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University of Nevada, Reno

Methodologies and Applications of Data Coordinate Conversion for Roadside LiDAR

A dissertation submitted in partial fulfillment of the Requirements for the degree of Doctor of Philosophy in Civil and Environmental Engineering

By Yuan Tian

Dr. Hao Xu / Dissertation Advisor

May 2021

THE GRADUATE SCHOOL

We recommend that the thesis prepared under our supervision by

Yuan Tian

entitled

Methodologies and Application of Data Coordinate Conversion for Roadside LiDAR

be accepted in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Hao Xu, Ph.D., Advisor

Zong Tian, Ph.D., Committee Member

Elie Hajj, Ph.D., Committee Member

Hongchao Liu, Ph.D., Committee Member

Scott Kelly, Ph.D., Graduate School Representative

David W. Zeh, Ph.D., Dean, Graduate School

May 2021

ABSTRACT

Light Detection and Ranging (LiDAR) is becoming more popular in applications of the transportation field, including traffic data collection, autonomous vehicles, and connected vehicles. Compared with traditional methods, LiDAR can provide high-resolution-micro-traffic data (HRMTD) for all road users without being affected by the light condition. Unlike the macro data collected by traditional sensors containing traffic flow rates, average speeds, and occupancy information, the HRMTD can provide higher accuracy and more detailed multimodal all-traffic trajectories data. But there are still some limitations when using it. The first one is that the raw data is in LiDAR’s coordinate system, which greatly affects the visibility of the data. Secondly, the detection range limits its further development. Although LiDAR can detect data within 200 m from itself, the effective detection range is 50 - 60 m. What’s more, the occlusion issue occurred from time to time.

To overcome these limitations, data mapping and integration methods are needed. This research proposed the data integration and mapping method for roadside LiDAR sensors. There is a total of six main steps in this method: reference points collection, reference points matching, transformation matrix calculation, time synchronization, data integration, and data mapping. The raw LiDAR data is in the Cartesian coordinate system. In this coordinate system, the position of each LiDAR point is represented by (x,y,z). To map these points on the GIS-based software based on the WGS 1984 coordinate system, the coordinate system of the LiDAR data should be transformed. After converting the LiDAR data into Geographic Coordinate Systems, the ICP method is applied to integrate the data collected by multiple LiDAR sensors. Compared with the original LiDAR data, the longitude, latitude, and elevation information are added to the processed ii dataset. The new dataset can be used as the input for the HRMTD processing procedures for roadside LiDAR.

Other than benefiting the autonomous vehicle(AV) system and connected vehicle(CV) system, the

HRMTD can also serve other transportation applications. This research provides an application using the HRMTD obtained from roadside LiDAR data to extract lane and crosswalk-based multimodal traffic volumes. This method has three main steps: start and endpoint selection, detection zone selection, and threshold learning. The second step is the primary step of the method, which can be divided into four sub-steps: location searching, data comparison, size searching, and best zone selection. A whole day of data collected in the real world is used to verify the method and compared with the manually counted traffic volume, and the result shows that the accuracy of this traffic volume extraction method reaches 95% or higher. This research will significantly change how traffic agencies assessing road network performance and add great traffic values to the existing probe-vehicle data and crowd-resourced data.

Keywords: data mapping, data integration, roadside LiDAR

iii

ACKNOWLEDGEMENTS

The completion of this study was not possible without the support of several people. With endless love and appreciation, I would like to extend my earnest gratitude and thankfulness to the persons who helped me during this research.

I owe my deepest gratitude and appreciation to my advisor, Dr. Hao Xu. His expertise and instructions helped me flourish during my journey at the Transportation Engineering program at the University of Nevada, Reno (UNR).

I would also like to express my appreciation and truly gratefulness to Dr. Zong Tian, Dr. Scott

Kelley, Dr. Elie Hajj, and Dr. Hongchao Liu for serving on my committee.

My sincere thanks also go to my lab mates Fei Guan, Trevor Whitley, Shradha Toshniwal, Yuxin Tian,

Aobo, Rui, Xiaolong, and Jianyuan Xu for their support in my life.

TABLE OF CONTENTS

ABSTRACT ...... i

Acknowledgements ...... iii

Table of Contents ...... iv

LIST OF TABLES ...... vi

LIST OF FIGURES ...... vii

CHAPTER 1. INTRODUCTION ...... 1

1.1 Background Introduction ...... 1

1.2 Problem Statement ...... 4

1.3 Objectives of the Study ...... 5

CHAPTER 2. LITERATURE REVIEW ...... 7

2.1 Introduction and Applications of LiDAR ...... 7

2.2 HRMTD and Its Application Based on Roadside LiDAR ...... 11

2.3 Data Mapping ...... 16

2.4 Data Integration ...... 21

CHAPTER 3. METHODOLOGY ...... 25

3.1 Reference Points Collection ...... 28

3.1.1 Reference points in WGS 1984 coordinate system ...... 28 3.1.2 Reference points in LiDAR point cloud ...... 32 3.2 Reference Points Matching ...... 33

3.3 Transformation Matrix Calculation ...... 37

3.4 Time Synchronization ...... 43

3.5 Data Integration ...... 44

3.6 Data Mapping ...... 46

CHAPTER 4. SENSITIVITY ANALYSIS ...... 48

4.1 Number of the Reference Points ...... 51

4.2 Distribution of the Reference Points ...... 52

CHAPTER 5. CASE STUDY ...... 55

5.1 Data Mapping Result with GPS Devices ...... 55

5.2 Data Mapping Result without GPS Devices ...... 57

5.3 Data Integration Result ...... 63

CHAPTER 6. APPLICATION OF IMPROVED HRMTD ...... 70

6.1 Introduction ...... 70

6.2 Methodology ...... 72

6.3 Performance Evaluation ...... 77

CHAPTER 7. CONCLUSION ...... 82

REFERENCE ...... 84

LIST OF TABLES

Table 1 Parameters of VLP-32C LiDAR sensor ...... 2

Table 2 Different LiDAR sensors ...... 7

Table 3 Summary of the transformation methods...... 17

Table 4 Features of Trimble R2 GNSS Receiver...... 30

Table 5 Distance and direction for each zone ...... 49

Table 6 Number of LiDAR points for each vehicle ...... 65

Table 7 Comparison of vehicles’ parameters...... 65

Table 8 Average relative error ...... 66

Table 9 Volume for McCarran & Evans ...... 68

Table 10 Lane-based volume evaluation ...... 81

Table 11 Pedestrian/bicycle volume evaluation ...... 81

vii

LIST OF FIGURES

Figure 1 LiDAR’s coordinate system (5)...... 3

Figure 2 LiDAR sensor and raw data ...... 4

Figure 3 An example of airborne LiDAR system (9) ...... 8

Figure 4 Onboard LiDAR on a self-driving vehicle (15) ...... 9

Figure 5 An example of the roadside LiDAR system ...... 11

Figure 6 Flow chart of data pre-processing ...... 12

Figure 7 Raw data and trajectory file ...... 14

Figure 8 Flow chart of the proposed method ...... 27

Figure 9 Differential GPS-DGPS(68) ...... 29

Figure 10 Trimble R2 GNSS Receiver system ...... 30

Figure 11 Reference points collection using Google Earth ...... 32

Figure 12 Reference point collection in LiDAR point cloud ...... 33

Figure 13 Relationship between ECEF and WGS 1984 (67) ...... 34

Figure 14 GPS points collected at Blue Parking Lot ...... 49

Figure 15 Reference points distribution zone ...... 50

Figure 16 Offset change based on different number of reference points ...... 52

Figure 17 The average offset for different scenarios ...... 54

Figure 18 Data collection site ...... 55

Figure 19 Data mapping result with GPS devices ...... 57

Figure 20 Reference points collected by Google Earth ...... 58

Figure 21 Data mapping result without GPS devices ...... 59

Figure 22 Offset distribution ...... 60

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Figure 23 Result of two LiDAR sensors ...... 61

Figure 24 Vehicle equipped with GPS device ...... 62

Figure 25 Dynamic vehicle data matching results ...... 63

Figure 26 Data collection sites ...... 64

Figure 27 Performance of data integration method ...... 67

Figure 28 Total trajectories for all road users in 30 mins ...... 68

Figure 29 Trajectories for 6 vehicles ...... 69

Figure 30 Diagram of intersection installed with LiDAR ...... 73

Figure 31 Traversal search ...... 75

Figure 32 Data collection site ...... 79

Figure 33 MAPE change along Z ...... 80

CHAPTER 1. INTRODUCTION

1.1 Background Introduction

Intelligent Transportation Systems (ITS) is an advanced application that aims to offer innovative services relating to different modes of transportation and enable road users to be better informed and make safer, more coordinated, and 'smarter' use of transport networks (1). There are two leading areas in ITS: connected vehicle(CV) system and autonomous vehicle(AV) system. As part of the ITS, the CV system is designed to transmit traffic information between vehicles or vehicles and traffic infrastructures. All road users, including vehicles, pedestrians, and others, and infrastructures share data through wireless commutation technology in an ideal CV system. The shared information, including heading, speed, movement-related information, and operational status, can be used to avoid crashes, decrease travel times, and reduce fuel consumption (1). However, in the current condition, only a few vehicles are equipped with CV onboard units, and it will take a lot of time and money to equip all the vehicles with the devices. So, the mixed traffic condition

(both connected vehicle and unconnected vehicle exist together) will continue for a long time (3). To overcome the problems caused by the mixed traffic condition, the sensors installed on the road or roadside are then used. In general, the traffic data collected by traditional sensors installed on the road or roadside, such as loop detectors, video detectors,

Bluetooth sensors, and radar, is mainly macro data which only contains traffic flow rates, spot speed, average speeds, and occupancy. All these macro traffic data cannot meet the requirement of the CV system (4). To better serve the CV system, high-resolution micro traffic data (HRMTD) is needed (5). Compared with the macro traffic data, the HRMTD 2 can provide more detailed and higher accuracy traffic trajectories for all road users. The all-traffic trajectory data contains the direction, speed, and location information of all road users, and this information is updated every 0.1 seconds. On the other hand, the HRMTD can also benefit the AV systems by providing more detailed traffic data.

Recently, Light Detection and Ranging (LiDAR) sensors are becoming more popular in the transportation field applications, including traffic data collection, auto-driving, and connected vehicles. Because it can detect objects' precise position information without being affected by the light condition, the LiDAR sensor can provide HRMTD by collecting real-time accurate position data for all road users. This study is based on VLP-32C LiDAR sensors (shown in Figure 2(a)) of Velodyne Lidar’s Ultra Puck. The VLP-32C sensor uses

32 laser beams paired with the detectors to scan the surrounding environment. The detect range of the VLP-32C LiDAR sensor is up to 200m with a 360-degree horizontal field of view (FoV) and a 40-degree vertical field of view. The detailed parameters are shown in

Table 1.

Table 1 Parameters of VLP-32C LiDAR sensor

Parameter value Parameter value Range 200m Weight 925g Number of laser beams 32 Operating Temp -20°C to +60°C Horizontal FoV 360° GPS Timesync 100 Mbps Vertical FoV 40° Horizontal Resolution 0.1° – 0.4° Refresh rate 5-20 Hz Vertical Resolution 0.33° (min)

The working principle of LiDAR is that when the laser beam emitted by LiDAR hits the object, it will be reflected and received by the LiDAR receiver. By combining the laser beam’s direction and the time difference between the emitted and received laser beams, the object can be located. With the 360-degree horizontal FoV and a 40-degree vertical FoV,

LiDAR can store the object's three-dimensional information in the point cloud. During

LiDAR data collection, after completing a 360° scan, the VLP-32C LiDAR generates approximately 1,200,000 3D points in dual return mode and stores them into the point cloud. All these points are in LiDAR’s Cartesian coordinate system, whose origin is located at the center of the sensor 37.34 mm from the base. The positive direction of the y-axis is in the opposite direction of the wire on the sensor. The positive direction of the x-axis is clockwise perpendicular to the y-axis, and the positive direction of the z-axis is the direction from the origin to the top of the sensor. The LiDAR coordinate system shows in

Figure 1.

Figure 1 LiDAR’s coordinate system (5)

All objects and the surrounding environment within the detection range can be detected and represented in three dimensions. One frame of raw LiDAR data is shown in Figure

2(b).

(a) VLP-32C LiDAR sensor (b) Raw LiDAR data

Figure 2 LiDAR sensor and raw data

1.2 Problem Statement

Even the roadside LiDAR sensor can supply more accurate high-resolution micro traffic data than traditional sensors, and there are still some limitations when using it.

1. The first one is that all the results of these studies and raw data are based on

LiDAR’s Cartesian coordinate system. The raw data can be displayed in specific

software instead of displaying in the GIS-related software that can show the road

base map, which greatly affects the visibility of the data.

2. Secondly, the HRMTD provided by roadside LiDAR sensor cannot be directly used

in AV systems without location information for each road user. To provide accurate

location information of the surroundings for the AV, longitude and latitude

information is needed.

3. Thirdly, the detection range limits its further development. Although LiDAR can

detect data within 200 m from itself, the effective detection range varies according

to the surrounding environment, it’s hard to capture the road users whose distance

to the LiDAR sensor is longer than that.

4. The last one is the occlusion issue. the occlusion issue occurred from time to time.

The occlusion means that the road users farther from the sensor are blocked by the

road users closer to the sensor. Since roadside LiDAR is installed at the height of 9

to 15 ft from the ground due to its vertical field of view, the rays it emits can easily

be blocked by a truck. In other cases, if two vehicles drive side by side, the one that

is far away from the sensor is likely to be blocked by the other one. Due to these

factors, the trajectory data in the file processed by a single LiDAR sensor are

usually limited or divided into several small segments.

1.3 Objectives of the Study

1. This research aims to develop an automatic method to map the data collected by

roadside LiDAR sensors. The method should be easily applied to any site for data

collection.

2. This research needs to propose an algorithm to integrate the data collected by

multiple roadside LiDAR sensors. By applying these methods to the existing

procedures of extracting HRMTD based on roadside LiDAR, the expanded all-

traffic trajectory data with longitude, latitude, and elevation information can be

available.

3. Other than benefiting the CV system, the improved HRMTD can also serve other

transportation applications. This research should provide more applications for

improved HRMTD.

The following part introduces different applications of LiDAR and the data integration and mapping methods for different source data. Then chapter 3 presents an integration and mapping method for the data collected by roadside LiDAR sensors. Chapter 4 provides the sensitivity analysis for the proposed method. Chapter 5 carries out the validations for the major steps in the proposed method. Chapter 6 introduces one of the applications of the processed data by this research. At last, chapter 7 concludes the research and future works.

CHAPTER 2. LITERATURE REVIEW

2.1 Introduction and Applications of LiDAR

After the laser's invention, the first LiDAR-like system called "Colidar"-an acronym for

"Coherent Light Detecting and Ranging" was introduced in 1961 by the Hughes Aircraft

Company (7). This system was intended for satellite tracking by combining laser-focused imaging with distance calculated through measuring the time difference for a signal sending and returning. The “LiDAR” was first mentioned as a stand-alone word in 1963, suggested it originated from the combination of "light" and "radar" (8).

Currently, there are two types of LiDAR sensors: Flash LiDAR and Scanning LiDAR. For flash LiDAR, the entire field of view is illuminated with a wide diverging laser beam in a single pulse. But, it can only provide high-resolution on focused areas. While the scanning

LiDAR uses mechanical rotation to spin the sensor for 360-degree detection with high scanning speed. The scanning LiDAR is much safer than flash LiDAR as the laser goes in more than one direction. Table 2 shows the widely-used different LiDAR sensors.

Table 2 Different LiDAR sensors

Type Name Manufacturer Field of view Detection range Leddar Pixell 180° 50m Leddar M16 9° to 95° 100m Leddar Vu8 20°, 48° and 100° 215m Leddartech Flash LiDAR LeddarOne 3° 40m Leddar T16 10° to 48° 50m Leddar IS16 45° 50m VUX-1UAV 330° 350m Riegl MiniVUX1UAV 360° 250m Alpha Prime 360° x 40° 150m Scanning Ultra Puck 360° x 40° 200m LiDAR Puck Velodyne 360° x 40° 100m Puck LITE 360° x 40° 100m Puck Hi-Res 360° x 20° 100m

HDL-32E 360° x 40° 100m HDL-64E 360° x 26.9° 120m VelaDome 180° x 180° 200m OS0 360° x 90° 50m OS1 Ouster 360° x 45° 120m OS2 360° x 22.5° 240m

The applications of LiDAR sensors can be divided into three groups: airborne LiDAR, onboard LiDAR, and roadside LiDAR.

Airborne LiDAR is that attached the LiDAR sensor to a helicopter or aircraft during flying to collect a 3-D point cloud point. It is usually used for digital elevation models. Figure 3 shows an example of the airborne LiDAR system.

Figure 3 An example of airborne LiDAR system (9) The airborne LiDAR was first used to collect clouds and pollution at the beginning of the

1980s by the US National Center for atmospheric research (10). Later, when entering the mid-1990s, the commercial airborne LiDAR systems have been operational (11). And then,

9 there has been much research on Digital Elevation Models (DEM), Digital Terrain Models

(DTM), Contours of varying intervals, Slope maps, Planimetric Mapping, Tree height analysis, Cut and Fill modeling, Ortho-rectification in combination with imagery using airborne LiDAR (12).

Onboard LiDAR means that while data collection, the sensor is installed on a moving vehicle. It is an important part of autonomous driving technology. In 2005, inspired by the

DARPA challenge, David Hall, founder of Velodyne Acoustics, built a spinning LiDAR to mount on top of a vehicle for self-driving, and then it finished the desert race in

DARPA’s 2007 Urban Challenge (13). After that, onboard LiDAR was widely used in a self-driving vehicle to detect the basic road shape and topological to ensure safety and, finally, plan the path (14). Figure 4 shows the onboard LiDAR on a self-driving vehicle system.

Figure 4 Onboard LiDAR on a self-driving vehicle (15)

To extend the application of the LiDAR sensor, Lee (16) installed it on a stationary object to collect traffic data in 2012. In the research, the LiDAR was mounted on a parked vehicle next to the road to do the vehicle classification using collected vehicles’ shape information.

Later, in 2017, the Center for Advanced Transportation Education and Research (CATER) of the University of Nevada, Reno (UNR) began to install the LiDAR sensor on the roadside to extract high-resolution traffic data of each road user. After that, the “roadside

LiDAR” has been identified and is still in use today. The roadside LiDAR system means a system that installs the LiDAR sensor on a fixed object to collect data. Besides the LiDAR sensor, there are some other essential accessories to make up the roadside LiDAR system, including：

• Computer: connect and control sensors, collect data.

• Hard drive: store collected LiDAR point cloud.

• Power supply: power the sensor and the computer.

• Cabinet: the storage for the devices.

• Other equipment: used to install and uninstall the devices.

The sample of the roadside LiDAR system is shown in Figure 5.

Figure 5 An example of the roadside LiDAR system With roadside LiDAR, regardless of whether there is CV system equipment installed on the vehicle, the operating information of each vehicle will be collected to be future used in the CV system if it is within the detection range. Besides, information about pedestrians, non-motorized vehicles, and other road users will also be collected.

2.2 HRMTD and Its Application Based on Roadside LiDAR

At present, the most important role of roadside LiDAR is to get the high-resolution micro traffic data (HRMTD) for each road user. Xu (5) documented the complete and mature algorithms and procedures developed for extracting high-accuracy high-resolution trajectory data from roadside LiDAR sensors. The main four steps to get multimodal all-

12 traffic trajectories data include background filtering, data clustering, data classification, and object tracking. The flow chart is shown in Figure 6.

Figure 6 Flow chart of data pre-processing The data collected by the roadside LiDAR sensor includes the data for all road users and the traffic environment. To focus on road users’ information, the background filtering step is applied to exclude the LiDAR point for traffic environment, including trees, buildings, road surfaces, and noise points. After the background filtering step, the point data representing the same road users are still separated. The data clustering step is to group the points which belong to the same road user together. The density-based spatial clustering application with noise (DBSCAN) which was first proposed by Martin Ester in 1996 (17), is one of the most common clustering algorithms and most cited in the scientific literature

(Most cited data mining articles according to Microsoft academic search; DBSCAN is on

13 rank 24, in 2010). Given a set of points in some space, the DBSCAN can cluster the points that were closely packed together into the same group. After all points that belonged to the same object were clustered together, a reference point needed to be identified to locate each object (18). The backpropagation artificial neural network (BP-ANN) was applied to identify each clustered point. The data classification step is applied to distinguish the different objects by their features collected LiDAR point cloud.

After processing, the trajectory file for each road user is available, and one example is shown in Figure 7(b). In the picture, the trajectories for all road users are shown according to the location of the LiDAR point, and each point contains lots of information: location, timestamp, speed, lane information, object-ID, direction, longitude, latitude, elevation, size, and other information—the points with same object-ID form a complete trajectory for one road user.

(a) Raw LiDAR data

(b) Trajectory files extracted from raw LiDAR data

Figure 7 Raw data and trajectory file

After the high-accuracy high-resolution trajectory data from roadside LiDAR sensors were available, the application study has been gradually started. Wu (19) presented a systematic procedure to identify the road boundary based on the trajectories. In the research, the pedestrian and vehicles were separated first according to Backpropagation (BP) ANN model, and then the road boundary nearest to the LiDAR sensor was identified based on the number of vehicles’ points in each group. Generally, the group with the greatest number of points should be the vehicles in the traffic lane nearest to the sensor after only counted the nearest points in each clustering group. This method later proved to be very effective, even for the road having a curve, so that the processed trajectory files can better serve the

ITS and CV system.

In addition to being applied to road infrastructure study, the high-accuracy high-resolution trajectory data also can be used for traffic safety and operation. Wu(20) proposed a vehicle-

15 pedestrian near-crash identification method with the processed roadside LiDAR data to improve safety. Three parameters were needed as the inputs: Time Difference to the Point of Intersection; Distance between Stop Position and Pedestrian; and Vehicle-pedestrian speed-distance profile. All these parameters were calculated based on the processed high- accuracy high-resolution trajectory data, and the final thresholds were determined by combining them. In the result, the TDPI<2.5 s or 0 < DSPP < l TC or vehicle speed within area A in the speed-distance profile will be identified as the near-crash and

2.5 s ≤ TDPI≤3.5 s or vehicle speed within area B in the speed-distance profile will be recognized as the crash. In this way, the engineers can analyze the before-and-after pedestrian safety assessment of one specific site and identify the site with the highest pedestrian crash risk from the site's pool.

The processed high-accuracy high-resolution trajectory data also can be applied to obtain traffic operations such as traffic volume, speed, queue, and density (21). But for now, there is only one research related to this part. Wu (22) documented a real-time queue length detection method based on it. In this method, the vehicles with speed under 5km/h were considered as in a queue, and the average length of the vehicle is 6m. Based on these assumptions, the simple rule-based method's trajectories were analyzed to get the real-time queue length. To reduce the error caused by the occlusion issue, historical data was used to replace the data with occlusion. The proposed method can directly detect the queue length with high accuracy under different scenarios, benefiting the engineers’ work.

2.3 Data Mapping

The Geographic Coordinate Systems is a methodology to define the location of a feature in space based on the characteristic of the Earth (23). The true shape of the Earth is not a regular ellipsoid, so there are several Geographic Coordinate Systems for the different datasets. The purpose of this step is to map the LiDAR data using GIS-related software.

Three coordinate systems are involved: Cartesian coordinate system, Earth-Centered,

Earth-Fixed (ECEF) coordinate system, and World Geodetic System (WGS) 1984 coordinate system. The raw LiDAR data is in the Cartesian coordinate system. In this coordinate system, the position of each LiDAR point is represented by (x,y,z) according to the distance to the sensor. At the same time, the data in GIS-related software can be represented in two different coordinate systems- the ECEF coordinate system, a kind of

Cartesian coordinate system, and the WGS 1984 coordinate system.

The WGS 1984 coordinate is an internationally universal geographic coordinate system, due to that the ellipsoid it is based on is the one that best fits the whole shape of the earth.

The location information in WGS 1984 can be expressed as (longitude, latitude, elevation).

The latitude is the angle between the equatorial plane and the straight line that passes through that point and the center of the Earth, while the longitude is the angle east or west of a reference meridian to another meridian that passes through that point.

The ECEF coordinate system is the corresponding Cartesian coordinate system of the WGS

1984, both of them are based on the same ellipsoid. The characteristics of the ECEF coordinate system are (24):

• The origin of the system is at the center of the Earth.

• The direction of the Z-axis is from the origin to the North Pole.

• The direction of the X-axis is from the origin to 0 degrees longitude at the Equator.

• The direction of the Y-axis is from the origin to 90 degrees east longitude at the

Equator.

Since both ECEF and WGS 1984 are based on the characteristics of the same ellipsoid, the data in two coordinate systems can be converted to each other. For the data conversion between the ECEF and WGS 1984, Heiskanen (25) developed the conversion equations according to the ellipsoid's characteristics. To better analyze and study the GIS, the data in

WGS 1984 usually need to be converted into the local Geographic Coordinate Systems whose ellipsoid can best fit the local geoid. Some researchers (26)(27)(28)(29)(30) documented the procedures to transform two different geodetic datums. In their research, several points collected in both coordinated systems were needed as reference points. The values of these reference points in Geographic Coordinate Systems were then transformed into the corresponding Cartesian coordinate system according to the characteristics of the ellipsoids. The parameters of the transformation matrix can be available based on paired reference points. And at last, the data in one coordinate system can be converted into the other one. The transformation methods used in geodesy to produce distortion-free transformations from one datum to another are list in Table 3.

Table 3 Summary of the transformation methods

Authors Method Description Data requirement Two translations, one Vaníček, P. (26). Four-parameter rotation, one scale 2-D data factor Three translations and Only 2 transformations Lichti, D. (31). Six-parameter three rotations considered

Suitable for the Three translations, conversion of Seven- Janssen, V. (28). three rotations, one geographic coordinate parameter scale factor systems with small rotation angles Three translations, Eight- X-axis and y-axis have Andrei, O. (32). three rotations, two- parameter the same scale factor scale factors Based on the Three translations, Nine- geographic coordinate Andrei, O. (32). three rotations, three parameter systems with small scale factors rotation angles Used for airborne Three translations, LiDAR data, the Twelve- three rotations, three Maes F. (33). reference points were parameter scale factors, and three collected by Trimble skew distortions MensiGS200. Combined Combined Suitable for any 3-D Suetin, P. K. (34). transformation transformation matrix datasets

Based on the data transformation for Geographic Coordinate Systems, there are also some studies on LiDAR data mapping. Lichti, D. (31) used the six-parameter transformation method to map the airborne laser scanner data with digital photogrammetric data. In his research, ten reference points were used, and this method can map the data collected by the airborne laser scanner. But in this research, the accurate GPS information for the digital photogrammetric data was already known which is not suitable for all the situations. Later, in 2013, Wu (35) improved the airborne LiDAR data mapping method, the authors used

Trimble MensiGS200 devices to collect 5 reference points for the airborne LiDAR data, and they also compared three different transformation methods: 6-parameter, 7-parameter, and 12-parameter transformation method. In the conclusion, the 7-parameter transformation result was better than the 6-parameter transformation but was worse than the 12-parameter transformation method based on nine study points. Even this research had

19 a sensitivity analysis about the number of the reference points, it still didn’t provide a solid instruction for the reference points collection. Inspired by the airborne LiDAR data mapping, Mao (36) applied the data mapping steps into onboard LiDAR data. In the paper, they provided a novel least squares collocation-based method to map the onboard LiDAR data. The six-parameter transformation and least-squares collocation methods were used to do the transformation step, and for the sensitivity analysis, they compared the results from the different number of reference points. There were also some limitations: firstly, all vehicles need to be installed the POS devices and the second one is that they only compare

3 different number of the reference points for the sensitivity analysis, the more detailed study is needed. Liu(37) also presented a coordinate transformation method to unify the three-dimensional (3D) points between different coordinate systems. The proposed method was also based on the 6-parameter transformation method, but without requiring neither the initial values nor the iterations. In this way, this method can reduce the processing time.

Then from 2019 to 2021, Liu(38)(39) introduced two methods to map the onboard LiDAR data. For these two papers, the seven-parameter transformation methods were applied with pre-known reference points. The difference between these two methods was that the first one used weighted total least squares to do the data optimization while the second one was based on the kinemics state constraints converted measuring Kalman Filter and the

Levenberg Marquardt Wavelet neural network.

Besides the 3-D LiDAR data, there are also some studies related to other types of LiDAR data mapping. When using the airborne LiDAR, the GIS-based map or map pictures are usually needed to display the result. Hodgson (40) used an airborne LiDAR at a flying height of 1207 meters above ground level to collect countywide elevation data. In this

20 research, the x-y coordinates of LiDAR points were located in the field, and their elevations were surveyed. To match the two datasets, the vertical heights were measured using the rapid-static GPS techniques at each reference point of airborne LiDAR. In addition to the detection of elevation, James (41) adopted airborne LiDAR data to map the gullies and headwater streams under the forest canopy, and firstly the data were converted to shapefiles using ArcGIS. Then the coordinate was also re-projected from the state plane into UTM coordinate. After processed by Arc Hydro software, the LiDAR data are used to generate a TIN, and then the TINs are used to create DEM. At last, the contour map can be obtained to present the gullies and headwater streams. Joseph (42) applied the airborne LiDAR to mapping forest carbon data. In this paper, the LiDAR metrics of forest canopy structure data can be converted to aboveground carbon density and combined with maps derived from satellite data, and the airborne LiDAR data can be mapped. To improve the matching accuracy, Salah (43) combined the LiDAR data and aerial images to provide a more accurate classification of terrain cover. A total of 22 feature attributes were generated firstly. A self-organizing map was selected to fuse the data, and after a series of image processing steps, the building can be extracted accurately. Inspired by successful applications of LiDAR in the forestry field, Kempeneers (44) presented a fused method to map the coastal dune vegetation by taking advantage of the LiDAR sensor and airborne digital camera. In this method, the camera provides limited multispectral data, which is not as detailed and accurate as needed, so the LiDAR sensors are required to supply the extra information to finish the map. Zhang (45) proposed a method for odometry and mapping using range measurements from onboard LiDAR. The velocity of the LiDAR was first estimated according to perform odometry at a high frequency but low fidelity, then map

21 the LiDAR data under a lower frequency. In addition to the fusion of two data sources, there are also some studies trying to map the different sources of data into a GIS-based dataset. In 1995, Novak (46) focused on the mobile mapping system. The data captured by mobile devices, including land-related data from airplanes, cars, or trains, was extracted automatically on the mobile platform and then transferred to a multimedia geographic database. In 2006, Bell (47) mapped the cancer data in GIS-related software to inform the public. In his study, by linking the cancer information with the GIS-related software to show the distribution of cancer in the country. Since the output information was only accurate to the state-scale, the requirements for the latitude and longitude of the source data were not high. Göçer (48) combined different types of data by creating a database structured on the geometric model.

The methods mentioned for airborne LiDAR and onboard LiDAR data mapping were based on the moving LiDAR sensors, which were different from the roadside LiDAR system. What’s more, the transformation methods used in these papers were better for the data from two different Geographic Coordinate Systems because they will assume that the rotation angles were small enough. As a non-geographic coordinate system, the processing of LiDAR data needs to consider more transformation steps.

2.4 Data Integration

The data integration method can be summarized as three types: point-based integration, line-based integration, and plane-based integration method (49). The Iterative Closest Point

(ICP) method is the widely used integration method. It is first formulated by Besl and

McKay(50) and extended by Chen and Medioni (51). The main idea of the ICP is that one

22 point, the reference, is kept fixed, while the other one has transformed to best match the reference (52). By calculating the unique transformation that can obtain the minimum of the mean square distance between the two points clouds, the ICP iteratively greatly improved the registration of two-point clouds that overlap (53). Wei (54) presents a new effective refinement algorithm for the line-based integration method for palmprint alignment by applying the ICP to the principal refinement lines. Based on the traditional

ICP methods, many researchers have developed numerous ICP extension methods(55)(56)(57).

Rahmat (58)presented a proper coordinate transformation method for antenna data and feed horns data. These two datasets were in different coordinate systems. In his way, the antenna data in the spherical coordinate can be transformed into the Cartesian coordinate system.

And then, in the Eulerian Angeles step, the data in two Cartesian coordinate systems can be matched. Yao (59) improved the transformation models in the 3D coordinate system.

Comparing the traditional transformation methods: Bursa-Wolf, Molodensky, and

WTUSM, the researchers found that these methods were only used when the rotation angles were small enough. Based on this, a technique that fitted 3D coordinate transformation with any angle using Lodrigues matrix, including addition, subtraction, multiplication, and division, was applied to reduce the equation's complexity.

Due to LiDAR’s widely used in topographic data collection, some experts successfully integrated the LiDAR data and digital imagery to improve the mapping procedures.

Rottensteiner (60) generated the 3D building models by LiDAR data and aerial images. In the method, the building regions were detected firstly, then the roof planes were detected

23 by applying a curvature-based segmentation technique. After that, the integration data were used in the reconstruction process to increase the reconstructed models' quality. Using the centroids of rectangular building roofs as control points, a methodology for integrating photogrammetric images and lidar datasets was proposed (61). In this method, if 2D

LiDAR coordinates were used as the input, the accuracy was 0.5m. The typical application of the onboard LiDAR is to serve the self-driving vehicles that act as an eye to provide a

360-degree view of the surrounding. Achieving automotive autonomy requires artificial intelligence to process and integrate data from a suite of sensors, including cameras, microwave radar, ultrasonic sensors, and onboard LiDAR (62). Erke (63) combined two independent calibration processes to address the relationship between the data collected by cameras and onboard LiDAR. The LiDAR used in this research was Velodyne-HDL-32

LiDAR. In this research, the two datasets in two different coordinate systems were calibrated into the same robot platform coordinate or an arbitrarily fixed coordinate first, and then through the same coordinate, the two datasets can be matched. Similar work was carried out by Taylor (64). In his work, the LiDAR scan was projected onto the camera's image using a camera model to integrate them together. Both of the methods mentioned before need a transformation step, and there are also some algorithms are based on the shared features in two different sensors. In 2015, Gaurav (65) reported an algorithm to calibrate the LiDAR-camera system. The main principle of this method was that the correlation between the onboard LiDAR reflectivity and the intensity of the camera was maximized, and then these two values can be matched correctly.

Most of the existing integration methods for LiDAR data are based on multiple data sources, but these methods cannot solve the problems with the current application of the

24 roadside LiDAR sensor. Wu (66) proposed a semi-automatic points registration method called points-aggregation-based partial iterative closest point algorithm for roadside

LiDAR points registration. In this method, there were two significant steps: XY data registration and Z adjustment. For the data collected by different LiDAR sensors, the first step was to synchronize the time. In his research, the corresponding frame was founded by the minimum offset between two frames from two different sensors. The partial ICP method was then applied to find the critical points in the shared detection range without considering the Z-axis. A Triangle Matching method was then used to register points in

XY coordinates. The value of Z was used in the next step to adjust the register points in Z- axis. In the previous study (4), an innovative procedure called revolution and rotation- based method was introduced to integrate multiple roadside LiDAR sensors’ data. This method's advantage is that the corresponding ground points collected by different LiDAR sensors can be matched with the revolution and rotation-based method.

There are still some limitations when using these methods. Firstly, some assumptions are required to perform the algorithm: the locations of the LiDAR sensors are setting up horizontally with inclination, the location of the GPS sensor and the LiDAR are pre- measured, and there are overlapping parts of the ground surface in different LiDAR sensors. But in real data collection, these assumptions may not be accurate, especially the placement of LiDAR sensors and whether there are overlapping parts of the ground surface in different LiDAR sensors. What’s more, this method is based on 2D data and then extends to 3D data; the accuracy can be improved. Since all raw data is needed as input, the length of time it takes to process the data is also a significant drawback. To expand the use of the roadside LiDAR, all these issues need to be urgently addressed.

CHAPTER 3. METHODOLOGY

This part introduces the methodology for roadside LiDAR data integration and mapping.

The flow chart of the algorithm is shown in Figure 8. There are seven main steps in this method: reference point collection, reference point matching, transformation matrix calculation, time synchronization, data integration, and data mapping. The raw LiDAR data is in the Cartesian coordinate system. In this coordinate system, the position of each LiDAR point is represented by (x,y,z) according to the distance to the sensor. To map these points on the GIS-based software based on the WGS 1984 coordinate system, the coordinate system of the LiDAR data should be transformed. The data point collected in these two coordinate systems at the same time is called the reference point.

The first step in the method is to collect these reference points. The data point in the

Cartesian coordinate system can be directly selected from the raw LiDAR data using veloview, while there are two ways to collect these corresponding points in WGS 1984 coordinate system: the first one is that collect these points using a high-precision GPS device, and the other one is based on GIS-related software. After all reference points are available, the values of the reference points in the WGS 1984 coordinate system will first be converted into ETEF coordinate system. Then the transformation matrix will be calculated according to the values of reference points in two coordinate systems. If there are more than four reference points collected, the Least Square method will be used to optimize the transformation matrix. For multiple roadside LiDAR sensors, the data collected in the same time period will be select to do the data integration based on the simplified ICP method. At last, after all data are integrated together in ECEF coordinate

26 system, another transformation step will be applied to transform all the data into WGS

1984 coordinate system.

Compared with the original LiDAR data, the longitude, latitude, and elevation information are added to each point. In addition, the range of data is greatly expanded due to the data integration. The new dataset can be used as the input for the HRMTD processing procedures for roadside LiDAR.

GIS-based software GPS devies

Raw roadside LiDAR data Point data with GPS information

Reference points selection

Reference points matching

Transformation matrix calculation

Four reference points?

Y Least-squares method

Single sensor?

N Y Time synchronization

Data integration

Data mapping

GIS-based LiDAR data

Figure 8 Flow chart of the proposed method

3.1 Reference Points Collection This part presents how to collect the reference points both in LiDAR’s Cartesian coordinate system and the WGS 1984 coordinate system.

3.1.1 Reference points in WGS 1984 coordinate system There are two ways to collect reference points in the WGS 1984 coordinate system. The first one is using the high-precision GPS device, while the second one is that collect these points in GIS-based software. Normally, both can be used as the input for the data integration and mapping method, but in some special cases, only the method with GPS devices can be applied. The list of these special cases is as follows.

• The GPS data has not been updated.

• No reference points can be selected from GIS-based software.

• The GIS-based software is not available.

The high-precision GPS device can be used to collect the reference points only if the device is available. But, due to the high price, this assumption is not necessarily true. For a newly- built intersection, roundabout, or road segment, or, for some data collection sites, the GIS- based software has not been updated in time. The longitude, latitude, and elevation cannot be found using this software. For some other sites, although the GPS information has been updated to the latest, there are not enough reference points that can be found within the detection range of LIDAR. This situation usually happened in remote places or in the wild field. In some special cases, the GIS-based software is not available, and the high-precision

GPS device is the only option to collect data. Under these circumstances, the reference points can be collected by the high-precision GPS device.

The biggest difference between these two methods is that Google Earth cannot provide accurate elevation information for a specific point. The influence of elevation on the results is discussed in detail in section 3.2.

3.1.1.1 Reference points collected by GPS devices

Based on the principle of difference, the GPS satellite positioning measurement can provide precise location information, including longitude, latitude, and elevation. The differential GPS-DGPS is using the accurate information of the reference station to calculate the difference between the measured satellite pseudoranges and actual pseudoranges, and then sends this value to the user in real-time or afterward to correct their measurement data. The differential GPS-DGPS is shown in Figure 9.

Figure 9 Differential GPS-DGPS(68)

The Trimble R2 Global Navigation Satellite System (GNSS) Receiver system (shown in

Figure 10) is used in this research to collect data. The Trimble R2 GNSS Receiver system contains a GNSS antenna, receiver, computer for users to collect data, Bluetooth, Wi-Fi, an optional internal 450 MHz radio with a receive option which can be used as a rover, and a battery in a rugged light-weight unit. Detailed features are list in Table 4.

Table 4 Features of Trimble R2 GNSS Receiver

Features value Horizontal precision 8 mm +1 ppm RMS Vertical precision 8 mm +1 ppm RMS Weight 1.08 kg Channels 220 Update rate 5 Hz Operating Temp -20°C to +55°C

Figure 10 Trimble R2 GNSS Receiver system Within the detection range of the installed roadside LiDAR, use the Trimble R2 to collect multiple (at least four) GPS points as reference points.

3.1.1.2 Reference points collected by GIS-based software

The method introduced in the previous section is based on the high-precision GPS device-

Trimble R2. The device's high price limits the widespread use of this method, so a simple and cheaper way needs to be founded. This section introduces another solution to collect the reference points by GIS-related software. The commonly used GIS-based software includes Google Map, Bing Map, Google Earth, and ArcGIS. In this research, Google Earth is selected due to it can provide higher precision longitude and latitude information for the base map without paying any additional fees. On the other hand, the operability of Google

Earth is better than Google Map or Bing Map.

Due to the reference point selection using Google Earth is manually selected, the measurement error will be larger than the previous method. To reduce this error, objects with a fixed location and obvious features will be selected as reference points. Usually, the poles installed at the intersection or on the road segments, corner of the buildings, corner of the road curves, and traffic signs within the LiDAR detection range will be selected as the reference points. One example of reference points collection using Google Earth is shown in Figure 11. The four red icons are the reference points collected for this intersection.

Figure 11 Reference points collection using Google Earth 3.1.2 Reference points in LiDAR point cloud Due to the data used in this research was collected by Velodyne VLP-32, the only software to display the LiDAR data cloud point is VeloView. According to the reference points defined by the previous steps, the data of the corresponding point will be determined through Veloview. One example of reference point collection in the LiDAR point cloud is shown in Figure 12. The traffic pole was selected as the reference point. Even there are multiple LiDAR points for the same object, only one is needed.

Figure 12 Reference point collection in LiDAR point cloud 3.2 Reference Points Matching

The reference points collected by the previous step have two coordinate systems: The cartesian coordinate system and WGS 1984 coordinates system. To match the same reference point in the two coordinate systems, a third coordinate system, Earth-Centered, Earth-Fixed (ECEF) coordinate system, is introduced. The data in the ECEF coordinate system is another way of representing the position of a point on the earth. The relationship between ECEF and WGS 1984 is shown in Figure 13. The reference point data in WGS 1984 coordinate system can be directly converted to the ECEF coordinate system based on Equation (1).

Figure 13 Relationship between ECEF and WGS 1984 (67)

 XNH=+( )cos cos   YNH=+( ) cos sin  (1)  Z= N1 − e2 + H sin ( )  

Where,

N –Curvature radius of the ellipsoidal ring; e –First eccentricity of the ellipsoid;

X-The x coordinate value of the reference point in the ECEF;

Y-The y coordinate value of the reference point in the ECEF;

Z- The z coordinate value of the reference point in the ECEF;

 –The latitude of the reference point;

 –The longitude of the reference point;

H- The elevation of the reference point.

The influence of elevation on the results is discussed below for two different methods two collect reference points.

N can be calculated based on Equation (2), e represents the first eccentricity of the ellipsoid, which equals 0.00332.

a N = (2) W

Where a represents the long radius of the ellipsoid, which is 6378137m, and W represents the first auxiliary coefficient, it can be obtained from the equation below.

W=−(1 e22 sin  ) (3)

Where e represents the first eccentricity of the ellipsoid and  presents the latitude of the point. Due to e=0.00332 and the 푠푖푛2  ∈[0,1], the thresholds of w are [0.999994,1]. The values of the W and N can be rounded to:

푊 = √1 − 푒2 ∗ 푠푖푛2  = 1

푎 푁 = = 푎 = 6378137푚 푊

1 − 푒2 = 1

The equation (1) can be simplified to:

XNH=( +) cos  cos   YNH=( +) cos  sin  (4)  ZNH=( +) sin 

Considered the elevation(H) threshold for the regular city in the USA is [50m, 1600m]; they are small enough compared to the Curvature radius of the ellipsoidal ring, which means they have little effect on calculation results.

Assuming the error is  m, the relative error for  can be calculated as:

vv−  =AE100% (5) vE

Where  represents the relative error, vA is the actual value observed, and vE is the expected value.

 =  =  = 1.5676  10−−77   , 1.5678  10   (6) XYZ NH+ 

When  =1000m , which means there is a 1000m offset when collecting the elevation for the reference points, there is a relative error of 1.5cm for the outputs, which can be acceptable.

Based on the analysis, the tolerance for the elevation (H) is high enough. The GPS information provided by the map software can be used to calculate the transformation matrix.

3.3 Transformation Matrix Calculation After the previous step, the values of the reference points in the WGS 1984 coordinate system can be converted into the ECEF coordinate system. For the two Cartesian coordinates, LiDAR’s Cartesian coordinate system and ECEF coordinate system, the same reference point has different values in them because their origin and direction vectors are different. To transform the data in LiDAR’s Cartesian coordinate system to the ECEF coordinate system, the reference points are expressed in homogeneous coordinates. The value of the reference point in LiDAR’s Cartesian coordinate system is expressed as

[xi y i z i 1] , and the value of the same reference point in ECEF is expressed as

[XYZi i i 1]. A combined transformation matrix T is needed to transform the data in the LiDAR’s Cartesian coordinate system into the ECEF coordinate system based on

Equation (7).

[Xi Y i Z i 1]= [ x i y i z i 1]* T (7)

There are four main transformation steps that make up the combined transformation matrix

T: scaling, rotation, shear mapping, and translation. T is a square matrix of order 4 and can be expressed as below.

a11 a 12 a 13 a 14 a a a a T = 21 22 23 24

a31 a 32 a 33 a 34  a41 a 42 a 43 a 44

a11 a 12 a 13 a a a In the transformation matrix, 21 22 23 generate fundamental transformations such a31 a 32 a 33

as scaling, rotation, and shear mapping. a41 a 42 a 43  produces the translation along the

a14 a a X, Y, and Z directions.  44  represents overall scaling transformation. 24 represents a34 projection transformation which is not used in this research.

Scaling

Scaling transformation is a transformation that enlarges or reduces a three-dimensional object without changing the origin and directions. In the transformation matrix T, the

elements a11 , a22 , a33 on the main diagonal function act as the local proportional

transformation, while the element a44 acts as a whole proportional transformation. The scaling transformation matrix can be represented as:

sx 0 0 0 0s 0 0 y Ts = 0 0sz 0  0 0 0 1

Where, sx , s y and sz indicates scaling on the x-axis y-axis and z-axis, respectively.

Rotation

The rotation transformation is to rotate the angle θ around the origin at any point on the plane. Generally, the counterclockwise direction is positive, and the clockwise direction is negative. Rotation transformation can be divided into three forms: rotation around the x- axis, y-axis, and z-axis. The transformation matrix of each transformation is

1 0 0 0 cos 0− sin 0 0 cos sin 0 0 1 0 0 T = , T = , RX 0− sin cos 0 RY sin 0 cos 0   0 0 0 1 0 0 0 1

cos sin 0 0 −sin cos 0 0 T =  RZ 0 0 1 0  0 0 0 1

Where  represents the angle of rotation, TRX represents the transformation matrix around

the x-axis, TRY represents the transformation matrix around the y-axis, and TRZ represents the transformation matrix around the z-axis.

Shear mapping

The shear mapping transform refers to a plane figure obtained by scaling the directional distance of each point of the graph to a straight line parallel to the direction in a certain direction. The shear mapping transformation matrix can be represented as:

10mmyz11 mm10 xz12 TSH = mmxy2210  0 0 0 1

Where, mx1 and mx2 represent the shear mapping value along the x-axis direction, my1

and my 2 represent the shear mapping value along the y-axis direction, mz1 and mz 2 represent the shear mapping value along the z-axis direction.

Translation transformation

Translational transformation refers to the transformation of three-dimensional objects along the x-axis, y-axis, and z-axis without changing the object's size and direction. The transformation matrix can be represented as:

1 0 0 0 0 1 0 0 T =  t 0 0 1 0  Tx Ty Tz 1

Where, Tx , Ty , Tz represents the distance translated on the x-axis y-axis and z-axis, respectively.

The formula for converting two spatial Cartesian coordinates is as follows:

According to the calculation rules of the matrix, the solution of the transformation matrix

T can be obtained from Equation (9). Due to the order of the T, at least four reference points are needed based on the equation.

−1 x1 y 1 z 111   X 1 Y 1 Z 1  x y z11   X Y Z  2 2 2   2 2 2  T = (8) x3 y 3 z 311   X 3 Y 3 Z 3      x4 y 4 z 411   X 4 Y 4 Z 4 

Where, the same number indicates the same reference point.

T- Transformations matrix.

[xi y i z i 1]- Reference point in the LiDAR’s Cartesian coordinate system.

[XYZi i i 1]- Reference point in the ECEF coordinate system.

Least-squares

In theory, GPS point data will always have errors that cannot be eliminated, such as instrument error, method error, and operational error. Even though these errors cannot be eliminated, but they can be reduced by collecting more reference points. When the number of GPS data points is greater than 4, the problem can be regarded as an overdetermined system which means there are more equations than unknowns. The least-squares method is adopted to solve the overdetermined system problem. The least-squares process is a mathematical optimization technique. It finds the best function match for the data by minimizing the squares' sum of the errors. The least-squares method can be used to quickly

42 obtain anonymous data and minimize the sum of the squares of the errors between the obtained data and the actual data.

Assuming that the number of reference points is m, matrix A represents the (x, y, z) information collected by LiDAR, and matrix B is the transformed (x, y, z) information which can be represented by (X, Y, Z). The overdetermined system can be represented as

AT= B (9)

x1 y 1 z 1 1 XYZ1 1 1 1 x y z 1 XYZ 1 Where, A = 2 2 2 . T is the transformation matrix. B = 2 2 2 ,     xm y m z m 1 XYZm m m 1 and m>4.

There is no solution for the overdetermined system generally; to get the most appropriate one, let the equations "try to be established ", the residual square function S is introduced.

S() T=− AT B (10)

WhenTT= S takes the minimum value and is recorded as:

TST= arg min( ( )) (11)

When the value of ST()is differentiated to the minimum value, then

AATABTT* = (12)

If the matrix AAT is a non-singular matrix, then T has a unique solution,

TAAAB= ()TT−1 (13)

3.4 Time Synchronization Since the road users are moving almost every time, the locations of road users keep changing. Besides, each LiDAR sensor's start time is not necessarily the same; time synchronization is essential. The first step of the integration method is to select the data collected during the same time. The timestamp information provided by the LiDAR dataset is a 32-bit unsigned integer marking the moment of the first data point in the first firing sequence of the first data block. The time stamp’s value is the number of microseconds elapsed since the top of the hour. So, the real-time information for the frame 푖can be calculated based on the equation (15).

푇 = 3600 ∗ (푇 + 푛 ) + 푇푖푚푒푠푎푡푚푝 (푚푖푛) /1000000 { 푖−푠푡푎푟푡 푠푡푎푟푡 푖 푖 (14) 푇푖−푒푛푑 = 3600 ∗ (푇푠푡푎푟푡 + 푛푖) + 푇푖푚푒푠푎푡푚푝푖(푚푎푥) /1000000

Where, 푇푖−푠푡푎푟푡is the start time of the frame 푖 (second). 푇푖−푒푛푑is the end time of the frame

푖 (second). 푇푠푡푎푟푡is the time when the LiDAR starts working (h). 푛푖is the number of hours between sensors start working and frame 푖 (Non-zero integer). 푇푖푚푒푠푎푡푚푝푖(푚푖푛)is the minimum timestamp in the frame 푖. 푇푖푚푒푠푎푡푚푝푖(푚푎푥)is the maximum timestamp in the frame 푖.

For the specific frame i of LiDAR I, the time period is [푇푖−푠푡푎푟푡,푇푖−푒푛푑 ], the time period

T of the corresponding frame from the LiDAR sensor 2 should satisfy the condition of

Equation (16).

푇 = 푚푖푛{ (푇푗−푠푡푎푟푡 − 푇푖−푠푡푎푟푡) ∪ (푇푗−푒푛푑 − 푇푖−푒푛푑)} (15)

Where, 푇푗−푠푡푎푟푡 is the start time of any frame 푗in the dataset collected by the other LiDAR sensors (second). 푇푗−푒푛푑 is the end time of any frame 푗in the dataset collected by the other

LiDAR sensors (second).

3.5 Data Integration After the coordinate system transformation and time synchronization steps, the data collected by multiple roadside LiDAR sensors during the same time period can be expressed in the ECEF coordinate system, but there are still some errors that cause the data to not be completely matched. There are two main errors in the previous steps. The first is the error caused by the measurement. When collect GPS data using GPS devices or Google

Earth, both will produce some measurement errors. For the data collection with GPS devices, the value of the reference point in the WGS 1984 coordinate system is based on the center of the GPS receiver, while its corresponding point in lidar data is the point on the surface of the receiver. As mentioned before, the measurement error will be larger when selecting the reference points from Google Earth due to it does not offer the elevation information for a specific point. The other error is caused by the calculation. In the process of data calculation, due to the choice of different accuracy, the calculation error will be generated. These errors cannot be overcome. To better match the data collected by multiple roadside LiDAR sensors, the data integration step should be applied.

The Iterative Closest Point (ICP) method is the widely used integration method for 3-D data. The principle of this method is that the reference point in the target dataset is kept fixed, while the other one in the source dataset matches it by transformation. But in the

LiDAR data point cloud used in this research, the system will generate more than 37,000

45 points each 0.1 second which is a huge task for normal ICP. On the other hand, the ICP method is usually used for the datasets in different coordinate systems. While in this research, the data collected from multiple LiDAR sensors has already been converted into the same coordinate system- the ECEF coordinate system. The specific part of data to be used as the target dataset and source dataset needs to be identified first. And to simplify the process, the iterative step is removed in this research.

There are four steps in this method, the details are as follows.

Step 1: Key points selection

Same as the reference points selection in the previous step, the key point dataset is in the same way: the poles installed at the intersection or on the road segments, the parked vehicles, corner of the buildings, corner of the road curves, and traffic signs within the

LiDAR detection range will be selected as the reference points. The key points for the same object are determined and store into two different dataset-target datasets Pt and source dataset Ps.

Step 2: Nearest point search

According to the distance formula between two points, find the corresponding point in the

Ps dataset for each point in Pt. The corresponding point in the Ps should have the shortest distance to the point in Pt. The nearest point method shows in Equation (16)

d=min d d = ( x − x )2 + ( y − y ) 2 + ( z − z ) 2 (16) j i i j i j i j i 

Where, d j is the shortest distance between two corresponding points i and j. di is the distance between the points i in the Ps and the fixed-point j in Pt.

Step 3: Transformation parameters calculation

For the two corresponding point datasets, two transformation parameters are needed: the rotation matrix R* and translation vector t * . The two parameters are calculated according to equation (17).

2 1 Ps R*, t *= arg min Ptii − ( R  Ps + t ) (17) Rt, Ps i=1

Step 4: Data conversion

Based on the transformation parameters and calculated in step 3, the data in the Ps will be converted into Pt.

3.6 Data Mapping To display the roadside LiDAR data on the GIS-based software, the integrated data in the

ECEF coordinate system needs to be transformed to the WGS 1984 coordinate system, which is a widely used geodetic coordinate system by the map software, including Google

Earth, Google Map, and Bing Map.

According to the characteristics of the earth, the data in the ECEF can be converted into

WGS 1984 using Equation (18):

Y   = arctan( )  X  Z+ e'23  b  sin    = arctan  (18) X2+ Y 2 − e 2 a cos 3   Z  H = −N ()1− e2  sin 

aZ Where,  = arctan. b+ X22 Y

N - Curvature radius of the ellipsoidal ring. e - First eccentricity of the ellipsoid. e' - Second eccentricity of the ellipsoid. a - Long radius of the ellipsoid. b - Short radius of the ellipsoid.

X- The x coordinate value of the point in the ECEF.

Y- The y coordinate value of the point in the ECEF.

Z- The z coordinate value of the point in the ECEF.

 - The latitude of the point.

 - The longitude of the point.

H- The elevation of the point.

CHAPTER 4. SENSITIVITY ANALYSIS

After the data mapping step, the LiDAR point cloud can be converted into a WGS-1984 coordinate system which then can be mapped into the GIS-based software. Mapping the

LiDAR data can promote the use of LiDAR sensors because it can make the results of

LiDAR data more intuitive on the real map, while other software can only display the three- dimensional effect of LiDAR data. For the mapping step, at least four reference points are needed. And in general, the more reference points, the more accurate the result. However, it takes more time and money to collect extra reference points, so the most reasonable number and distribution of reference points need to be determined to guide users to apply the integration and mapping method.

Two hundred thirty-three points shown in Figure 14 were collected at Blue Parking Lot of

UNR, Reno, NV, USA, by the Trimble R2 GPS device. Due to the size of the Trimble R2 is small enough, the farther it was from the sensor, the harder it was to be collected. Even the distance to the farthest point from the sensor was 100m in this data collection, and it is difficult to find the corresponding point from the lidar point cloud. When using the Trimble

R2 to collect reference points, these points should be located within 100 meters from the sensor. Based on the LiDAR sensor location, the distribution of the GPS points can be divided into 12 zones. The boundaries of each zone were shown in Figure 15. The radius of the inner circle is 12.5m, the radius of the outer circle is 25m, and the origin of the circle is where the LiDAR sensor is. Two perpendicular straight lines intersected at the center of the circles, dividing the entire detection area into twelve parts, and each part represented one zone. Based on the direction and distance, each zone's name can be defined, as shown

49 in Table 5. For example, there are three zones for northeast: northeast near zone, northeast middle zone, and northeast far zone. The detailed zone information is shown in Figure 15.

In the picture, the different color represents different reference points distribution zone.

Table 5 Distance and direction for each zone

Boundary Distance Direction Inside the inner circle Near Northeast Northwest Southeast Southwest Between the two circles Middle Northeast Northwest Southeast Southwest Outside of the outer circle Far Northeast Northwest Southeast Southwest

The influence of different distribution and numbers of the reference points on mapping is analyzed according to these points. For these GPS points, some of them were selected as the reference points, and the others were used to verify the accuracy of the results by calculating the offset between the measured GPS point A ( LatA, LonA) and the calculated

GPS point B ( LatB , LonB ) for the same point.

Figure 14 GPS points collected at Blue Parking Lot

Figure 15 Reference points distribution zone

The offset between the measured GPS point A ( LatA, LonA) and the calculated GPS point

B ( LatB , LonB ) can be calculated based on the Great Circle Distance Equation (19).

D = R arccos(sin( LatA )  sin( LatB ) + cos( LatA )  cos( LatB )  cos( LonA − LonB )) (19)

Where, R is the average radius of the earth which equals 6,371,004m, D is the offset between two points(m).

The great-circle distance is the shortest distance between two points on the surface of a sphere, measured along the sphere's surface. The distance between two points in Euclidean space is the length of a straight line between them, but there are no straight lines on the sphere. In spaces with curvature, straight lines are replaced by geodesics. Geodesics on the sphere are circles on the sphere whose centers coincide with the sphere's center and are

51 called great circles. The Earth is nearly spherical, so great-circle distance formulas give the distance between points on the Earth's surface correct to within about 0.5%.

4.1 Number of the Reference Points The reference points are crucial for the LiDAR data integration and mapping method, but it will take some time and money to collect them. In theory, the more reference points collected, the smaller the error of the measurement. However, the cost of time and money will also increase. When using GIS-based software for data collection, the surrounding environment also limits the number of reference points that can be collected. As mentioned before, the minimum number of reference points for LiDAR data integration and mapping is four, and when there are more than four reference points, the least square method will be applied to optimize the method. The most suitable number of reference points will be given in this part. The reference points were randomly selected from the GPS point cloud with the number from 4 to 80, and the rest points were used to calculate the offset. For a specific number of reference points type, there were ten groups of data analyzed, which means this number of reference points was randomly selected ten times. Then the average offsets were obtained for the different number of reference points, and the detailed information was shown in Figure 16. In this figure, the blue dots are the average offsets for each number of reference points, and the red line is the regression line which can be expressed as:

 9 4x 13 y =  5x (20) 0.138 13  x

Where, y is the average offset and x is the number of reference points.

0.6

0.5

0.4

0.3

0.2 Average Average offset(m)

0.1

0 0 10 20 30 40 50 60 70 80 90 Number of reference points

Figure 16 Offset change based on different number of reference points

Based on the regression function, when the number of the reference point equals 13, the offset is minimal, which equals 0.138m.

4.2 Distribution of the Reference Points The distribution of the reference points is shown in Table 5. Based on the distribution, there are eight different scenarios:

• Scenario1: all the reference points were selected from the same zones near the

sensor.

• Scenario2: the reference points were selected from different zones near the senor.

• Scenario3: all the reference points were selected from the same zones in the middle.

• Scenario4: the reference points were selected from different zones in the middle.

• Scenario5: all the reference points were selected from the same zones far from the

sensor.

• Scenario6: the reference points were selected from different zones far from the

senor.

• Scenario7: the reference points were selected from different zones in the same

direction.

• Scenario8: the reference points were selected from different zones in different

directions.

There were ten groups of data to analyze for each scenario, and in each group, 13 reference points were selected. The average offsets for each scenario are shown in Figure 17. For the reference points chosen from the same zone, the offset of scenario1 equals scenario 3 and smaller than scenario 5, which means when the reference point's available collection area is in the same direction, the location within 25 meters from the sensor should be the suitable place. By comparing scenario 1 and 2, scenario 3 and 4, and scenario 5 and 6, scattered reference points get more minor errors than clustered reference points. For scattered reference points, the farther away from the sensor, the smaller the error is.

0.7

0.6

0.5

0.4

0.3

Average Average offsett(m) 0.2

0.1

0 Scenario1 Scenario2 Scenario3 Scenario4 Scenario5 Scenario6 Scenario7 Scenario8 Different scenarios

Figure 17 The average offset for different scenarios

In conclusion, when collecting reference points, if there is no location restriction, the suitable place is distributed around the sensor. The distance is greater than 25m or scattered to varying distances in all directions of the sensor. When there is no enough place to collect reference points in all directions, the suitable distance to collect the reference points is within 25 meters.

CHAPTER 5. CASE STUDY

5.1 Data Mapping Result with GPS Devices

The developed method for LiDAR data mapping was evaluated with the data collected at the intersection of N McCarran Blvd and Evans Ave in Reno, Nevada, shown in Figure 18.

There are two VLP-32c LiDAR sensors installed at the northeast and southwest corners of the intersection. The heights of the two LiDAR sensors are 2.74 m and 2.83 m. In the figure below, the yellow marks are the positions where the LiDAR sensors are located. For each

LiDAR sensor, 13 reference points were collected within 25 m. The red points are the marks for the reference points of LiDAR installed in the northeast corner, and the green dots are the position where the reference points are collected under the southwest corner

LiDAR sensors.

Figure 18 Data collection site

Figure 19(a) shows the data mapping result for one frame of raw data collected by the

LiDAR sensor installed at the southwest corner, and Figure 19(b) shows the data mapping result for one frame of raw data collected by the LiDAR sensor installed at the northeast corner.

(a) Data mapping result for the LiDAR sensor installed at the southwest corner

(b) Data mapping result for the LiDAR sensor installed at the northeast corner Figure 19 Data mapping result with GPS devices

5.2 Data Mapping Result without GPS Devices

The same dataset is used to evaluate the LiDAR data mapping method without GPS devices. The exact number of reference points are selected from Google Earth; at this intersection, all these reference points are selected from the traffic poles shown in Figure

20.

Figure 20 Reference points collected by Google Earth Figure 21(a) shows the data mapping result for one frame of raw data collected by the

LiDAR sensor installed at the southwest corner, and Figure 21(b) shows the data mapping result for one frame of raw data collected by the LiDAR sensor installed at the northeast corner.

(a) Data mapping result for the LiDAR sensor installed at the southwest corner

(b) Data mapping result for the LiDAR sensor installed at the northeast corner Figure 21 Data mapping result without GPS devices

The offset between the two methods is calculated according to 1 frame data. The average offset for the data collected from the southwest sensor is 2.21m (the total number of the

LiDAR point is 37,832). The average offset for the data collected from the northeast sensor is 2.53m (the total number of the LiDAR point is 37,509). The offset distribution for the southwest sensor is shown in Figure 22. In the picture, the x-axis and y-axis represent the position of the point ((0,0) represents the sensor location), and the z-axis represents the offset. From the picture, the farther the point is from the sensor, the greater the offset. This is related to the selected position of the reference point. Since the LiDAR sensor is usually installed next to the road, the offset of the two methods for the road users traveling on the road is smaller than the average.

Figure 22 Offset distribution Since the precise latitude and longitude information of the static objects such as trees, buildings, and road edges around the LiDAR cannot be obtained, the algorithm can only be judged visually. This paper selects the data of two LiDAR sensors simultaneously to

61 transform and display the results on Google Earth. The result is shown in Figure 21. Based on the LiDAR data visualization in Google Earth, the boundaries of buildings and roads are well matched. And the same objects collected by different LiDAR sensors can be matched together. In Figure 23, the red circles mark the vehicle data, all vehicles are accurately matched to the corresponding lanes, and the vehicle data of the two LiDAR sensors can match each other.

Figure 23 Result of two LiDAR sensors

This study equipped the high-precision GPS equipment to the car for dynamic data, as shown in Figure 24. When the car passes the intersection with the installed LiDAR sensors, the longitude, latitude, and height information will be collected by the device, while when the car is within the LIDAR measurable range, the location information of the vehicle will be collected automatically. Based on CATER’s work (4), the vehicle's trajectory can be extracted, and the extracted trajectory is still represented by the original LiDAR point cloud

62 data, which can be converted into longitude, latitude, and elevation information using the method proposed in this research. The result shows in Figure 25.

Figure 24 Vehicle equipped with GPS device

In Figure 25, the red points were the points collected by the GPS device, which collected every second automatically while the car was driving. The green points are the trajectory of this data acquisition vehicle under these two installed LiDAR sensors. As can be seen in the picture below, the trajectory collected by the GPS device can match the trajectory obtained by the LiDAR sensors. And the max location error is less than 0.1m compared to the actual location.

Figure 25 Dynamic vehicle data matching results

5.3 Data Integration Result

The data integration method proposed in this research is through transforming the data in the Cartesian coordinate system to the data in the Geodetic Cartesian Coordinate System with the help of the GPS device. When collecting the reference points using a GPS device or map software, measurement errors are inevitable. To reduce the measurement error, 13 reference points were collected for each roadside LiDAR sensor. The LiDAR data collected at two sites in Reno, Nevada, were used to evaluate this developed procedure. The two sites are shown in Figure 26; the first site (b) is the blue parking lot of UNR, while the other site (c) is the intersection of McCarran & Evans in Reno.

(a) Sites location

(b) UNR Parking Lot (c) McCarran & Evans

Figure 26 Data collection sites

At the first data collection site, 4 VLP-32C LiDAR sensors were installed on the tripods at a distance of 2.43 m. above the ground. The positions of these four sensors made up a quad, and four cars (red ones) in the detection zones, three of which were parked in the parking space, and the other one ran along the black dotted line in the picture. The data of these four vehicles were used to verify the algorithm. Different color points in Figure 26

(b) mean the reference points for different sensors, and there were 13 reference points collected for each roadside LiDAR sensor. After the background filtering step, the processed data showed in Figure 27. In Figure 27 (a), different color points are processed

65 by different LiDAR datasets, and only the vehicles’ points are left without background points. After object clustering steps, the same object's points collected by various sensors were clustered together distinguished by different colors, shown in Figure 27 (b). The final mapping result showed in Figure 27 (c); all the points for the same vehicle were integrated and mapped precisely where they were. The number of LiDAR points for each vehicle collected by each LiDAR sensor is shown in Table 6; after the integration method, the number of points for each vehicle has increased significantly.

Table 6 Number of LiDAR points for each vehicle

Vehicle ID Sensor 1 Sensor 2 Sensor3 Sensor 4 Integration 1 284 261 715 223 1483 2 75 334 147 106 662 3 129 769 226 146 1270 4 98 647 192 269 1206 The measured length and width for the vehicles and calculated length and width were compared then, and the result shows in Table 7.

Table 7 Comparison of vehicles’ parameters

Vehicle True True Sensor 1 Sensor 2 Sensor 3 Sensor 4 Integration ID Length Width L W L W L W L W L W 1 4.87 1.83 4.31 1.82 3.71 1.65 3.69 1.73 4.53 1.62 4.83 1.87 2 4.47 1.80 4.25 1.48 4.08 1.54 4.15 1.52 4.09 1.60 4.62 1.72 3 4.85 1.83 3.68 1.78 4.11 1.06 4.19 1.46 4.03 1.55 4.50 1.82 4 5.56 2.23 4.96 1.94 5.43 1.84 5.05 2.19 5.14 2.21 5.65 2.25 The Average Relative Error (훿) of the vehicles’ parameters measured by each sensor and the values calculated by the integration method are shown in Table 8. The result shows that the integrated data has the smallest Average Relative Error in length and width measurement.

훿 = 퐴푣푔(훥/퐿) × 100% (21)

Where, 훥is the absolute error and 퐿is the true value.

Table 8 Average relative error

Sensor1 Sensor2 Sensor3 Sensor4 Integration Length 12.83% 12.53% 13.54% 9.98% 3.25% Width 8.51% 20.96% 10.76% 9.69% 2.02%

(a)Background filtering result

(b)Object clustering result

(c)Data mapping result

Figure 27 Performance of data integration method

At the second data collection site (Figure 26 (c)), two LiDAR sensors were installed on the poles at the northeast and southwest corners of the intersection, respectively. These two sensors continuously collect traffic data from April 2019, so the trajectories can be obtained based on Sun’s method. 30 mins data collected from 5:30 am to 6:00 am on April 24 were selected to get the trajectories information. The volume data for this time period is shown in Table 9. Before the integration method applied, the trajectory file processed from the data collected by the northeast sensor is shown in Figure 28(a), the trajectory field related to the southwest sensor is shown in Figure 28(b), while after the integration of fixed-

LiDAR sensing data in a global coordinate method, the combined trajectory result shows in Figure 28(c). By comparing these results, the detection range after the integration method is wider than using individual sensors.

Table 9 Volume for McCarran & Evans

Northbound Westbound Southbound Eastbound Lef Rig Lef Rig Lef Rig Lef Rig Directi t Throu ht t Throu ht t Throu ht t Throu ht on Tur gh Tur Tur gh Tur Tur gh Tur Tur gh Tur n n n n n n n n Volum e 36 0 10 82 136 4 46 12 16 10 118 60 (veh/h)

(a) Trajectories from northeast sensor (b) Trajectories from the southwest sensor

Figure 28 Total trajectories for all road users in 30 mins

Six vehicles were selected to evaluate the impact of the algorithm on an individual trajectory. In Figure 29(a), the blue points were the trajectories processed from the data collected by the northeast sensor, while the yellow ones mean the trajectories processed from the data collected by the southwest sensor. Different sensors can get information in different areas except for the same detection range. However, if the trajectory files obtained by independent sensors are directly mapped on Google Earth, there will be an offset in its

69 trajectory even for the same vehicle. The trajectory file for the same six vehicles when the algorithm is used is shown in Figure 29(b); since the two sensors' data have been integrated before the data mapping step, each vehicle can get a complete trajectory. What’s more, the integrated trajectory has more data information inside than the same trajectories processed by individual sensors.

(a)Before the integration method applied

(b)After the integration method applied

Figure 29 Trajectories for 6 vehicles

CHAPTER 6. APPLICATION OF IMPROVED HRMTD

By applying this method to the existing procedures of extracting HRMTD based on roadside LiDAR, the expanded all-traffic trajectory data with longitude, latitude, and elevation information can be available. Other than benefiting the CV system, this data can also serve other transportation applications. This part provides an application using the improved HRMTD to extract lane and crosswalk-based multimodal traffic volumes.

6.1 Introduction

The traffic volume, including lane-based traffic volume and pedestrian (bicycle) crossing volume, is important for traffic signal design, traffic safety, and traffic management.

Traditional methods mainly depend on fixed loop detectors and cameras, and there are many models produced based on point detector data, including linear model (21), nonlinear model (69), and other depth learning models represented by artificial neural networks (70).

These models can give us a basic solution with traditional data, but the shortcomings are still obvious. The loop detector only can provide limited information for road users. Also, it cannot track the vehicles’ trajectory or count the pedestrian and bicycle volume. Even the camera can give more information than the loop detectors, but it is easily affected by light and the environment. With the latest development of technology in vehicle positioning and detection, probe vehicle and high-resolution trajectory data have received increasing attention. The trajectory provided by the probe vehicle can offer rich and timely information on the traffic arrival and departure processes at intersections and road segments, which can provide another way to estimate the traffic performance combined with signal timing. Anuar (71) recently utilized the probe vehicle trajectory data to estimate

71 the freeway traffic volume based on shockwave theory. By identifying the shockwave, which is the boundary between free-flow and congestion, flow and speed can be calculated and predicted on the freeway, but the method does not apply to the intersection with signal control. For the signalized intersection, Zheng (72) developed an approach to estimate traffic volume signalized intersections using GPS trajectory data under low penetration rates. In the research, the estimation problem was formulated as a maximum likelihood problem that can be solved by expectation maximization. However, the method is simple and basic, and it is hard to get a precisely result. In order to improve the method used to estimate traffic performance based on probe trajectories, Li (73) proposed a cycle-by-cycle queue length estimation method by solely using probe data without the assumptions that signal timings, arrival patterns, and penetration rates are known, which was usually used in other methods. On the basis of this method, Yao (74) presents a generic hybrid method that combined a probabilistic model and shockwave theory to estimate the cycle-based flow based on limited captured trajectories, especially under a low penetration rate. In the method, first, the researchers divided the cycle-based flow into stopped vehicles and non- stopped vehicles. Then the trajectories of the stopped vehicles were used to reconstruct the queuing, and the dissipate shockwaves, like mentioned before, which are then used to calculate the progression ratio provided by the HCM 2010 to cover various arrival patterns as well as prescribe a limit to the headway of the non-stopped flow. At last, the cycle-based volume is obtained by a maximum likelihood estimation using an expectation- maximization procedure. All these methods are based on certain assumptions and estimates and require probe-connected vehicles to offer the trajectories. But these methods cannot be applied to pedestrians and bicycles. On the other hand, if the traffic doesn’t follow the

72 assumptions, for example, the traffic on the freeway or there is congestion, that will be a great challenge to use these methods.

With the latest innovative use of LiDAR sensors, road user’s trajectory data obtained from roadside LiDAR sensors is becoming more attractive for traffic performance evaluation.

However, there are still many errors in the trajectory data due to the occlusion issue. To get the more accurate lane-based and crosswalk-based traffic counts, this research provides an automatically best detection zone searching method. In this method, the input is the integrated and mapped trajectory data processed by the previous steps. The start and end of the searching point should be determined first. Then a traversal search step is applied to find the detection zone for each lane or each crosswalk. The threshold learning step is used to determine when to stop the traversal search. A whole day of data collected in the real world is used to verify the method and compared with the manually counted traffic volume, and the result shows that the accuracy of this traffic volume extraction method reaches 95% or higher. This research will significantly change how traffic agencies assessing road network performance and add great traffic values to the existing probe-vehicle data and crowd-resourced data.

6.2 Methodology

This section introduces the proposed method to evaluate lane-based and crosswalk-based volume according to the integrated trajectories by the previous study. This method has three main steps: start and endpoint selection, detection zone selection, and threshold learning. The second step is the primary step of the method, which can be divided into four sub-steps: location searching, data comparison, size searching, and best zone selection.

Start and endpoint selection

To calculate the volume, one detection zone should be set along the traffic lane like the loop detector. In theory, the detection zone should be put on upstream of the intersection without merging traffic from other direction, but due to the detection range of the LiDAR sensor and characteristic of the road segment or intersection, a suitable area A where can put the detection zone should be determined first. The start and end points refer to the boundary of area A, and the width of area A equals the lane width.

Figure 30 Diagram of intersection installed with LiDAR

A diagram of the intersection installed with the LiDAR sensor is shown in Figure 30. In the picture, the LiDAR is installed at the northwest corner of the intersection, and the inside

74 of the blue circle is the detection range of the sensor; there are three types of conflict points: crossing point (blue), diverging point (yellow), and merging point (purple). For the southbound of the intersection, right turn vehicles share the same lane with though vehicles, while for the westbound, straight traffic vehicles and left-turn vehicles diverge as they approach the intersection, but they travel in the same lane before the diverging point. After crossing the intersection, vehicles from different directions will merge. To get each lane’s volume in each direction, the detection zone should be set before the merging point on the departure lane. On the other hand, area A should be set after the diverging point (the point where vehicles traveling in two directions sharing the same lane diverging). Consider the detection range of the LiDAR sensor, the start and endpoint of area A is defined as:

• The start point is the diverging point.

• The start point is when the vehicle enters the sensor's detection range if there

is no diverging point within the range.

• The endpoint is the first crossing point in the direction of vehicle travel.

• The endpoint is the merging point if there is no crossing point in this lane.

• The endpoint is when the vehicle exits the detection range if there is no

crossing point or merging point.

For the pedestrian and bicycle crossing volume, area A equals the crosswalk area, which means the start point and endpoint are the crosswalk boundaries.

Detection zone selection

Due to the LiDAR sensor's limitation, some vehicles will be blocked on some road segments; the trajectories for these vehicles then will be broken into several small parts.

On the other hand, some noise points will be mistakenly recognized as road users.

Therefore, at different locations in area A, various sizes of detection zones will give different volume results. An automatic traversal search step is applied to reduce the error and get the closest result to the true value. Traversal search is the critical step of the lane- based volume calculation method, and there are two major parts in this step: size searching and location searching, as shown in Figure 31.

(a)Location searching (b) size searching

Figure 31 Traversal search

Step 1 is the location searching, starting from the start point recognized by the previous step with the length equals 0.1 meters and the width equals the land width. The searching direction is from the start point to the endpoint of area A and puts a detection zone every

0.1 meters. The total number of the detection zone can be calculated based on Equation

(1).

Nl = INT ( L l ) (22)

Where, 푁푙is the number of the detection zones, 퐿 is the length of area A, 푙 is the length of the detection zone.

For each detection zone under length 푙, the volume for each zone is counting the number of trajectories in this zone during time period t:

푉푙(푖, 푡) = 퐶푂푈푁푇(푡푟푎푗푒푐푡푟푖푒푠(푡)) (23)

Step 2 is to compare 푉푙푖 with the true value 푉푡푟푢푒 and the result can be obtained from

Equation (25).

1, 푖푓 푉푙(푖, 푡) >= 푉푡푟푢푒(푡) 휆푙(푖, 푡) = { (24) 0, 푖푓 푉푙(푖, 푡) < 푉푡푟푢푒(푡)

Where, the 푉푙(푖, 푡) is the calculated volume for the detection zone 푖 during the time period t, and the 푉푡푟푢푒(푡) is the true value manually counted during time period 푡.

Step 3 is to determine whether the traversal search stops. The number of the detection zones where the volume is not less than the true volume can be calculated.

휆 = {(푖, 푡)|휆 (푖, 푡) = 1} { 푙 푙 (25) 휙푙 = 푐푎푟푑(휆푙)

When 휙푙reaches a specific value Z, the traversal search stops. The value Z is obtained from the threshold learning step. If 휙푙 < 푍, the size searching will be applied, let 푙 = 푙 + 0.5, then back to step 1, while if 휙푙 >= 푍 , end the traversal search.

Step 4 is the best detection zone selection. The mean average percentage error (MAPE) of the volume is selected as the index to determine the best detection zone among all the zones. Zone B with the smallest MAPE is the detection zone for this lane.

1 푉푖−푉푡푟푢푒 푀퐴푃퐸 = ∑푁 × 100% (26) 푁 푉푡푟푢푒

Where, N is the number of zones, 푉푖is the volume for the detection zone푖, 푉푡푟푢푒is the true value.

Threshold learning

The value Z is calculated in this step. In general, the smaller the value of Z, the faster the data processing, but if Z is too small, it may exclude the optimal solution. A Threshold

Learning step is used to calculate the Z. The greater the value of Z, the greater the value of MAPE for the best detection zone, but the growth rate of MAPE will become slower and slower. Combining data processing speed and accuracy requirements of results, Z is determined by

푀퐴푃퐸 −푀퐴푃퐸 푆푙표푝푒 = 푖 푖−1 (27) 푍푖−푍푖−1

Where, 푀퐴푃퐸푖 is the MAPE for the best detection zone when 푍 = 푍푖.

When the slope first become 0 or negative, the value of 푍푖 is used as the 푍.

6.3 Performance Evaluation

Due to the different traffic patterns, the proposed algorithm is evaluated by two different cases. The data collected at the first site is used to evaluate the method for the lane-based volume, and the second one is used to test the method for the pedestrian and bicycle volume. One LiDAR sensor was installed in the southwest corner of the McCarran & Evans intersection, Reno, Nevada, the USA, at the height of 3 m, as shown in Figure 32(a). This sensor can detect eastbound and northbound vehicles. There are 3 through lanes, one left turn lane, and one right-turn lane on the eastbound while there is one left turn lane, one through lane, and one right-turn lane on the northbound. Figure 24(a) shows the blue points are the trajectories and the yellow rectangles are the volume detection zones. The researchers manually counted the lane-based volume for a whole day (2019-4-24) every 30 minutes. Therefore, there is a total of 384 traffic volume data (48 for each lane) available

78 for this intersection. Among these data, randomly selected 115 data (30% of the total data) as the training dataset to train the algorithm, the other is used as the test dataset to verify the result. Of the 115 randomly selected data, 11 are the eastbound left-turn data, 16 are the first though lane (close to the left turn lane) of the eastbound, 17 are the second through lane (middle though lane) of the eastbound, 14 are the third though lane of the eastbound,

9 are the right turn lane of the eastbound, 17 are the left turn lane of the northbound, 15 are the though lane of the northbound, and 16 are the right turn lane of the northbound. The second site is Greenvalley & Amargosa Trail, Henderson, NV, the USA showed in Figure

32(b). The blue points are the vehicles’ trajectories, the grey points are the pedestrians/bicycles’ trajectories, and the yellow rectangles are the volume detection zones. One LiDAR sensor was installed at the median of the road near the crosswalk, and the crosswalk is frequently used during school time. Two days (9/16/2019~9/17/2019) data collected during school time were selected. The pedestrian/bicycle volume was counted every 5 minutes, a total of 96 data were available.

(a) Site A

(b) Site B

Figure 32 Data collection site

Threshold learning

The value Z should be first determined based on the training dataset. The value of Z should be a positive integer. As the value of z changes from 1 to 100, the mean average percentage error (MAPE) of the test data changes, as shown in Figure 33. According to equation (1.6),

80 the value of Z equals 8 for the lane-based volume calculation. This means for this intersection when there are eight volumes calculated from the detection zone for each lane that is no less than the true values, the traversal search stops. The value of Z is 6 for the pedestrian/bicycle volume calculation.

Figure 33 MAPE change along Z

Detection zone setting

After the value of Z is available, each lane's best detection zone can be determined by the method proposed in this research, and the detection zone for each lane is shown in Figure

32. The yellow rectangles are the determined zones. The result can be concluded that the size and location of each lane's detection zone vary due to different distances to the sensor.

Usually, the farther the lane is from the LiDAR sensor, the larger its detection zone. For the same lane, the best detection range is closest to the sensor.

Volume calculation

The volume for the test dataset is calculated and compared with the true values, and the results show in Table 10 and Table 11. The average absolute error (AAE) and the mean

81 average percentage error are selected to verify the result based on Equation (5) and

Equation (28).

∑푛 |푋 −퐿 | 퐴퐴퐸 = 푖=1 푖 푖 (28) 푛

Where, X is the calculated volume, L is the counted volume.

Table 10 Lane-based volume evaluation

Calculated Counted average Direction Lane average volume AAE MAPE volume(veh/h) (veh/h) Left turn lane 25 26 1.00 86.41% Left-through 245 244 1.56 98.36% lane Middle- 259 259 0.06 97.99% Eastbound through lane Right-through 45 46 1.06 94.20% lane Right turn 183 183 0.06 98.12% lane Left turn lane 183 185 1.50 97.76% Though lane 33 33 0.12 91.82% Northbound Right turn 165 165 0.01 98.99% lane The volume is rounded to an integer. Table 11 Pedestrian/bicycle volume evaluation

Counted average Calculated average Direction AAE MAPE volume(ped/h) volume (ped/h) West to East 13 14 1.75 91.35% East to West 6 5 1.06 88.24% The volume is rounded to an integer.

From the result, when the lane-based traffic volume is large enough (greater than

100veh/h), the MAPE is greater than 95%, while when the lane-based traffic volume is less than 100 veh/h, the AAE is around 1, which means there is an error of one vehicle between the true traffic volume and the volume obtained by the proposed method every 30 minutes on average.

CHAPTER 7. CONCLUSION

This research developed an automatic method to map the data collected by roadside LiDAR sensors. There are seven main steps in this method: reference point collection, reference point matching, transformation matrix calculation, and data mapping.

In this method, there were different ways to collect the reference points: collect reference points from GIS-based software and collect them using a high-precision GPS device. These two methods can be applied to a different conditions for data collection.

The number and the distribution of the reference points were then analyzed. Based on the study, the best number of the reference points and what’s the distribution of these points were identified. These are can be used as recommendations for the users to map the roadside LiDAR point cloud.

This research also proposed a data integration method for multiple roadside LiDAR sensors. This method can be included in the mapping method. After transformation matrix calculation, all the data collected by multiple roadside LiDAR sensors can be converted into ECEF coordinate system. Based on the time synchronization, the data collected at the same time by different sensors can be selected. The simplified ICP method then was applied to integrate the data.

By applying these methods to the existing procedures of extracting HRMTD based on roadside LiDAR, the expanded all-traffic trajectory data with longitude, latitude, and elevation information can be available. Other than benefiting the CV system, this data can also serve other transportation applications. This research provides an application using the

HRMTD obtained from roadside LiDAR data to extract lane and crosswalk-based multimodal traffic volumes.

Future research will focus on expanding the application of the improved HRMTD. In addition to server the CV system, the improved HRMTD also can be used for near-crash analysis, traffic performance evaluation, adaptive traffic signal control, and automatic pedestrian/wildlife-crossing warning systems.

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