Recently, to improve safety and convenience in driving, numerous sensors are mounted on cars to operate advanced driver assistant systems. Among various sensors, vehicle dynamic sensors can measure the vehicle motions such as speed and rotational angular speed for dead reckoning, which can be applied to develop a land vehicle positioning system to overcome the weaknesses of the GNSS technique. In this paper, three land vehicle positioning algorithms that integrate GNSS with vehicle dynamic sensors including a wheel speed sensor (WSS), a yaw rate sensor (YRS), and a steering angle sensor (SAS) are implemented, and then a performance evaluation was conducted during GNSS outages. Using a loosely coupled strategy, three integration algorithms are designed, namely, GNSS/WSS, GNSS/WSS/YRS, and GNSS/WSS/YRS/SAS. The performance of the three types of integration algorithm is evaluated based on two data sets. The results indicate that both the GNSS/WSS/YRS integration and the GNSS/WSS/YRS/SAS integration could estimate the horizontal position with meterlevel accuracy during 30second GNSS outages. However, the GNSS/WSS integration would provide an unstable navigation solution during GNSS outages due to the accuracy limitation of the computed yaw rate using WSS.
The vehicle positioning technique is a key component in car navigation to find and guide routes. Typical car navigation uses a lowcost GNSS (Global Navigation Satellite Systems) receiver that can provide the position and velocity of a vehicle with an accuracy that is appropriate for navigation. However, the major drawback of the GNSS based positioning technique is that the performance depends on the satellite signal reception environment. In particular, cars often move near buildings and tunnels where the GNSS signal environment is poor, and thus the GNSS based positioning technique cannot guarantee continuity and reliability of positioning [
Recently, several ADAS (Advanced Driver Assistance Systems) such as ABS (Antilock Brake System), ESC (Electronic Stability Control), and ACC (Adaptive Cruise Control) have been applied to most passenger cars for driver and passenger safety [
In this study, in order to overcome the limitations of the GNSS based positioning technique, three land vehicle positioning algorithms that integrate GNSS with vehicle dynamic sensors (WSS, YRS, and SAS) are implemented, and the performance evaluation was conducted in GNSS signal blockage situations. A description of the integration strategies as well as mathematical models of three types of the GNSS/vehicle dynamic sensors is presented in Section
DR is the process of estimating the current position based on the previous position using the velocity and the traveling direction measured by DR sensors. To calculate the horizontal position of the vehicle based on DR, the vehicle’s velocity and yaw information are required. To apply vehicle dynamic sensors for the twodimensional DR navigation, the relationship of the vehicle dynamic sensors and navigation information is summarized in the Table
Relationship of the vehicle dynamic sensors and navigation information for DR.
Sensor name  Velocity  Yaw rate  Others 

Wheel speed sensor (WSS)  Directly  Derived from the differential of left and right wheel speed  — 
Steering angle sensor (SAS)  —  Derived from kinematic model  Can estimate the side slip by kinematic relationship 
Yaw rate sensor (YRS)  Directly 
To implement a twodimensional DR navigation based on vehicle dynamic sensors, three different combination strategies are designed to ensure that the vehicle dynamic sensors’ information is not duplicated. The strategies for twodimensional DR navigation based on vehicle dynamic sensors are summarized in Table
Description of combination strategies of vehicle dynamic sensors for DR.
Combination strategies  Description 

WSS  (i) Nonholonomic constraints are applied in lateral direction 


WSS/YRS  (i) Nonholonomic constraints are applied in lateral direction 


WSS/YRS/SAS  (i) The side slip angle is computed by SAS and side slip ratio 
In this study, three integration algorithms are proposed by integrating GNSS and a twodimensional DR navigation based on combination strategies of vehicle dynamic sensors using a loosely coupled mode. In addition, three integration algorithms are implemented through the extended Kalman filter. The output of integration algorithm rate is set to 50 Hz. The GNSS measurements are the position and the velocity calculated from the C/A code and the Doppler measurements at a GNSS receiver. The GNSS measurement update rate is set to 1 Hz.
A block diagram of the GNSS/WSS integration algorithm is shown in Figure
Block diagram of GNSS/WSS integration algorithm.
To define the velocity in the body frame using the vehicle’s speed, we assume that the center of the body frame is set to the center of the rear wheel axle, the vehicle drives on a flat road, and no wheel slip occurs. In addition, assuming that the direction of the vehicle’s speed at the rear axle is equal to the longitudinal axis of the body frame, the velocities in the body frame are defined as follows:
When a vehicle turns, the left and right wheel speeds are different. The speed measured by the individual WSS varies from along track while the vehicle is turning [
The yaw angle of the vehicle could be computed by numerical integration using the yaw at the previous time and the yaw rate, which is written as follows:
The velocities in the navigation frame could be transformed by using
In EKFbased GNSS/WSS integration, the state vector of the navigation error is composed of the latitude and longitude error, the north and east velocity error, and the yaw error. The state vector of the sensor error is composed of the average and the difference of the left and right WSS scale factor, defined as random constants. The white noise vector includes the white noise of WSS derived vehicle speed and the white noise of WSS derived yaw rate. The dynamic model for the GNSS/WSS integration is given in
The measurement model is generally expressed as follows:
In this study, the GNSS measurement vector consists of difference between the latitude, the longitude, the north velocity, and the east velocity estimated from DR based on vehicle dynamic sensors and GNSS receiver, as shown below:
The design matrix and the variancecovariance matrix for GNSS measurements are shown, respectively, as follows:
Figure
Block diagram of GNSS/WSS/YRS integration algorithm.
Comparing the GNSS/WSS integration, the GNSS/WSS/YRS integration performs not only the GNSS measurement update but also the ZIHR (Zero Integrated Heading Rate) measurement update [
The design matrix and the variancecovariance matrix for ZIHR are shown, respectively, as follows:
Figure
Block diagram of GNSS/WSS/YRS/SAS integration algorithm.
Considering the side slip angle, the velocities in the body frame are defined as follows:
The measurement vector and the variancecovariance matrix for both the GNSS measurement model and the ZIHR measurement model are the same as that of GNSS/WSS/YRS integration. The design matrices for measurement models in the GNSS/WSS/YRS/SAS integration are expressed as follows:
The test vehicle (Figure
Specifications of vehicle dynamic sensors.
Vehicle dynamic sensor  Output range  Resolution  Output rate 

Wheel speed sensor  0~511.75 km/h  0.125 km/h  50 Hz 
Yaw rate sensor  −40.95~40.95 deg/s  0.01 deg/s  100 Hz 
Steering angle sensor  −3276.8~3276.6 deg  0.1 deg  100 Hz 
Test vehicle.
Two trajectories were used in the performance evaluation of the three GNSS/vehicle dynamic sensors integration algorithms during GNSS outages. An experiment for two trajectories data acquisition was conducted in the Daegu Technopolis area, Korea. These trajectories include various driving circumstances encountered during typical driving on urban roads with frequent stops, acceleration, deceleration, and speed bumps. However, since two trajectories were set in different paths in the same area, the two trajectories data were different in vehicle motion and driving condition. To compare the performance of three GNSS/Vehicle dynamic sensors integration algorithms during GNSS outages, fifteen GNSS outages of 30 seconds were simulated in each trajectory. The simulated GNSS outages covered a wide range of vehicle dynamics such as straight portions, turns, slopes, high speed, slow speeds, and jumping.
Figure
The first trajectory (red line: simulated GNSS outage).
Velocity and attitude of the first trajectory (red line: simulated GNSS outage).
Velocity in body frame
Attitude
First, the drift error of the navigation solution during GNSS outages was analyzed in accordance with the integration strategies. Table
Average RMS error of horizontal position during GNSS outages for first trajectory.
Integration strategies  Average of RMS error of horizontal position during GNSS outages [m]  

First epoch  Last epoch  Difference (last − first)  
GNSS/WSS  2.03  9.16  7.13 
GNSS/WSS/YRS  1.77  7.18  5.41 
GNSS/WSS/YRS/SAS  1.75  6.09  4.34 
Average RMS error of horizontal velocity during GNSS outages for first trajectory.
Integration strategies  Average of RMS error of horizontal velocity during GNSS outages [m/s]  

First epoch  Last epoch  Difference (last − first)  
GNSS/WSS  0.25  0.43  0.18 
GNSS/WSS/YRS  0.22  0.28  0.06 
GNSS/WSS/YRS/SAS  0.22  0.26  0.04 
Average RMS error of yaw during GNSS outages for first trajectory.
Integration strategies  Average of RMS error of yaw during GNSS outages [deg]  

First epoch  Last epoch  Difference (last − first)  
GNSS/WSS  1.07  2.61  1.54 
GNSS/WSS/YRS  0.74  1.74  1.00 
GNSS/WSS/YRS/SAS  0.60  1.41  0.81 
The maximum horizontal position error values during the fifteen outages are presented in Figure
Cumulative relative frequency table of maximum horizontal position error for GNSS outages of first trajectory.
Integration strategies  Maximum horizontal position error  

≤5 m  ≤10 m  
GNSS/WSS  27% (4 out of total 15 outages)  87% (13 out of total 15 outages) 
GNSS/WSS/YRS  33% (5 out of total 15 outages)  93% (14 out of total 15 outages) 
GNSS/WSS/YRS/SAS  53% (8 out of total 15 outages)  93% (14 out of total 15 outages) 
Maximum horizontal position error for GNSS outages of first trajectory.
Details of the horizontal position error, the longitudinal velocity error, and the yaw error during GNSS outages F.
The test data for the second trajectory were acquired by driving a different path of 15.6 km for 39 min. The GNSS outages were selected by the same criteria. Figure
The second trajectory (red line: simulated GNSS outage).
Velocity and attitude of the first trajectory (red line: simulated GNSS outage).
Velocity in body frame
Attitude
Table
Average RMS error of horizontal position during GNSS outages for second trajectory.
Integration strategies  Average of RMS error of horizontal position during GNSS outages [m]  

First epoch  Last epoch  Difference (last − first)  
GNSS/WSS  1.91  15.54  13.62 
GNSS/WSS/YRS  1.65  5.86  4.22 
GNSS/WSS/YRS/SAS  1.64  5.57  3.93 
Average RMS error of horizontal velocity during GNSS outages for second trajectory.
Integration strategies  Average of RMS error of horizontal velocity during GNSS outages [m/s]  

First epoch  Last epoch  Difference (last − first)  
GNSS/WSS  0.16  0.97  0.81 
GNSS/WSS/YRS  0.12  0.32  0.20 
GNSS/WSS/YRS/SAS  0.12  0.28  0.17 
Average RMS error of yaw during GNSS outages for second trajectory.
Integration strategies  Average of RMS error of yaw during GNSS outages [deg]  

First epoch  Last epoch  Difference (last − first)  
GNSS/WSS  0.52  5.75  5.23 
GNSS/WSS/YRS  0.36  2.88  2.52 
GNSS/WSS/YRS/SAS  0.34  2.80  2.46 
Figure
Cumulative relative frequency table of maximum horizontal position error for GNSS outages of second trajectory.
Integration strategies  Maximum horizontal position error  

≤5 m  ≤10 m  
GNSS/WSS  27% (4 out of total 15 outages)  60% (9 out of total 15 outages) 
GNSS/WSS/YRS  53% (8 out of total 15 outages)  93% (14 out of total 15 outages) 
GNSS/WSS/YRS/SAS  67% (10 out of total 15 outages)  93% (14 out of total 15 outages) 
Maximum horizontal position error for GNSS outages of second trajectory.
This study presents the performance evaluation of a land vehicle positioning system encompassing GNSS combined with a twodimensional DR based on vehicle dynamic sensors. To develop GNSS/vehicle dynamic sensor based positioning algorithms, vehicle dynamic sensors used WSS, YRS, and SAS, which were already installed in the test vehicle. Three twodimensional DR mechanisms were designed to ensure that the vehicle dynamic sensors’ information is not duplicated. The GNSS/vehicle dynamic sensors integrations were implemented by EKF through a loosely coupled mode. The GNSS measurement are the position and the velocity calculated using the C/A code and the Doppler measurements from GPS and GLONASS at a GNSS receiver. The developed algorithms were tested on two trajectories acquired in various driving circumstances. A performance evaluation was conducted in fifteen simulated GNSS outages during 30 seconds for each trajectory. The results indicate that the integration algorithm with all the vehicle dynamic sensors together (GPS/WSS/YRS/SAS) provided the best performance. With respect to two trajectories, the maximum horizontal position error of both GNSS/WSS/YRS and GNSS/WSS/YRS/SAS integration was smaller than 10 m in 28 out of the total 30 GNSS outages. And the maximum horizontal positon error of GNSS/WSS integration was smaller than 10 m in 22 out of the total 30 GNSS outages. It is estimated that the GNSS/WSS integration would provide an unstable navigation solution during GNSS outages in comparison to both GNSS/WSS/YRS and GNSS/WSS/YRS/SAS integration since the accuracy of the computed yaw angle by using WSS could be significantly degraded due to frequent wheel slipping and skidding. Therefore, the proposed GNSS/vehicle dynamics sensor integrations excluding GNSS/WSS integration could be applied to an automotive navigation system with meterlevel accuracy to overcome the limitations of the GNSS based positioning technique. Indeed, these algorithms might provide alternative solutions to the use of a lowcost MEMSbased IMU.
The authors declare that they have no conflicts of interest.
This work was supported by the DGIST R&D Program of the Ministry of Science, ICT & Technology of Korea (17NT01) for Joonghee Han and Chiho Park. Also, this work was supported by the 2016 Research Fund of the University of Seoul for Jay Hyoun Kwon.