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Experimental Validation: Perception and Localization Systems for Autonomous Vehicles using the Extended Kalman Filter Algorithm Cover

Experimental Validation: Perception and Localization Systems for Autonomous Vehicles using the Extended Kalman Filter Algorithm

International Journal on Smart Sensing and Intelligent Systems
Volume 17 (2024): Issue 1 (January 2024)
By: ,  ,   and    
Open Access
|Feb 2024
Figures & tables

Figures & Tables

Table 1:

The EKF parameter details.

ParameterInformation
β^k− The estimated state
fNon-linear model system
hMeasurement model system
vkMeasurement noise
zkIMU measurement
Wk − 1Dynamic system noise
β^k−1+ The estimated updates state
VThe linear velocity of the robot
ΔtTime derivative
θThe steering angle of the robot
QkDynamic system noise matrix Q=[10−40000010−40000010−40000010−40000010−4]
HkIMU measurement matrix Hodometry+IMU=[1000001000001000001000001]
RkMeasurement noise matrix R=[10−40000010−40000010−40000010−40000010−4]
FkJacobians matrix, Fk=[10−Vk−1ΔtsinθkΔtcosθk001Vk−1ΔtcosθkΔtsinθk00010Δt0001000001]

[i] EKF, extended Kalman Filter; IMU, inertial measurement unit.

Table 2:

The steps of the EKF-SLAM Algorithm.

EKF-SLAM Algorithm

  1. The initial step is to initialize the previous estimated value (b_prev) and the previous covariance error (p_prev) with a value of 0.

  2. Initialize the predicted state (b_new) based on Eq. (1)

  3. Initialize the prediction error covariance (p_new) based on Eq. (2)

  4. Obtain the optimal gain (K) based on Eq. (3)

  5. Obtain an estimate of the state of the update (b) based on Eq. (4)

  6. The estimation of the state of the update is the result of the KF displayed

  7. Get the updated covariance error (K) based on Eq. (5)

  8. The updated state estimate value is stored as the previous estimate, and then the state estimation algorithm returns to step 2

  9. The error covariance update value is stored as the prior covariance, and then the error covariance algorithm returns to step 3.

[i] EKF, extended Kalman filter; KF, Kalman filter; SLAM, simultaneous localization and mapping.

Figure 1:

The hardware wiring and schematics.

Figure 2:

The physical look of a robot.

Table 3:

The details of robot parameters.

ParameterValue
Battery12.6 V (DC)
Dimension242.9 × 192.2 mm
Steering servo9 kg/cm torque
Wheel motor240 RPM
Wireless2.4G/5G dual-band WIFI, Bluetooth 4.2
Driving typeAckerman steering dual gearmotor rear wheel drive

[i] RPM, revolutions per minute.

Figure 3:

The scenario of physical world and measurement.

Figure 4:

Encoders' schematic diagram.

Figure 5:

The Localization and perception block diagram. ROS, robot operating system.

Figure 6:

The map generated using the Hector-SLAM algorithm. SLAM, Simultaneous localization and mapping.

Table 4:

The maximum and minimum distance values of the LiDAR data.

Maximum (m)Minimum (m)
Measured data6.8080.15
Actual value (reference)6.540.09
Error (%)467

[i] LiDAR, light detection and ranging.

Table 5:

Gyroscope orientation measurements.

X orientationY orientationX referenceY referenceX errorY error
−0.01−0.0100−0.01−0.01
−0.01−0.0100−0.01−0.01
−0.010.0200−0.010.02
−0.010.0300−0.010.03
−0.010.0300−0.010.03
0.000.03000.000.03
−0.010.0300−0.010.03
0.000.00000.000.00
0.000.00000.000.00
−0.010.0300−0.010.03
Errors in average (%)12
Table 6:

Accelerometer measurements.

XYX referenceY referenceX errorY error
0.02−0.02000.02−0.02
0.01−0.01000.01−0.01
−0.03−0.0200−0.03−0.02
−0.06−0.0200−0.06−0.02
−0.07−0.0200−0.07−0.02
−0.060.0100−0.060.01
−0.06−0.0300−0.06−0.03
0.010.01000.010.01
−0.010.0000−0.010.00
−0.06−0.0200−0.06−0.02
Error in average (%)42
Table 7:

The comparison of the encoder results and the reference in X-axis.

X position from odometryX referenceError
0.950.970.02
0.950.970.03
0.950.970.03
0.950.970.03
0.950.980.03
0.950.980.04
0.950.980.04
0.950.990.04
0.950.990.04
0.951.000.05
Error in average (%)3
Table 8:

The comparison of the encoder results and the reference in Y-axis.

Y position from odometryY referenceError
0.020.020.00
0.020.020.00
0.020.020.00
0.020.020.00
0.020.020.00
0.010.020.01
0.010.020.01
0.020.020.02
0.070.020.05
0.070.020.05
Error in average (%)2
Table 9:

Comparison between the EKF positions and the reference.

X position (EKF)X referenceY position (EKF)Y referenceError XError Y
0.970.970.020.020.000.00
0.980.970.020.020.010.00
0.980.970.020.020.010.01
0.980.970.020.020.010.01
0.990.980.020.020.010.02
0.990.980.020.020.010.04
1.000.980.020.020.020.04
1.010.990.020.020.020.04
1.010.990.020.020.020.04
1.021.000.020.020.020.05
Error in average (%)13
RMSE0.110.15

[i] EKF, extended Kalman filter; RMSE, root mean square error.

Figure 7:

Comparison of EKF position estimation results with references. During the experiment, we focus on two coordinates as the mobile robot moves—namely, the X and Y coordinates. Label A represents the robot's motion along the X coordinate, while label B corresponds to its movement along the Y coordinate. EKF, extended Kalman filter.

Figure 8:

RViz visualization.

DOI: https://doi.org/10.2478/ijssis-2024-0002 | Journal eISSN: 1178-5608
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Language: English
Submitted on: Aug 28, 2023
Published on: Feb 7, 2024
Published by: International Journal on Smart Sensing and Intelligent Systems
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Experimental validation,
extended Kalman filter,
ground mobile robot,
robot operating system,
simultaneous localization and mapping
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2024 Bambang Lelono Widjiantoro, Katherin Indriawati, T. S. N. Alexander Buyung, Kadek Dwi Wahyuadnyana, published by International Journal on Smart Sensing and Intelligent Systems
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 17 (2024): Issue 1 (January 2024)
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