Conditionally Minimax Nonlinear Filter and Unscented Kalman Filter: Empirical Analysis and Comparison
We present the results of the analysis and comparison of the properties of two concepts in state filtering problems for nonlinear stochastic dynamic observation systems with discrete time: sigma-point Kalman filter based on a discrete approximation of continuous distributions and conditionally minimax nonlinear filter that implements the conditionally optimal filtering method based on simulation modeling. A brief discussion of the structure and properties of the estimates and justifications of the corresponding algorithms is accompanied by a significant number of model examples illustrating both positive applications and limitations of the efficiency for the estimation procedures. The simplicity and clarity of the considered examples (scalar autonomous regressions in the state equation and linear observations) allow us to objectively characterize the considered estimation methods. We propose a new modification of the nonlinear filter that combines the ideas of both considered approaches.
Keywordsnonlinear stochastic observation system unscented transform unscented Kalman filter conditionally optimal filtering conditionally minimax nonlinear filter simulation modeling
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This work was supported by the Russian Foundation for Basic Research, project no. 19-07-00187-a.
- 1.Julier, S.J., Uhlmann, J.K., and Durrant-Whyte, H.F., A New Approach for Filtering Nonlinear Systems, Proc. IEEE Am. Control Conf. (ACC’95), 1995, pp. 1628–1632.Google Scholar
- 3.Julier, S.J., The Scaled Unscented Transformation, Proc. IEEE Am. Control Conf. (ACC’02), 2002, pp. 4555–4559.Google Scholar
- 13.Li, X., Liu, A., Yu, C, and Su, F., Widely Linear Quaternion Unscented Kalman Filter for Quaternion-Valued Feedforward Neural Network, IEEE Signal Process. Lett, 2017, vol. 24, no. 9, pp. 1418–1422.Google Scholar
- 17.Jochmann, G., Kerner, S., Tasse, S., and Urbann, O., Efficient Multi-Hypotheses Unscented Kalman Filtering for Robust Localization, Led. Notes Comput. Sci. (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7416 LNCS, 2012, pp. 222–233.Google Scholar
- 19.Pugachev, V.S., Recurrent Estimation of Variables and Parameters in Stochastic Systems Defined by Difference Equations, Dokl. Math., 1978, vol. 243, no. 5, pp. 1131–1133.Google Scholar