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Statically Fused Unbiased Converted Measurements Kalman Filter

Authors: Zhengkun Guo, Yanbin Li, Wenqing Wang, Bo Zou


Active radar and sonar systems often report Doppler measurements in addition to the position measurements such as range and bearing. The tracker can perform better by making full use of the Doppler measurements. However, due to the high nonlinearity of the Doppler measurements with respect to the target state in the Cartesian coordinate systems, those measurements are not always fully exploited. This paper mainly focuses on dealing with the Doppler measurements as well as the position measurements in Polar coordinates. The Statically Fused Converted Position and Doppler Measurements Kalman Filter (SF-CMKF) with additive debiased measurement conversion has been presented. However, the exact compensation for the bias of the measurement conversion are multiplicative and depend on the statistics of the cosine of the angle measurement errors. As a result, the consistency and performance of the SF-CMKF may be suboptimal in the large angle error situations. In this paper, the multiplicative unbiased position and Doppler measurement conversion for two-dimensional (Polar-to-Cartesian) tracking are derived, and the SF-CMKF is improved by using those conversion. Monte Carlo simulations are presented to demonstrate the statistic consistency of the multiplicative unbiased conversion and the superior performance of the modified SF-CMKF (SF-UCMKF).

Keywords: Measurement conversion, Doppler, Kalman filter, estimation, tracking.

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[1] S. V. Bordonaro, P. Willet and Y. Bar-Shalom, “Tracking with converted position and Doppler measurements,” Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, Vol.81370D, 2011.
[2] Y. Bar-Shalom, X. Li, and T. Kirubarajan, “Estimation with applications to tracking and navigation: theory, algorithms, and software,” Wiley, Vol.53, no.6, pp.993-999, 2001.
[3] Y. Bar-Shalom, “Negative correlation and optimal tracking with range rate measurements,” IEEE Transactions on Aerospace and Electronic Systems, Vol.37, no.3, pp.1117-1120, 2001.
[4] L. Cui, X. Wang, Y. Xu, H. Jiang, and J. Zhou, “A novel switching unscented Kalman filter method for remaining useful life prediction of rolling bearing,” Measurement, Vol.135, pp.678-684, 2019.
[5] Z. Duan, C. Han, and X. Li, “Comments on unbiased converted measurements for tracking,” IEEE Transactions on Aerospace and Electronic Systems, Vol.40, no.4, pp.1374-1377, 2004.
[6] D. Franken, “Consistent unbiased linear filtering with polar measurements,” International Conference on Information Fusion, pp.1-8, 2007.
[7] R. Garcia and P. Pardal, H. Kuga, and M. Zanardi, “Nonlinear filtering for sequential spacecraft attitude estimation with real data: Cubature Kalman Filter, Unscented Kalman Filter and Extended Kalman Filter,” Advances in Space Research, Vol.63, no.2, pp.1038-1050, 2019.
[8] S. Julier, and J. Uhlmann, “New extension of the Kalman filter to nonlinear systems,” SPIE, Vol.3068, pp.182-193, 1997.
[9] S. Julier, and J. Uhlmann, “Consistent debiased method for converting between polar and Cartesian coordinate systems,” Proceedings of the 1997 SPIE Conference on Acquisition, Tracking, and Pointing, pp.110-121, 1997.
[10] S. Julier, J. Uhlmann, and H. Durrantwhyte, “A new method for the nonlinear transformation of means and covariances in filters and estimators,” IEEE Transactions on Automatic Control, Vol.45, no.3, pp.477-482, 2000.
[11] D. Lerro, and Y. Bar-Shalom, “Tracking with debiased consistent converted measurements versus EKF,” IEEE Transactions on Aerospace and Electronic Systems, Vol.29, no.3, pp.1015-1022, 1993.
[12] X. Li, and V. Jilkov, “A survey of maneuvering target trackingPart I: Dynamics models,” IEEE Transactions on Aerospace and Electronic Systems, Vol.39, no.4, pp.1333-1364, 2004.
[13] X. Lai, W. Yi, Y. Cui, C. Qin, X. Han, T. Sun, L. Zhou, and Y. Zheng, “Capacity estimation of lithium-ion cells by combining model-based and data-driven methods based on a sequential extended Kalman filter,” Energy, Vol.216, 1 February, 119233, 2021.
[14] P. Suchomski, “Explicit expressions for debiased statistics of 3D converted measurements,” IEEE Transactions on Aerospace and Electronic Systems, Vol.35, no.1, pp.368-370, 1999.
[15] X. Song, Y. Zhou, and Y. Bar-Shalom, “Unbiased converted measurements for tracking,” IEEE Transactions on Aerospace and Electronic Systems, Vol.34, no.3, pp.1023-1027, 1998.
[16] J. Xiu, Y. He, G. Wang, and X. Tang, “Constellation of multisensors in Bearing-only Location System,” IEEE Proceedings on Radar, Sonar and Navigation, Vol.152, no.3, pp.215-218, 2005.
[17] G. Zhou, M. Pelletier, T. Kirubarajan, and T. Quan, “Statically fused converted position and Doppler measurement Kalman filters,” IEEE Transactions on Aerospace and Electronic Systems, Vol.50, no.1, pp.300-318, 2014.