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Particle filtering for nonlinear dynamic state systems with unknown noise statistics

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Abstract

In this paper, we provide a tutorial for the applications of cost-reference particle filter (CRPF) to problems in signal processing disciplines. CRPF works in particle filtering (PF) framework although it may not be viewed as a Bayesian approach because the estimation is not based on the expected posterior function. CRPF has an interesting feature, i.e., the information of the noise statistics is not needed in its applications as opposed to the cases of the Kalman filter and standard PF approaches that work in dynamic state systems. Therefore, it is highly effective when the noise information is not available; nevertheless, it may not show optimal performance in general. In this paper, we introduce and disseminate this useful approach that is not known to many researchers even in related fields, and show how to effectively apply to problems which we provide as examples.

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Acknowledgments

This research was supported by “Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF-2011-0009255)” and “the Ministry of Science, ICT and Future Planning, Korea, under the ‘IT Consilience Creative Program’ (NIPA-2014-H0201-14-1001) supervised by the National IT Industry Promotion Agency.”

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  1. Future IT Innovation Laboratory, Pohang University of Science and Technology, Pohang, South Korea

    Jaechan Lim

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Appendix

Appendix

1.1 MATLAB m-files for tracking a target by CRPF with Gaussian mixture noise

In this appendix section, we provide m-files for MATLAB simulations as shown in Figs. 20–21. The m-file generates the result that CRPF tracks a target in 2-D space, and the measurement noise is a mixture Gaussian. Three MATLAB figures are generated: the first one shows the track of a target and the estimated tracking by CRPF, and next two figures show the error with respect to each coordinate (Fig. 21).

Fig. 20
figure 20

A MATLAB m-file for tracking a target by CRPF with Gaussian mixture noise

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Fig. 21
figure 21

A MATLAB m-file function, “resampling 2” in Fig. 20, a selection (resampling) algorithm

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Lim, J. Particle filtering for nonlinear dynamic state systems with unknown noise statistics. Nonlinear Dyn 78, 1369–1388 (2014). https://doi.org/10.1007/s11071-014-1523-x

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