS manufacturers employ Delta-Sigma-modulation schemes to operate MEMS gyroscopes (see e.g., [27–29]). Major benefits are low size and low power consumption. The switching typically takes place between only two voltage levels. A similar pulse modulation scheme is ternary pulse modulation [30,31], which employs three voltage levels. The use of positive, negative, and zero voltage levels provides additional degrees of freedom for pick-off electronics and can completely avoid accumulation of bound charges along oxide planes in less-sophisticated chip structures. The introduction of electrostatic springs for frequency matching is simple when a separate set of electrodes is provided, or alternatively—as in our case—a time multiplex modulation scheme is employed using D/A-converters and a single A/D converter. We found this tradeoff suitable to achieve very high performance, while sacrificing some size and power consumption. Our highly-optimized time multiplex scheme achieves the following functions with quasi-parallelism: (i)

Sensors 2017, 17, 567 9 of 22 performance range. However, there are also drawbacks in terms of complexity and redundancy and the alternative is to reserve aging margins in the speciﬁcation and to monitor key characteristics during the manufacturing process. This is especially true for the enclosed vacuum, as it can be seen from the error model in [26] that the stability of the resonator quality factors directly affects the long-term stability of the instrument bias.

3.3. Operating Principles Various MEMS manufacturers employ Delta-Sigma-modulation schemes to operate MEMS gyroscopes (see e.g., [27–29]). Major benefits are low size and low power consumption. The switching typically takes place between only two voltage levels. A similar pulse modulation scheme is ternary pulse modulation [30,31], which employs three voltage levels. The use of positive, negative, and zero voltage levels provides additional degrees of freedom for pick-off electronics and can completely avoid accumulation of bound charges along oxide planes in less-sophisticated chip structures. The introduction of electrostatic springs for frequency matching is simple when a separate set of electrodes is provided, or alternatively—as in our case—a time multiplex modulation scheme is employed using D/A-converters and a single A/D converter. We found this tradeoff suitable to achieve very high performance, while sacrificing some size and power consumption. Our highly-optimized time multiplex scheme achieves the following functions with quasi-parallelism: (i) Excitation mode drive; (ii) excitation mode pick-off; (iii) detection mode rate and quadrature rebalancing; (iv) detection mode pick-off; (v) detection mode resonant frequency matching with excitation mode; and (vi) DC quadrature control of detection mode. All voltage stimuli are summed at a single charge amplifier connected to the proof mass’s silicon layer and are demultiplexed and demodulated by signal processing in a digital signal processor or FPGA/ASIC. Due to MEMS-chip imperfections such as asymmetries, the quadrature over temperature becomes a performance limiting factor. The time multiplexed scheme therefore provides quadrature compensation components in the DC and AC domains, where the DC-regulator is the slower control loop compared to the AC loop by far, with bandwidth still high enough to follow temperature changes. The major control loops for control of constant excitation oscillation and for force-rebalancing of the detection oscillation are operated in the bandpass domain and are augmented by noise shaping at the torquers. The overall behavior is very much comparable to a ternary pulse or Delta-Sigma-modulation technique, however avoiding auxiliary electrodes for special functions. As a background task, the excitation resonator frequency is tracked to derive clock and demodulation signals. In addition, artificial out of band noise and a sensor model are used to estimate the basic detection resonator parameters. The local temperature at the MEMS gyro can be monitored very precisely by using the natural resonance frequency sensitivity of the silicon. Research groups have reported similar approaches [32].

3.4. Performance and Outlook So far, with our MEMS-IMU product [33] on a series production scale, a performance of 10◦/h (1σ) residual bias for the MEMS gyroscopes has been speciﬁed in the datasheet. With the optimized technology, design and operating principle described above, MEMS gyroscopes have been assembled into our MEMS-IMU as a research test vehicle. The recent improvements indicate that bias errors over temperature <1◦/h are within reach for series production. Example data of three optimized gyroscopes measured in the MEMS-IMU over temperature and evaluated in the range of −20 ◦C and +75 ◦C ambient temperature are shown in Figure5. To our knowledge, such performance for a triad of silicon MEMS gyros in an IMU has not been published before. With further optimizations through improvements in algorithms and auxiliary control loops, we expect that 0.5◦/h MEMS dual-mass gyroscopes should be feasible on a broad series production scale. Sensors 2017, 17, 567 9 of 21

Excitation mode drive; (ii) excitation mode pick-off; (iii) detection mode rate and quadrature rebalancing; (iv) detection mode pick-off; (v) detection mode resonant frequency matching with excitation mode; and (vi) DC quadrature control of detection mode. All voltage stimuli are summed at a single charge amplifier connected to the proof mass’s silicon layer and are demultiplexed and demodulated by signal processing in a digital signal processor or FPGA/ASIC. Due to MEMS-chip imperfections such as asymmetries, the quadrature over temperature becomes a performance limiting factor. The time multiplexed scheme therefore provides quadrature compensation components in the DC and AC domains, where the DC-regulator is the slower control loop compared to the AC loop by far, with bandwidth still high enough to follow temperature changes. The major control loops for control of constant excitation oscillation and for force-rebalancing of the detection oscillation are operated in the bandpass domain and are augmented by noise shaping at the torquers. The overall behavior is very much comparable to a ternary pulse or Delta-Sigma-modulation technique, however avoiding auxiliary electrodes for special functions. As a background task, the excitation resonator frequency is tracked to derive clock and demodulation signals. In addition, artificial out of band noise and a sensor model are used to estimate the basic detection resonator parameters. The local temperature at the MEMS gyro can be monitored very precisely by using the natural resonance frequency sensitivity of the silicon. Research groups have reported similar approaches [32].

3.4. Performance and Outlook So far, with our MEMS-IMU product [33] on a series production scale, a performance of 10°/h (1σ) residual bias for the MEMS gyroscopes has been specified in the datasheet. With the optimized technology, design and operating principle described above, MEMS gyroscopes have been assembled into our MEMS-IMU as a research test vehicle. The recent improvements indicate that Sensors 2017, 17, 567 10 of 22 bias errors over temperature <1°/h are within reach for series production. Example data of three optimized gyroscopes measured in the MEMS-IMU over temperature and evaluated in the range of The−20 °C next and true +75 MEMS °C ambient revolution temperature with a are jump shown in performance in Figure 5. To over our about knowledge two orders, such of performance magnitude forhowever, a triad is of likely silicon to MEMS rely on gyros class IIin quad an IMU mass has gyroscope not been designspublished [25 before.].

Figure 5.5. MEMS gyroscopes temperature-cycledtemperature-cycled and evaluated in our MEMS MEMS-IMU-IMU SN1880 as a test vehicle andand evaluated inin thethe temperaturetemperature rangerange fromfrom −−20 ◦°CC to +70+70 ◦°CC ambient. Temperature was stabilized at at −−15,15, −54,−54, −10,− +30,10, +30,+75, and +75, +10 and °C +10 for ◦2C h, forwith 2 h,intermediate with intermediate ramps of ramps1 K/min. of The 1 K/min. three Thesubgraphs three subgraphs show 60 s showmedian 60 sfiltered median rotation ﬁltered rate rotation data ratein [°/h] data over in [ ◦temperature/h] over temperature in [°C] for in the [◦ C]three for gyrothe three axes gyro X, Y, axes and X, Z Y,respectively. and Z respectively. The three The temperatures three temperatures were measured were measured locally locally at each at gyro. each gyro.The The1σ bias 1σ biaserrors errors over over temperature temperature of the of three the three gyroscopes gyroscopes are 0.8, are 0.8,0.4, 0.4,and and0.6°/h 0.6 respectively.◦/h respectively.

4. Fiber Optic Gyros

4.1. Background For more than 25 years, NG LITEF has been continuously improving its Fiber Optic Gyroscope products based on its breakthrough closed loop signal processing technology with random modulation and auxiliary control loops [13], the Multifunction Integrated Optics Chip (MIOC or I/O Chip) and dedicated coil winding and potting technology. Two mature FOG architectures have evolved: (i) the 0.05◦/h class of FOG triads with cooled superluminescent diode (SLD) light source used in the NG LITEF AHRS, marine and land navigation products [20]; and (ii) the 1◦/h to 6◦/h class of single axis µFORS FOGs suitable e.g., to build dedicated IMUs and for stabilization applications operating under harsh environmental conditions. The MIOC chip is fabricated in compliance with quality standard DIN/ISO 9001 in NG LITEF production laboratories using Lithium Niobate (LiNbO3) as the material basis. Since the early 1990s more than 190,000 different types of optical chips have been produced for our own use in Fiber Optic Gyroscopes and for systems based on our FOGs. The MIOCs are manufactured using the annealed proton-exchange technique on x-cut Lithium Niobate wafers [34] and integrate the standard functions of (i) a polarizer; (ii) a main coupler/beam splitter; and (iii) a broadband electro-optical push-pull phase modulator on a single chip. For miniaturized single axis Fiber Optic Gyroscopes of the µFORS product family, modiﬁed MIOCs were developed to further optimize integration efﬁciency. The so-called Mixed-Signal MIOC [35] which integrates, in addition to the standard functions mentioned above, a full 12-bit Digital-to-Analog Converter. The latter is realized through 12 binary-weight divided electrodes for electro-optical phase modulation and an additional small electro-optical phase shifter (see Figure6). Sensors 2017, 17, 567 10 of 21

With further optimizations through improvements in algorithms and auxiliary control loops, we expect that 0.5°/h MEMS dual-mass gyroscopes should be feasible on a broad series production scale. The next true MEMS revolution with a jump in performance over about two orders of magnitude however, is likely to rely on class II quad mass gyroscope designs [25].

4. Fiber Optic Gyros

4.1. Background For more than 25 years, NG LITEF has been continuously improving its Fiber Optic Gyroscope products based on its breakthrough closed loop signal processing technology with random modulation and auxiliary control loops [13], the Multifunction Integrated Optics Chip (MIOC or I/O Chip) and dedicated coil winding and potting technology. Two mature FOG architectures have evolved: (i) the 0.05°/h class of FOG triads with cooled superluminescent diode (SLD) light source used in the NG LITEF AHRS, marine and land navigation products [20]; and (ii) the 1°/h to 6°/h class of single axis µFORS FOGs suitable e.g., to build dedicated IMUs and for stabilization applications operating under harsh environmental conditions. The MIOC chip is fabricated in compliance with quality standard DIN/ISO 9001 in NG LITEF production laboratories using Lithium Niobate (LiNbO3) as the material basis. Since the early 1990s more than 190,000 different types of optical chips have been produced for our own use in Fiber Optic Gyroscopes and for systems based on our FOGs. The MIOCs are manufactured using the annealed proton-exchange technique on x-cut Lithium Niobate wafers [34] and integrate the standard functions of (i) a polarizer; (ii) a main coupler/beam splitter; and (iii) a broadband electro-optical push-pull phase modulator on a single chip. For miniaturized single axis Fiber Optic Gyroscopes of the µFORS product family, modified MIOCs were developed to further optimize integration efficiency. The so-called Mixed-Signal MIOC [35] which integrates, in addition to the standard functions mentioned above, a full 12-bit

SensorsDigital2017-to,-Analog17, 567 Converter. The latter is realized through 12 binary-weight divided electrodes11 of for 22 electro-optical phase modulation and an additional small electro-optical phase shifter (see Figure 6). The advantage of the binary-weight divided electrode structure of the phase modulator is the Thepossibility advantage to drive of the the binary-weight electrodes from divided our electrode digital ASIC structure [11] ofwi theth no phase further modulator need of is thean ad possibilityditional toDAC. drive the electrodes from our digital ASIC [11] with no further need of an additional DAC. In the digital ASIC,ASIC, look-uplook-up RAM is implemented which can be used to correct bit errors of all individual digital digital electrodes electrodes to to maximize maximize the the accuracy accuracy of the of the optical optical Digital-to-Analog Digital-to-Analog Converter Converter [36]. By[36] introducing. By introducing this feature, this feature not only, not can only all bitcan errors all bit be errors minimized be minimized but also the but use also of non-binary the use of ornon the-binary combination or the combination of binary/non-binary of binary/non- electrodesbinary electrodes would would be possible. be possible. The The combination combination of binary/non-binaryof binary/non-binary electrodes electrodes also also allows allow 16-bits 16 resolution-bit resolution with withat least at 15-bit least 15accuracy-bit accuracy for the foroptical the D/Aoptical converter D/A converter without without increasing increasing the chip the length chip length and cost. and Additionally, cost. Additionally, the look-up the look table-up can table be usedcan be to used optimize to optimize the linearity the linearity of the phase of the modulation.phase modulation.

Figure 6. Waveguide and Electrode structure of a mixed signal 12-bit MIOC. Figure 6. Waveguide and Electrode structure of a mixed signal 12-bit MIOC.

The additional small phase shifter of the Mixed-Signal MIOC introduces an optical phase shift of π/32The which additional is used small as an phase input shifter for the of thecontrol Mixed-Signal of the modulation MIOC introduces frequency an tracking optical phase[37]. Most shift π ofFOG/32 properties which is depend used as on an temperature input for the and control tolerances of the always modulation exist in frequency the production tracking process [37]. of Most the FOGfiber propertiescoil. However, depend if the on modulation temperature frequency and tolerances of a FOG always is existmaintained in the productionat a fixed constant process ofcycle the ﬁbertime, coil.that cycle However, time generally if the modulation does not frequencymatch the ofmomentary a FOG is transit maintained frequency at a ﬁxed of the constant light passing cycle time,the FOGs that optical cycle time path generally, making doesthe FOG not matchsusceptible the momentary to synchronous transit crosstalk frequency that of contributes the light passing to the thebiasSensors FOGserror. 2017 optical,To 17 , adapt567 path, the modulation making the frequency FOG susceptible to the actual to synchronous conditions over crosstalk temperature that contributes, the transit11 of to 21 the bias error. To adapt the modulation frequency to the actual conditions over temperature, the transit time of time the oflight the can light be can used be to used obtain to obtaina way ato way control to control the modulation the modulation frequency. frequency. For that For reason, that reason,the additional the additional modulation modulation correlated correlated to the to the detected detected signal signal allows allows the the operat operationion of anan auxiliary auxiliary controlcontrol loop loop for for a Voltage a Voltage Controlled Controlled Oscillator Oscillator (VCO) (VCO) which which for its for part its is usedpart isto usedcontrol to the control internal the modulationinternal modulation frequency. frequency. The concept The is concept shown i ins shown Figure in7 and Figure technically 7 and technically realized byrealized a Direct by Digital a Direct SynthesizerDigital Synthesizer (DDS). (DDS).

(a) (b)

FigureFigure 7. 7. (a(a)) Block Block diagram diagram showing showing a a single-axis single-axis closed-loop closed-loop FOG FOG including including signal signal processing processing datapath;datapath; ( b(b)) Block Block diagram diagram showing showing FOG FOG modulation modulation frequency frequency tracking. tracking.

On average, a three-fold bias improvement on a series production scale has been achieved for our µFORS products through this method and experiments showed that which such improved Mixed Signal-MIOCs the performance of navigation grade Fiber Optic Gyroscopes can be achieved. Lithium Niobate and modified Lithium Niobate with annealed proton exchange waveguide formation show a low intrinsic conductivity which results in a high-pass-type behavior of an electro-optical modulator also termed phase bleed. The typical cut-off frequency is lower than 1 mHz (−3 dB value) as shown in Figure 8. The high-pass-type behavior of the modulator chips has, so far, limited the achievable angle random walk coefficient with closed loop operation in very sensitive applications. Only recently, NG LITEF developed a DC-free modulation scheme (see the following sections) to avoid low frequencies in the random modulation signal. A special new MIOC supports this modulation scheme with a relatively small push-pull half-wave voltage of 1.7 V on a moderate chip length of 30 mm.

(a) (b)

Sensors 2017, 17, 567 11 of 21

time of the light can be used to obtain a way to control the modulation frequency. For that reason, the additional modulation correlated to the detected signal allows the operation of an auxiliary control loop for a Voltage Controlled Oscillator (VCO) which for its part is used to control the internal modulation frequency. The concept is shown in Figure 7 and technically realized by a Direct Digital Synthesizer (DDS).

(a) (b)

SensorsFigure2017, 17 ,7 567. (a) Block diagram showing a single-axis closed-loop FOG including signal processing12 of 22 datapath; (b) Block diagram showing FOG modulation frequency tracking.

OnOn average,average, aa three-foldthree-fold biasbiasimprovement improvement onon aaseries seriesproduction production scalescale hashas beenbeenachieved achieved forfor ourourµ µFORSFORS products products through through this this method method and andexperiments experiments showed showed that which that whichsuch improved such improved Mixed Signal-MIOCsMixed Signal- theMIOCs performance the performance of navigation of navigation grade Fiber grade Optic Fiber Gyroscopes Optic Gyroscopes can be achieved. can be achieved. LithiumLithium Niobate Niobate and and modiﬁed modified Lithium Lithium Niobate Niobate with with annealed annealed proton proton exchange exchange waveguide waveguide formationformation show show a a low low intrinsic intrinsic conductivity conductivity which which results results in in a a high-pass-type high-pass-type behavior behavior of of an an electro-opticalelectro-optical modulator modulator also also termed termed phase phase bleed. bleed. The T typicalhe typical cut-off cut frequency-off frequency is lower is lower than 1 than mHz 1 (−mHz3 dB (− value)3 dB value) as shown as shown in Figure in Figure8. The 8 high-pass-type. The high-pass- behaviortype behavior of the of modulator the modulator chips chips has, sohas far,, so limitedfar, limited the achievable the achievable angle randomangle random walk coefﬁcient walk coefficient with closed with loop closed operation loop operation in very sensitive in very applications.sensitive applicati Onlyons. recently, Only NG recently LITEF, NG developed LITEF developed a DC-free modulationa DC-free modulation scheme (see scheme the following (see the sections)following to s avoidections) low to frequenciesavoid low frequencies in the random in the modulation random modulation signal. A special signal. newA special MIOC new supports MIOC thissupports modulation this modulation scheme with scheme a relatively with a smallrelatively push-pull small half-wavepush-pull half voltage-wave of 1.7voltage V on of a moderate1.7 V on a chipmoderate length chip of 30 length mm. of 30 mm.

(a) (b)

Figure 8. (a) Example of a measured electro-optical transfer function of LiNbO3 modulator chip with logarithmic scaling of frequency axis; (b) Derived model of the high-pass-type transfer function of a non-ideal phase modulator with linear scaling of the frequency axis.

Furthermore, the design of all MIOCs produced at NG LITEF is optimized to avoid residual intensity modulation coming from the interference of a secondary light path in the chip with the light paths in the modulated waveguides. Additionally, on all MIOCs the Z-faces of the crystal are coated with a conductive layer to short out the pyroelectric effect and to achieve high stability over strong temperature ramps [38].

4.2. Random Modulation and MIOCs with Phase Bleed in the FOG The technical concept of random modulation for the FOG is discussed in detail in reference [39] and its basics in [40–43]. The problem of the insensitivity sectors (also called dead zones) of the ﬁber optic gyroscope is brought up in [39,44,45] and at the same time the solution to the problem applying random modulation is stated. This solution is due to an improvement to the modulation procedure, which is controlled by a random data generator and which is applied to the correlation freedom of the demodulator reference signal. It was from the results of constructed Fiber Optic Gyroscopes that the effects of MIOC phase bleed in a closed loop FOG with random modulation was ﬁrst detected. In an ideal gyro experiencing a constant applied rate, the digital output would be centred on the applied rate with values symmetrically above and below this value. However, the situation for low input rates did not have a normal distribution but exhibited a preference for values in the region of Ω = 0. This is illustrated in Figure9 in which each top graph shows the gyro output over time and the lower graph is a distribution of the reported values. Sensors 2017, 17, 567 12 of 21

4.2. Random Modulation and MIOCs with Phase Bleed in the FOG The technical concept of random modulation for the FOG is discussed in detail in reference [39] and its basics in [40–43]. The problem of the insensitivity sectors (also called dead zones) of the fiber optic gyroscope is brought up in [39,44,45] and at the same time the solution to the problem applying random modulation is stated. This solution is due to an improvement to the modulation procedure, which is controlled by a random data generator and which is applied to the correlation freedom of the demodulator reference signal. It was from the results of constructed Fiber Optic Gyroscopes that the effects of MIOC phase bleed in a closed loop FOG with random modulation was first detected. In an ideal gyro experiencing a constant applied rate, the digital output would be centred on the applied rate with values symmetrically above and below this value. However, the situation for low input rates did not have a normal distribution but exhibited a preference for values in the region of Ω = 0. This is

Sensorsillustrated2017, 17in, Figure 567 9 in which each top graph shows the gyro output over time and the lower graph13 of 22 is a distribution of the reported values.

(a) (b)

Figure 9 9.. (a)) Measured time time signal signal and and value value distribution distribution histogram histogram for for low low applied applied rotation rotation rate rate of of approximately 12°/h; 12◦/h; (b (b) )Measured Measured time time signal signal and and value value distribution distribution histogram histogram for for special special case case of of applied rotation rate rate of of 0°/h. 0◦/h.

In the graph of Figure 9a, the input rate of the gyro is located at approximately 12°/h. Clearly, ◦ this isIn not the a graph normal of Figuredistribution9a, the about input the rate applied of the gyrorate and is located is rather at approximatelyunbalanced with 12 values/h. Clearly, that thisextend is not into a normalΩ = 0. If distribution the input rate about is theset appliedto zero then, rate and as is is rathershown unbalanced in Figure 9b, with there values is no that normal extend intodistributionΩ = 0. If in the the input measured rate is values set to zerobut, then,again, as an is emphasis shown in of Figure measurement9b, there isdata no normalaround distributionΩ = 0. The intime the plot measured clearly valuesshows regular but, again, constrictions an emphasis of the of measurementrotational speed data from around whichΩ the= 0.measurement The time plot clearlydistribution shows arises. regular NG constrictions LITEF circumvented of the rotational this behavior speed by from introduction which the of measurement an additional distribution dithering arises.modulation NG LITEF that also circumvented drives the this FOGs behavior auxiliary by gainintroduction control loop, of an howeveradditional at dithering the cost modulationof a basic thatlimitation alsodrives of achievable the FOGs angle auxiliary random gain walk control that persisted loop, however until recently at the. cost of a basic limitation of achievableAs explained angle random in section walk 4.1 that, the persisted real behavior untilrecently. of the phase modulator can be modelled with high-Aspass explained characteristic in Section as shown 4.1, thein Figure real behavior 8b and implemented of the phase modulatorinto our FOG can sensor be modelled simulation with high-passmodel. For characteristica frequency ω as= 0 shown—and also in Figure at very8b low and frequencies implemented—the into phase our modulators FOG sensor have simulation a lower Sensorsmodel.gain than 2017 For , at17 a ,higher 5 frequency67 frequencies.ω = 0—and also at very low frequencies—the phase modulators have13 a lowerof 21 gain than at higher frequencies. FigureFigure 1010aa shows shows simulated simulated rate rate values values and and their their distribution distribution for foran applied an applied rate rateof −10°/h. of −10 The◦/h. trTheend trend of the of outputthe output rate rate towards towards 0 is 0 clearly is clearly visible. visible. In FigureIn Figure 10 b10 areb are the the rate rate values values and and the the distributiondistribution for for a a zero zero-input-input rate. rate. Here, Here, too, too, the the preference preference of of the the initial initial rotation rotation rates rates is is zero zero and and it itis is apparentapparent that that the the rate rate value value signal signal is is constricted. constricted.

(a) (b)

Figure 10. Simulations including non-ideal MIOC transfer function; the dithering for auxiliary gain Figure 10. Simulations including non-ideal MIOC transfer function; the dithering for auxiliary gain control loop is off to emphasize the effects of MIOC phase bleed: (a) Simulated time signal and value control loop is off to emphasize the effects of MIOC phase bleed: (a) Simulated time signal and value distribution histogram for a low applied rotation rate of approximately −10°/h; (b) Simulated time distribution histogram for a low applied rotation rate of approximately −10◦/h; (b) Simulated time signal and value distribution histogram for applied rotation rate of 0°/h. signal and value distribution histogram for applied rotation rate of 0◦/h.

4.3. Approach with DC-Free Modulation

4.3.1. Preliminary Considerations Figure 11 shows the intensity over phase characteristic of the Sagnac interferometer.

Figure 11. Sagnac Interferometer characteristic with operating points showing the relative intensity over the Sagnac phase in radiants.

During the operation of the fiber optic gyroscope, the marked operating points are always controlled by the modulation signal at the MIOC. Regarding the choice of the sequence of the operating points, there are certain degrees of freedom that require careful consideration. These are expressed through the following items: 1. Without modulation, the peak of the interferometer characteristic would be steered where the slope is zero. Thus, the sensitivity of the sensor is also zero and there would be no directional information present. To avoid these disadvantages, the control uses points that lie where the slope is greatest. 2. If only points with the same sign were controlled, an applied rotation rate would lead to a DC voltage signal at the photodetector, which would be suppressed by the subsequent circuit stages. Therefore, work points with changing signs are controlled. This results in a modulation

Sensors 2017, 17, 567 13 of 21

Figure 10a shows simulated rate values and their distribution for an applied rate of −10°/h. The trend of the output rate towards 0 is clearly visible. In Figure 10b are the rate values and the distribution for a zero-input rate. Here, too, the preference of the initial rotation rates is zero and it is apparent that the rate value signal is constricted.

(a) (b)

Figure 10. Simulations including non-ideal MIOC transfer function; the dithering for auxiliary gain control loop is off to emphasize the effects of MIOC phase bleed: (a) Simulated time signal and value

Sensorsdistribution2017, 17, 567 histogram for a low applied rotation rate of approximately −10°/h; (b) Simulated time14 of 22 signal and value distribution histogram for applied rotation rate of 0°/h.

4.3.4.3. ApproachApproach withwith DC-FreeDC-Free Modulation Modulation

4.3.1.4.3.1. PreliminaryPreliminary ConsiderationsConsiderations FigureFigure 11 11 shows shows the the intensity intensity over over phase phase characteristic characteristic of of the the Sagnac Sagnac interferometer. interferometer.

FigureFigure 11. 11.Sagnac Sagnac Interferometer Interferometer characteristiccharacteristic withwith operatingoperating pointspoints showingshowing thethe relativerelative intensityintensity overover the the Sagnac Sagnac phase phase in in radiants. radiants.

During the operation of the fiber optic gyroscope, the marked operating points are always During the operation of the ﬁber optic gyroscope, the marked operating points are always controlled by the modulation signal at the MIOC. Regarding the choice of the sequence of the controlled by the modulation signal at the MIOC. Regarding the choice of the sequence of the operating operating points, there are certain degrees of freedom that require careful consideration. These are points, there are certain degrees of freedom that require careful consideration. These are expressed expressed through the following items: through the following items: 1. Without modulation, the peak of the interferometer characteristic would be steered where the 1. Withoutslope is zero. modulation, Thus, the the sensitivity peak of the of interferometerthe sensor is also characteristic zero and there would would be steered be no wheredirectional the slopeinformation is zero. present. Thus, the To sensitivity avoid these of thedisadvantages, sensor is also the zero control and thereuses points would that be no lie directional where the informationslope is greatest. present. To avoid these disadvantages, the control uses points that lie where the 2. slopeIf only is points greatest. with the same sign were controlled, an applied rotation rate would lead to a DC 2. Ifvoltage only points signal with at the the photodetector, same sign were which controlled, would an be applied suppressed rotation by rate the would subsequent lead to circuit a DC voltagestages. Therefore, signal at the work photodetector, points with which changing would sign bes suppressedare controlled. by the This subsequent results in circuita modulation stages. Therefore, work points with changing signs are controlled. This results in a modulation of the detector signal so that the signal lies in the transmission range of the following ampliﬁer stages. 3. If the control of the working points alternates periodically between positive and negative slopes, the drive signal at the MIOC would correlate with the demodulator reference of the detector signal. This results in an insensitivity in the sensor for small rotation rates. Therefore, the sequence of the signs of the slope at the operating points have to be chosen in a way that the mentioned correlation disappears. 4. The modulation must be such that a stable operation of the scale factor controller (auxiliary control loop) can be ensured for any input rotation rates of the sensor.

The MIOC has a lower transmission factor at very low frequencies than at medium and high frequencies. If the low frequencies and DC voltage were kept away from the MIOC, then the sensor errors must disappear since the drop of the transmission factor at low frequencies can no longer have an effect. The concept, therefore, is to modify the modulation scheme or, better, the statistical properties of the controlled work points so that the modulation signal at the MIOC has the mean eliminated; that is: it is a mean-free modulation as the expectation value would be zero. In addition to the above four objectives, a ﬁfth item arises:

5. The modulation must be such that the expected value of the MIOC drive signal becomes zero. Sensors 2017, 17, 567 14 of 21

of the detector signal so that the signal lies in the transmission range of the following amplifier stages. 3. If the control of the working points alternates periodically between positive and negative slopes, the drive signal at the MIOC would correlate with the demodulator reference of the detector signal. This results in an insensitivity in the sensor for small rotation rates. Therefore, the sequence of the signs of the slope at the operating points have to be chosen in a way that the mentioned correlation disappears. 4. The modulation must be such that a stable operation of the scale factor controller (auxiliary control loop) can be ensured for any input rotation rates of the sensor. The MIOC has a lower transmission factor at very low frequencies than at medium and high frequencies. If the low frequencies and DC voltage were kept away from the MIOC, then the sensor errors must disappear since the drop of the transmission factor at low frequencies can no longer have an effect. The concept, therefore, is to modify the modulation scheme or, better, the statistical properties of the controlled work points so that the modulation signal at the MIOC has the mean eliminated; that is: it is a mean-free modulation as the expectation value would be zero. In addition to the above four objectives, a fifth item arises: Sensors 2017, 17, 567 15 of 22 5. The modulation must be such that the expected value of the MIOC drive signal becomes zero.

However,However, it it is isnow now apparent apparent that that in the in above-described the above-described prior art prior method, art method, the degrees the of degrees freedom of havefreedom been have exhausted been exhausted by specifying by the specifying first four the objectives. first four Therefore, objectives. should Therefore, the fifth should property the fifth be applied,property this be applied, would be this at would the cost be of at thethe firstcost fourof the objectives. first four objectives. In particular, In particular, it is expected it is expected that the freedomthat the freedom from correlation from correlation between between the MIOC the control MIOC signalcontrol and signal the demodulatorand the demodulator reference reference would disappear.would disappear. This is a prerequisite This is a forprerequisite the disappearance for the of disappearance the lock-in effect of during the lock over-coupling-in effect during from theover MIOC-coupling signal from to the the detector MIOC signal.signal to This the has detector been confirmed signal. This by has simulation. been confirmed This statement by simulat appliesion. toThis the statement method in applies the current to the technicalmethod in concept the current with technical a modulation concept range with ofa modulation the MIOC signal range ofof 2theπ. However,MIOC signal it is nowof 2π. possible However, to increase it is now the possible control rangeto increase of the the MIOC control signal range to 4π ofand the thereby MIOC signal increase to the4π numberand thereby of degrees increase of freedom the number which of can degrees be used of fr ineedom controlling which the can work be used points. in In controlling this case, allthe fivework of points. the above-mentioned In this case, all objectivesfive of the canabove be- achieved.mentioned The objectives resulting can solutions be achieved. for the The 4π resultingcontrol rangesolutions of the for MIOC the 4π are control presented range in of the the following MIOC are sections. presented in the following sections.

4.3.2.4.3.2. StatisticalStatistical RoundingRounding TheThe mean mean value value freedom freedom ofof the the MIOC MIOC control control signal signal can can be be achievedachieved by by so-calledso-called statistical statistical roundingrounding [ 46[46].]. AsAs shownshown inin FigureFigure 12 12a,a, thethe wantedwanted signalsignal x푥∈∈[[0,0,q푞)) isis mixed mixed with with a a randomrandom numbernumber withwith a a distribution distribution shown shown in in Figure Figure 13 13a.a.

(a) (b)

FigureFigure 12. 12.( a(a)) Principle Principle of of statistical statistical rounding; rounding; ( b(b)) Resulting Resulting optimized optimized circuit circuit realization realization for for driving driving thethe MIOC. MIOC. Sensors 2017, 17, 567 15 of 21

(a) (b)

FigureFigure 13 13.. (a()a Probability) Probability distribution distribution function function of ofthe the random random variable variable R (randomR (random numbers numbers r); (br)); Resulting(b) Resulting distribution distribution function function of random of random variable variable Y (randomY (random numbers numbers y = xy + = r x).+ r).

A comparator then checks whether the output signal meets the y ≥ q condition. The probability A comparator then checks whether the output signal meets the y ≥ q condition. The probability P(y ≥ q) of the hatched area of Figure 13b is P(y ≥ q) of the hatched area of Figure 13b is x ( ) P y ≥ q = x. (6) P(y ≥ q) =q . (6) q This constructs the rounded signal 0 for y < q x = { . (7) r q for y ≥ q

Thus, the expected value for xr is x x E(x ) = P(y < q)∙0 + P(y ≥ q)∙q = (1 − ) ∙0 + ∙q = x . (8) r q q

The rounded signal xr thus corresponds to the input signal x. If signal x - xr is formed, then its expected value is

E(x − xr) = 0 (9) As a basic concept, q = π or q = 2π is selected and the MIOC, instead of a signal x, is fed with a mean-value-free signal, x − xr . For q = π , the transition from x to x − xr changes the MIOC signal. Hence the phase of the interferometer is changed by the value π, which changes the operating point to an operating point with an opposite slope. This measure changes the demodulator reference. For the situation of q = 2π , there is also a change of the operating point but the slope is unchanged. Owing to the periodicity of the interferometer characteristic, there are no other changes. Figure 12b shows the circuit realization of statistical rounding for mean-free-value (E(x − xr) = 0) of the MIOC signal. The unmodified signal is x(t) ∈ [0,q) . This, for example, could have a word width of 12 bits. q The weighting of the MSB is . To this signal, x(t), is added an equally-distributed random number 2 which also has the same word width of 12 bits. The condition x + r ≥ q is signaled by the carry bit—the sum itself is not used. If the signal is now formed into a 13-bit number, with the carry bit forming the new MSB, then this number can be interpreted as a two’s-complement number and is mean-free since the new MSB has the weight of –q . The signal x − xr with E(x − xr) = 0 can be now fed to a D/A-converter which, in turn, controls the MIOC. As already explained above, two different cases are possible: 1. q = π which results in a modulation range of the MIOC of 2π (henceforth referred to as 2π-modulation). 2. q = 2π which results in a modulation range of the MIOC of 4π (henceforth referred to as 4π-modulation). It will now be shown how these modifications are incorporated into the current technical concept. This related part of the circuit is shown again in Figure 14.

Sensors 2017, 17, 567 16 of 22

This constructs the rounded signal ( 0 for y < q x = . (7) r q for y ≥ q

Thus, the expected value for xr is

x x E(x ) = P(y < q)·0 + P(y ≥ q)·q = 1 − ·0 + ·q = x . (8) r q q

The rounded signal xr thus corresponds to the input signal x. If signal x − xr is formed, then its expected value is E(x − xr) = 0 (9) As a basic concept, q = π or q = 2π is selected and the MIOC, instead of a signal x, is fed with a mean-value-free signal, x − xr. For q = π, the transition from x to x − xr changes the MIOC signal. Hence the phase of the interferometer is changed by the value π, which changes the operating point to an operating point with an opposite slope. This measure changes the demodulator reference. For the situation of q = 2π, there is also a change of the operating point but the slope is unchanged. Owing to the periodicity of the interferometer characteristic, there are no other changes. Figure 12b shows the circuit realization of statistical rounding for mean-free-value (E(x − xr) = 0) of the MIOC signal. The unmodiﬁed signal is x(t) ∈ [0, q). This, for example, could have a word width of 12 bits. q The weighting of the MSB is 2 . To this signal, x(t), is added an equally-distributed random number which also has the same word width of 12 bits. The condition x + r ≥ q is signaled by the carry bit—the sum itself is not used. If the signal is now formed into a 13-bit number, with the carry bit forming the new MSB, then this number can be interpreted as a two’s-complement number and is mean-free since the new MSB has the weight of –q. The signal x − xr with E(x − xr) = 0 can be now fed to a D/A-converter which, in turn, controls the MIOC. As already explained above, two different cases are possible:

1. q = π which results in a modulation range of the MIOC of 2π (henceforth referred to as 2π-modulation). 2. q = 2π which results in a modulation range of the MIOC of 4π (henceforth referred to as 4π-modulation).

It will now be shown how these modiﬁcations are incorporated into the current technical concept.

ThisSensors related 2017, part 17, 567 of the circuit is shown again in Figure 14. 16 of 21

FigureFigure 14. 14Modulation. Modulation stage stage and and phase phase accumulator accumulator used used in thein the current current design. design.

4.3.3. Mean-Value-Free MIOC Control with 4π-Modulation As already mentioned, compromises would be made in the implementation of mean-value-free 2π-modulation since the number of degrees of freedom was not sufficient for the control work points. This goal—a mean-value-free control of the MIOC—can be achieved by surrendering other conditions. If a control range of 4π for the MIOC signal is considered, then all simultaneous conditions for a correlation-free demodulation signal and a mean-free MIOC signal can be fulfilled. For statistical rounding, a quantization of q = 2π is chosen. The entire data path remains unchanged. Only here the D/A converter receives an additional bit as MSB with the weighting of 2π. This range expansion achieves a mean-value freedom at the D/A converter. The additional bit shifts the controlled operating points by an amount of 2π, which does not change the sign of the slope of the respective operating point, and thus leaves the demodulation signal unchanged. Thus, the non-correlation of the demodulation signal is restored but the MIOC control is now mean-value-free. However, the generation of the demodulation signal for the scale factor controller has to now be adapted for the new method. Figure 15 shows the resulting configuration.

Figure 15. Configuration for mean-value-free 4π-modulation.

The implementation is slightly simplified since there is now no longer any effect on the demodulation signal (this is stated again for emphasis). Note that the signal at the output of the phase accumulator is subjected to statistical rounding with q = 2π and that the additionally-obtained bit is fed as an MSB to the one-bit-wider D/A converter. In this example, the additional bit is also fed back into the register of the phase accumulator. This is necessary to derive the demodulation signal for the scale factor controller. Figure 16a shows the rate and value

Sensors 2017, 17, 567 16 of 21

Figure 14. Modulation stage and phase accumulator used in the current design. Sensors 2017, 17, 567 17 of 22 4.3.3. Mean-Value-Free MIOC Control with 4π-Modulation 4.3.3. Mean-Value-Free MIOC Control with 4π-Modulation As already mentioned, compromises would be made in the implementation of mean-value-free 2π-modulationAs already since mentioned, the number compromises of degrees would of be freedom made in was the implementation not sufficient of for mean-value-free the control work points.2π-modulation This goal— sincea mean the- numbervalue-free of degrees control of of freedom the MIOC was— notcan sufficient be achieved for the controlby surrenderi work points.ng other conditions.This goal—a If a mean-value-free control range control of 4π of for the the MIOC—can MIOC besignal achieved is considered by surrendering, then other all conditions. simultaneous If a control range of 4π for the MIOC signal is considered, then all simultaneous conditions for a conditions for a correlation-free demodulation signal and a mean-free MIOC signal can be fulfilled. correlation-free demodulation signal and a mean-free MIOC signal can be fulfilled. For statistical For statistical rounding, a quantization of q = 2π is chosen. The entire data path remains unchanged. rounding, a quantization of q = 2π is chosen. The entire data path remains unchanged. Only Onlyhere here the the D/A D/A converter converter receives receives an an additional additional bit bit as MSBas MSB with with the the weighting weighting of 2π of. This2π. This range range expansionexpansion achieves achieves a a mean-valuemean-value freedom freedom at the at D/A the converter. D/A converter. The additional The additionalbit shifts the controlledbit shifts the controlledoperating opera pointsting by points an amount by an ofamount 2π, which of 2π, does which not change does thenot sign change of the the slope sign of of the the respective slope of the respectiveoperating operating point, and point, thus leaves and the thus demodulation leaves the signal demodulation unchanged. signal Thus, the unchanged. non-correlation Thus, of the non-thecorrelation demodulation of the signaldemodulation is restored signal but the is restored MIOC control but the is nowMIOC mean-value-free. control is now However,mean-value the-free. However,generation the ofgeneration the demodulation of the signaldemodulation for the scale signal factor for controller the scale has tofactor now controller be adapted forhas the to newnow be adaptedmethod. for the Figure new 15 method. shows the Figure resulting 15 sho configuration.ws the resulting configuration.

Figure 15. Configuration for mean-value-free 4π-modulation. Figure 15. Configuration for mean-value-free 4π-modulation. The implementation is slightly simplified since there is now no longer any effect on the demodulation signal (this is stated again for emphasis). Note that the signal at the output of the The implementation is slightly simplified since there is now no longer any effect on the phase accumulator is subjected to statistical rounding with q = 2π and that the additionally-obtained demodulationbit is fed as signal an MSB (this to the is one-bit-widerstated again D/Afor emphasis) converter.. InNote this example,that the signalthe additional at the outputbit is also of the phasefed back accumulator into the register is subjected of the phase to accumulator. statistical This rounding is necessary with to derive q = the2π demodulation and that the additionallysignal for-obtained the scale factor bit is controller. fed as an Figure MSB 16toa the shows one the-bit rate-wider and valueD/A distributionconverter. In at appliedthis example, rate of the additional−10◦/h. bit Similarly, is also fed the back rates andinto valuethe register distribution of the for phase an input accumulator. rate of zero areThis shown is necessary in Figure to 16 deriveb. the demodulationBoth figures show signal a normal for distribution the scale of factor values. con Figuretroller. 17 shows Figure the 16 frequencya shows distribution the rate and of the value controlled operating points. The number of operating points has doubled from four to eight.

Sensors 20172017,, 1717,, 556767 17 17of 21of 21

distribution atat appliedapplied raterate of of − −10°/h.10°/h. Similarly, Similarly, the the rates rates and and value value distribution distribution for for an an input input rate rate of of zero areare shownshown inin Figure Figure 16 16b.b. Both Both figures figures show show a anormal normal distribution distribution of of values. values. Figure Figure 17 17 shows shows the the frequencyfrequency distribution distribution of of the the controlled controlled operating operating points. points. The The number number of of operating operating points points has has Sensors 2017, 17, 567 18 of 22 doubled fromfrom fourfour toto eight. eight.

((aa)) (b()b )

FigureFigure 16.1616.. SimulationsSimulationsSimulations including including including non non non-ideal-ideal-ideal MIOC MIOC MIOC transfer transfer function function and and and m mean-value-freeeanmean-value-value-free-free 44π4ππ-Modulation:--ModulationModulation: : ( (a)(aa)) Simulated SimulatedSimulated time timetime signal signalsignal and andand value valuevalue distribution distributiondistribution histogram histogramhistogram for forfor an anan applied appliedapplied rotation rotationrotation rate of approximately −10°/h; (b) Simulated time signal and value distribution histogram for applied raterate ofof approximatelyapproximately− −1010°/h;◦/h; ( (b)b) Simulated Simulated time time signal signal and value distribution histogram forfor appliedapplied rotation rate of 0°/h. rotationrotation raterate ofof 00◦°/h./h.

Figure 17. Frequency distribution of operating points with mean-value-free 4π-modulation. Figure 17.17. Frequency distribution of operatingoperating pointspoints withwith mean-value-freemean-value-free 44ππ-modulation.-modulation. 4.4. Discussion and Outlook 4.4.4.4. DiscussionDiscussion andand OutlookOutlook Our method demonstrates that FOG sensor errors in the form of periodic phases can be fed back with OurOura sensor methodmethod output demonstratesdemonstrates signal from thatthat zero FOGF OGto a sensor sensorfrequency errorserrors-dependent inin thethe formform transmission ofof periodicperiodic function phasesphases cancan of the bebe fedfedMIOC backback withwith aa attenuation sensorsensor outputoutput at low signalsignal frequencies. fromfrom zerozero These toto aa frequency-dependentfrequency errors can-dependent be eliminated, transmissiontransmission if low frequencies functionfunction ofof the andthe MIOC MIOC DC withvoltagewith attenuation attenuation are kept away at at low low from frequencies. frequencies. the MIOC These by These a errorsmean errors- canfree be candrive. eliminated, be eliminated, if low if frequencies low frequencies and DC and voltage DC arevoltage keptIt has are away alsokept from away been the shownfrom MIOC the bythat MIOC a mean-free the by m eana mean- drive.value-free freedom drive. of the MIOC control signal can be producedItIt has has by also also subtracting been been shown shown a signal that that the quantized mean-value the mean by- valueq freedom = π freedomor q of = the 2π , MIOC ofobtained the control MIOC by statistical signal control can signalrounding be produced can of be bytheproduced subtracting original by MIOCsubtracting a signal control quantized a signal signal. by quantized q When= π orq by=q π =q, = this2 π, obtainedor results q = 2π in by, obtained astatistical MIOC by roundingcontrol statistical range of rounding the of original 2π. of MIOCMeanthe original-value control- free MIOC signal. range control Whenof freedom q signal.= canπ , Whenbe this produced results q = π , in here this a MIOC only results by control modifying in a range MIOC the of modulation control 2π. Mean-value-free range scheme, of 2π. rangewherebyMean- ofvalue freedomother-free sensor range can properties be of produced freedom can can here be beimpaired. only produced by modifying Setting here onlyq = the 2π by modulationgives modifying a MIOC the scheme, control modulation whereby range scheme,of other4π. sensorInwhereby this propertiescase, other the sensormean can- be valueproperties impaired.-free state can Setting becan impaired. beq achieved= 2π givesSetting without a MIOCq = detriment2πcontrol gives a rangeto MIOC the ofmodulation control 4π. In thisrange scheme case, of the4π. mean-value-freeandIn this thus case, without the mean state adversely can-value be affecting- achievedfree state other withoutcan sensorbe achieved detriment properties. without to the modulation detriment to scheme the modulation and thus withoutscheme adverselyand thus without affecting adversely other sensor affecting properties. other sensor properties. Breaking the MIOC phase-bleed-induced noise limitation through means of an improved and efﬁcient signal processing has paved the way for further FOG applications with navigation grade demands.

Sensors 2017, 17, 567 19 of 22

5. Comparison of Fiber Optic and MEMS Gyroscopes Both types of sensors are equally suitable to build strapdown navigation and AHRS systems. Since MEMS gyroscopes have entered the high-end tactical grade performance of 1–5◦/h they have started to replace some Fiber Optic Gyroscopes due to their inherent cost, size, weight, and power (CSWaP) advantages. Nevertheless, there are a number of implications that need to be considered during the selection process. From the fact that Fiber Optic Gyros do not contain moving parts it can be concluded that they perform generally much better over vibration, shock, and acoustic noise [µFORS]. Nevertheless, there is a sensitivity of the fiber coil towards mechanical stress that can be considered a temporary stress-induced Shupe effect [47]. However, this sensitivity only becomes apparent for performance ranges where MEMS gyroscopes are not available yet. Temperature related Shupe effect and magnetic sensitivity due to the Faraday effect are disadvantages of the FOG and advantages of the MEMS gyroscope. These types of environmental conditions can be shielded from FOG coils, however the mechanical construction and calibration effort generally affect size and cost. FOG noise is widely affected by the light source, electronics, and the signal processing scheme, while MEMS gyroscope noise is widely affected by the moveable mass and also electronics and the signal processing scheme. While MEMS are inherently associated with small size, it is unlikely that they will outperform FOG noise performance on a large scale. Nevertheless, MEMS performance can be scaled with size. One of the greatest advantages of FOG gyroscopes over MEMS gyroscopes is the achievable bandwidth. We have accomplished several hundreds of Hz bandwidth with MEMS, however FOGs due to their interferometric nature and simple deadbeat control scheme offer merely infinite bandwidth, only limited by the interface sampling frequency. For applications with very fast control loops—e.g., in some military domains—FOG is likely to remain the best choice. The following Tables2 and3 summarize technical parameters achieved within Northrop Grumman LITEF’s MEMS and Fiber Optic Gyroscopes in serial production. After all, it is clear that FOGs are performance-scalable and will continue to remain the predominant gyro sensor for several years in applications that require better than 0.1◦/h bias and less than 0.05◦/rt(h) angle random walk. Very high performance FOGs can be found in marine systems with large scale factor (~1 km of fiber length and large diameter), where benign environmental conditions can be assumed. Alternatives such as Hemispherical Resonator Gyros (HRGs) and axisymmetric Class II MEMS Gyroscopes are however either already entering the market or are under intensive development. FOG and MEMS are both mature technologies that are suitable to meet the highest safety standards for aircraft certification. They both provide scalability and are therefore suitable technologies to span over orders of magnitude in performance.

Table 2. Typical values achieved by single-axis MEMS gyroscopes for the use in the Northrop Grumman LITEF MEMS IMU. All parameters tested on the IMU level.

Parameter Test Conditions Typ. Unit Dynamic range 1500 (max.) ◦/s Scalefactor repeatability −40 ◦C ≤ T ≤ 85 ◦C; 1σ 300 ppm Bias repeatability −40 ◦C ≤ T ≤ 85 ◦C; 1σ 1.2 ◦/h ◦ Bias instability (Allan deviation) 0.1 /h√ Angle random walk 0.1 ◦/ h Vibration rectiﬁcation error rms 0.09 ◦/h/g2 −3 dB bandwidth 240 Hz Sensors 2017, 17, 567 20 of 22

Table 3. Typical values achieved by single-axis FOGs for the use in the Northrop Grumman LITEFs FOG-IMU based systems. All parameters tested on the IMU level.

Parameter Test Conditions Typ. Unit Dynamic range 1500 (max.) ◦/s Scalefactor repeatability −40 ◦C ≤ T ≤ 71 ◦C; 1σ 30 ppm Bias repeatability −40 ◦C ≤ T ≤ 71 ◦C; 1σ 0.015 ◦/h ◦ Bias instability (Allan deviation) 0.0012 /h√ Angle random walk 0.005 ◦/ h −3 dB bandwidth 8000 Hz

6. Conclusions Based on applications, customer needs, and our long-term experience in the field we revisited the requirements for tactical and navigation grade inertial sensors in navigation applications and presented NG LITEF’s recently accomplished improvements in the domains of MEMS accelerometers, MEMS gyroscopes, and Fiber Optic Gyroscopes to fulfill these requirements. For MEMS accelerometers, lateral structures provide excellent linearity and pressure insensitivity. For MEMS gyroscopes, an optimized chip design and operating scheme provide better than 1◦/h residual bias over temperature with excellent vibration and acoustic noise immunity. For Fiber Optic Gyroscopes, the MIOC phase-bleed-induced noise has been eliminated by means of signal processing and the bias over temperature has been improved by continuous adaption to the fiber length. We have also given a comparison of FOG and MEMS gyro technologies to assist system engineers with the process of inertial sensor type selection.

Author Contributions: O.D., G.D. and S.V. contributed Section4, while S.K., T.M. and S.Z. contributed Sections2 and3. Sections1,5 and6 were contributed by all authors. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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