An Adaptive Target Tracking Algorithm Based on EKF for AUV with Unknown Non-Gaussian Process Noise
Abstract
:1. Introduction
- We propose a target tracking method based on EKF (TT-EKF) to simultaneously estimate the states of an AUV and an MRS.
- We estimate the noise statistics of the heading and forward speed of an AUV and an MRS by using the variational Bayesian algorithm. The noisy forward speed is modeled by the Gaussian mixture distribution (GMD). The noisy heading angle is modeled by a von Mises (vM) distribution.
- We build a neural network compensator to make up for the prediction error caused by the process noise.
2. System Overview
3. Target Tracking Method Based on EKF
4. Adaptive Target Tracking Algorithm Based on EKF
5. Variational Bayesian
5.1. Modeling of Forward Speed and Heading
5.2. Parameters Estimation Based on VB
5.2.1. Parameter Estimation of GMD
5.2.2. Parameter Estimation of vM Distribution
5.3. Estimation of PNCM
6. Neural Network
7. Algorithm Process
- Initialization
- -
- Initilize the PNCM Q, the measurement noise covariance matrix R, the initial state .
- -
- Initilize the parameters used in VB algorithm.
- -
- Initilize the neural network parameters state , which contains the linkweight and threshold value.
- -
- Initilize the prediction error , whose all compents are equals to 0.
- Perform the algorithmFor do for each time instant
- -
- Predict state and its covariance matrix via Equations (5) and (6).
- -
- If
- -
- Perform the state updating via Equations (7)–(11) based on Extended Kalman filter.
- -
end For
8. MATLAB Simulation and Experimental Data Analysis
8.1. MATLAB Simulation
8.2. Experimental Data Analysis
- As the PNCM is unknown, we assumed the PNCM is , which is inaccurate. The contrast between the red lines and the blue lines indicates that the inaccurate process noise statistics leads to the degradation of the state estimation performance of TT-EKF.
- The contrast between the red lines and the green lines indicates that the state estimation performance of TT-EKF has been improved with the PNCM is estimated by VB algorithm.
- The contrast between the green lines and the black lines indicates that the state estimation performance of TT-EKF has been further improved with the prediction error compensator based on neural network.
9. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix B
Appendix C
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Weight | Mean | Variance | |
---|---|---|---|
1 | |||
2 |
Actual Q | Inaccurate Q | Estimated Q (without bp) | Estimated Q (with bp) | |
---|---|---|---|---|
5.6855 × 10 | 5.3567 × 10 | 5.7135 × 10 | 3.3989 × 10 | |
2.0301 × 10 | 7.2603 × 10 | 5.1868 × 10 | 4.8194 × 10 | |
L | 2.5986 × 10 | 1.2617 × 10 | 5.7582 × 10 | 5.1593 × 10 |
t | 100 s | 200 s | 300 s | 400 s |
---|---|---|---|---|
Actual position | (331.01,207.22) | (370.68,245.43) | (422.29,284.41) | (477.54,317.33) |
actual Q | (329.11,207.87) | (369.25,246.80) | (423.31,285.92) | (479.70,317.90) |
inaccurate Q | (323.96,207.45) | (363.40,245.09) | (414.81,283.07) | (473.37,315.39) |
estimated Q(no bp) | (326.53,207.59) | (366.73,246.62) | (420.99,285.78) | (477.17,317.72) |
estimated Q(bp) | (326.52,207.55) | (366.76,246.25) | (447.80,285.95) | (477.61,319.12) |
t | 500 s | 600 s | 700 s | 800 s |
Actual position | (535.55,344.73) | (594.86,369.41) | (654.22,393.33) | (713.85,415.49) |
actual Q | (533.87,344.7846) | (592.64,368.40) | (651.53,393.00) | (712.38,416.18) |
inaccurate Q | (526.65,342.11) | (584.92,365.57) | (642.26,389.63) | (700.71,412.20) |
estimated Q(no bp) | (531.37,344.63) | (590.19,368.26) | (649.19,392.91) | (710.20,416.11) |
estimated Q(bp) | (531.69,346.76) | (591.02,370.20) | (650.15,394.58) | (711.33,417.79) |
t | 900 s | 1000 s | 1100 s | 1200 s |
Actual position | (773.11,439.49) | (833.72,461.50) | (893.95,484.39) | (955.16,505.29) |
actual Q | (771.08,437.31) | (829.35,458.91) | (890.63,480.38) | (953.20,502.14) |
inaccurate Q | (757.83,432.76) | (817.41,454.64) | (879.46,476.35) | (942.66,498.38) |
estimated Q(no bp) | (768.99,437.29) | (827.15,458.86) | (888.36,480.31) | (950.90,502.07) |
estimated Q(bp) | (770.10,439.21) | (828.71,460.69) | (890.19,482.29) | (952.53,504.23) |
t | 1300 s | 1400 s | 1470 s | |
Actual position | (1015.0,527.84) | (1075.1,548.96) | (1116.2,564.99) | |
actual Q | (1015.4,525.38) | (1075.8,547.80) | (1117.3,562.70) | |
inaccurate Q | (1005.5,521.75) | (1066.0,544.10) | (1107.5,558.91) | |
estimated Q(no bp) | (1013.0,525.27) | (1073.4,547.68) | (1114.9,562.59) | |
estimated Q(bp) | (1014.7,527.47) | (1075.0,550.01) | (1116.6,564.98) |
t | 100s | 200 s | 300 s | 400 s |
---|---|---|---|---|
Actual position | (425.62,309.33) | (468.55,324.95) | (518.72,343.21) | (569.95,361.86) |
actual Q | (423.40,307.87) | (465.77,327.89) | (522.56,339.75) | (565.80,370.07) |
inaccurate Q | (418.16,307.41) | (459.91,325.95) | (514.08,337.08) | (559.67,367.68) |
estimated Q(no bp) | (420.67,307.57) | (465.98,324.37) | (519.27,342.07) | (564.27,369.43) |
estimated Q(bp) | (420.66,307.53) | (466.01,324.01) | (519.80,342.23) | (564.70,370.83) |
t | 500 s | 600 s | 700 s | 800 s |
Actual position | (619.21,379.78) | (667.99,397.54) | (716.69,415.27) | (774.61,436.35) |
actual Q | (617.92,379.42) | (664.96,395.76) | (712.44,416.51) | (772.05,436.80) |
inaccurate Q | (611.10,376.80) | (657.22,392.95) | (702.91,413.09) | (760.39,432.78) |
estimated Q(no bp) | (615.34,381.67) | (662.36,396.33) | (709.57,416.38) | (770.31,435.70) |
estimated Q(bp) | (615.66,383.80) | (663.20,398.27) | (710.53,418.05) | (771.45,437.38) |
t | 900 s | 1000 s | 1100 s | 1200 s |
Actual position | (833.52,457.79) | (889.72,478.24) | (942.95,497.62) | (993.39,515.98) |
actual Q | (829.13,457.78) | (880.61,481.03) | (936.05,494.27) | (986.33,516.49) |
inaccurate Q | (815.99,453.40) | (868.64,476.87) | (924.83,490.16) | (975.98,512.76) |
estimated Q(no bp) | (827.45,458.12) | (877.66,483.40) | (934.00,492.94) | (984.60,516.06) |
estimated Q(bp) | (828.57,460.04) | (879.21,485.23) | (935.84,494.92) | (986.23,518.22) |
t | 1300 s | 1400 s | 1470 s | |
Actual position | (1042.4,533.81) | (1091.1,551.54) | (1125.2,563.94) | |
actual Q | (1037.5,533.98) | (1087.7,552.10) | (1118.7,562.71) | |
inaccurate Q | (1027.3,530.24) | (1077.9,548.28) | (1108.8,558.88) | |
estimated Q(no bp) | (1034.5,533.93) | (1085.3,551.78) | (1116.0,562.42) | |
estimated Q(bp) | (1036.1,536.12) | (1086.8,554.10) | (1117.7,564.81) |
Weight | Mean | Variance | |
---|---|---|---|
1 | |||
2 |
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Dong, L.; Xu, H.; Feng, X.; Han, X.; Yu, C. An Adaptive Target Tracking Algorithm Based on EKF for AUV with Unknown Non-Gaussian Process Noise. Appl. Sci. 2020, 10, 3413. https://doi.org/10.3390/app10103413
Dong L, Xu H, Feng X, Han X, Yu C. An Adaptive Target Tracking Algorithm Based on EKF for AUV with Unknown Non-Gaussian Process Noise. Applied Sciences. 2020; 10(10):3413. https://doi.org/10.3390/app10103413
Chicago/Turabian StyleDong, Lingyan, Hongli Xu, Xisheng Feng, Xiaojun Han, and Chuang Yu. 2020. "An Adaptive Target Tracking Algorithm Based on EKF for AUV with Unknown Non-Gaussian Process Noise" Applied Sciences 10, no. 10: 3413. https://doi.org/10.3390/app10103413