In this note, a method of conditionally minimax nonlinear filtering (CMNF) of processes in nonlinear stochastic discrete-time controlled systems is proposed. The CMNF is derived by means of local nonparametric optimization of the filtering process given the class of admissible filters. Sufficient conditions for the existence of the CMNF are considered, and the properties of CMNF estimates are investigated. Results of the CMNF application to control and identification problems are presented.

The paper presents an application of the Conditionally-Minimax Nonlinear Filtering (CMNF) algorithm to the online estimation of underwater vehicle movement given a combination of sonar and Doppler discrete-time noisy sensor observations. The proposed filter postulates recurrent “prediction–correction” form with some predefined basic prediction and correction terms, and then they are optimally fused. The CMNF estimates have the following advantageous features. First, the obtained estimates are unbiased. Second, the theoretical covariance matrix of CMNF errors meets the real values. Third, the CMNF algorithm gives a possibility to choose the preliminary observation transform, basic prediction, and correction functions in any specific case of the observation system to improve the estimate accuracy significantly. All the features of conditionally-minimax estimates are demonstrated by the regression example of random position estimate given the noisy bearing observations. The contribution of the paper is the numerical study of the CMNF algorithm applied to the underwater target tracking given bearing-only and bearing-Doppler observations.

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