An Adaptive Target Tracking Method Utilizing Marginalized Cubature Kalman Filter with Uncompensated Biases

DENG Honggao; YU Runhua; JI Yuanfa; WU Sunyong; SUN Shaoshuai

doi:10.11999/JEIT240469

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DENG Honggao, YU Runhua, JI Yuanfa, WU Sunyong, SUN Shaoshuai. An Adaptive Target Tracking Method Utilizing Marginalized Cubature Kalman Filter with Uncompensated Biases[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240469

Citation:

DENG Honggao, YU Runhua, JI Yuanfa, WU Sunyong, SUN Shaoshuai. An Adaptive Target Tracking Method Utilizing Marginalized Cubature Kalman Filter with Uncompensated Biases[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240469

Citation:

DENG Honggao, YU Runhua, JI Yuanfa, WU Sunyong, SUN Shaoshuai. An Adaptive Target Tracking Method Utilizing Marginalized Cubature Kalman Filter with Uncompensated Biases[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240469

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An Adaptive Target Tracking Method Utilizing Marginalized Cubature Kalman Filter with Uncompensated Biases

doi: 10.11999/JEIT240469

DENG Honggao^{1, 4},
YU Runhua^{1, 2},
JI Yuanfa^{1, 2, 4},
WU Sunyong^{2, 3
,
,},
SUN Shaoshuai¹

1.
School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China
2.
Guangxi Key Laboratory of Precision Navigation Technology and Application, Guilin University of Electronic Technology, Guilin 541004, China
3.
School of Mathematics and Computing Science, Guilin University of Electronic Science and Technology, Guilin, 541004, China
4.
National & Local Joint Engineering Research Center of Satellite Navigation Positioning and Location Service, Guilin 541004, China

Funds: Guangxi Key Research and Development Project (AB23026150, AB23026147), The National Natural Science Foundation of China (U23A20280)

Received Date: 2024-06-11
Rev Recd Date: 2024-11-30

Available Online: 2024-12-09

Abstract

Abstract

Objective In radar target tracking, tracking accuracy is often influenced by sensor measurement biases and measurement noise. This is particularly true when measurement biases change abruptly and measurement noise is unknown and time-varying. Ensuring effective target tracking under these conditions poses a significant challenge. An adaptive target tracking method is proposed, utilizing a marginalized cubature Kalman filter to address this issue. Methods (1) Initially, measurements taken at adjacent time points are differentiated to formulate the differential measurement equation, thereby effectively mitigating the influence of measurement biases that are either constant or change gradually between adjacent observations. Concurrently, the target states at these moments are expanded to create an extended state vector facilitating real-time filtering. (2) Following the differentiation of measurements, sudden changes in measurement biases may cause the differential measurement at the current moment to be classified as outliers. To identify the occurrence of these abrupt bias changes, a Beta-Bernoulli indicator variable is established. If such a change is detected, the differential measurement for that moment is disregarded, and the predicted state is adopted as the updated state. In the absence of any abrupt changes, standard filtering procedures are conducted. The Gaussian measurement noise, despite having unknown covariance, continues to follow a Gaussian distribution after differentiation, allowing its covariance matrix to be modeled using the inverse Wishart distribution. (3) A joint distribution is formulated for the target state, indicator variables, and the covariance matrix of the measurement noise. The approximate posteriors of each parameter are derived using variational Bayesian inference. (4) To mitigate the increased filtering burden arising from the high-dimensional extended state vector, the extended target state is marginalized, and a marginalized cubature Kalman filter for target tracking is implemented in conjunction with the cubature Kalman filtering method. Results and Discussions The target tracking performance is clearly illustrated, indicating that the proposed method accurately identifies abrupt measurement biases while effectively managing unknown time-varying measurement noise. This leads to a tracking performance that significantly exceeds that of the comparative methods. The findings further support the conclusions by examining the Root Mean Square Error (RMSE). Additionally, the stability of the proposed method is demonstrated. The results reveal that the computational load associated with the proposed method is greatly reduced through marginalization processing. This reduction occurs because, during the variational Bayesian iteration process, cubature sampling and integration are performed multiple times. Once the target state is marginalized, the dimensionality of the cubature sampling is halved, and the number of sampling points for each variational iteration is also reduced by half. As a result, the computational load during the nonlinear propagation of the sampling points decreases, with the amount of computation reduction increasing with the number of variational iterations. Furthermore, the results demonstrate that marginalization does not compromise tracking accuracy, thereby further validating the effectiveness of marginalization processing. This finding also confirms that marginalization processing can be extended to other nonlinear variational Bayesian filters based on deterministic sampling, providing a means to reduce computational complexity. Conclusions This paper proposes an adaptive marginalized cubature Kalman filter to improve target tracking in scenarios with measurement biases and unknown time-varying measurement noise. The approach incorporates measurement differencing to eliminate constant biases, constructs indicator variables to detect abrupt biases, and models the unknown measurement noise covariance matrix using the inverse Wishart distribution. A joint posterior distribution of the parameters is established, and the approximate posteriors are solved through variational Bayesian inference. Additionally, marginalization of the target state is performed before implementing tracking within the CKF framework, reducing the filtering burden. The results of our simulation experiments yield the following conclusions: (1) The proposed method demonstrates superior target tracking performance compared to existing techniques in scenarios involving abrupt measurement biases and unknown measurement noise; (2) The marginalization processing strategy significantly alleviates the filtering burden of the proposed filter, making it applicable to more complex nonlinear variational Bayesian filters, such as robust nonlinear random finite set filters, to reduce filtering complexity; (3) This filtering methodology can be extended to target tracking scenarios in higher dimensions.
- Abrupt measurement biases,
- Beta-Bernoulli distribution,
- Inverse Wishart distribution,
- Variational Bayesian inference,
- Marginalized cubature Kalman filter

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References(21)

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