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Robust Linear Filter with Parameter Estimation Under Student-t Measurement Distribution

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Abstract

In this paper, we propose an approximate Kalman filter of measurements following Student’s t-distribution by using the variational Bayes approach. This approach can decompose the estimation of multivariate parameters into a univariate estimation. The recursive formula for the approximate posterior densities of parameters and states is derived in detail. Then, the asymptotic Bayesian Cramer–Rao lower bounds are derived for the proposed filter. Numerical simulations verify both the performance of the proposed filter and the variance lower bounds under time-varying noise. The efficiency of the proposed filter is also demonstrated in a real application, namely an integrated strapdown inertial navigation system/Doppler velocity log shipborne test for navigation.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61773133 and the Fundamental Research Funds for the Central Universities under Grants HEUCF181110.

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Authors and Affiliations

  1. College of Science, Harbin Engineering University, Harbin, 150001, China

    Zongyuan Wang

  2. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Zongyuan Wang & Weidong Zhou

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  1. Zongyuan Wang
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  2. Weidong Zhou
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Correspondence to Weidong Zhou.

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Wang, Z., Zhou, W. Robust Linear Filter with Parameter Estimation Under Student-t Measurement Distribution. Circuits Syst Signal Process 38, 2445–2470 (2019). https://doi.org/10.1007/s00034-018-0972-8

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