Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters
Abstract
1. Introduction
2. The Shifted Rayleigh Filter Algorithm
2.1. The Bearing Model
2.2. The Treatment of Clutter
3. Variational Bayesian Filtering
3.1. Conjugate Exponential Model
3.2. VB Approximation Method
- (1)
- The VB expectation step yields:
- (2)
- The VB maximization step yields that is conjugate and of the form
4. VB Based Adaptive Shifted Rayleigh Filter with Unknown Clutter Probability
- (1)
- Optimization of for fixed .
- (2)
- Optimization of for fixed .
Algorithm 1 : VB-SRF. |
(1) Initialization: , , , , , , (2) Prediction: where is the scale factor and . (3) Update: the update of VB-SRF utilizes iterate filtering framework. (3.a) First set: , , , , (3.b) Calculate state estimation and its covariance using SRF when the measurement is from the target: (3.c) For , iterate the following N (N denotes iterated times) steps: Calculate the fused state estimation and its covariance: where is a normalization term, and can be obtained using (A6). Update parameters: End for and set , , , , . |
5. Simulation Results
5.1. Scenario 1
5.2. Scenario 2
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
VB | Variational Bayesian |
SRF | Shifted Rayleigh Filter |
PDA | Probability Data Association |
EKF | Extended Kalman Filter |
MPEKF | Polar Coordinate EKF |
PLE | Pseudo-Linear Estimator |
UKF | Unscented Kalman Filter |
CKF | Cubature Kalman Filter |
PF | Particle Filter |
MEFPDA | Maximum Entropy Fuzzy Probabilistic Data Association |
SCKF | Square-root Cubature Kalman Filter |
CE | Conjugate Exponential |
KL | Kullback- Leibler |
EM | Expectation-Maximum |
RMS | Root Mean Square |
Appendix A. Derivation of f(θk|xk)
Appendix B. Derivation of f(θk|z1:k−1)
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Scenario 1 | Scenario 2 | |||||
---|---|---|---|---|---|---|
VB-SRF | 0 | 0 | 0.1% | 0 | 0 | 0 |
SRF | 0.9% | 1.6% | 2.9% | 0 | 0 | 2.7% |
MEFPDA-SCKF | 0 | 0 | 0 | 13.5% | 13.3% | 14.2% |
PDA-SCKF | 0 | 0 | 0 | 20.1% | 20.8% | 22.4% |
Scenario 1 | Scenario 2 | |
---|---|---|
VB-SRF | 0.7406 s | 1.0236 s |
SRF | 0.3690 s | 0.5779 s |
MEFPDA-SCKF | 0.2066 s | 0.3314 s |
MEFPDA-SCKF | 0.2092 s | 0.3128 s |
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Hou, J.; Yang, Y.; Gao, T. Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters. Sensors 2019, 19, 1512. https://doi.org/10.3390/s19071512
Hou J, Yang Y, Gao T. Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters. Sensors. 2019; 19(7):1512. https://doi.org/10.3390/s19071512
Chicago/Turabian StyleHou, Jing, Yan Yang, and Tian Gao. 2019. "Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters" Sensors 19, no. 7: 1512. https://doi.org/10.3390/s19071512
APA StyleHou, J., Yang, Y., & Gao, T. (2019). Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters. Sensors, 19(7), 1512. https://doi.org/10.3390/s19071512