![]() The target range is unobservable in the passive mode, which complicates the tracking significantly. First, in this case, the available observations are the bearings towards the target with or without the Doppler shift of the received signal caused by the radial target movement relative to the sonar. ![]() The object of this research is the long-range passive tracking problem of a maneuvering target by stationary multi-static sonar site. 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. All the features of conditionally-minimax estimates are demonstrated by the regression example of random position estimate given the noisy bearing observations. 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. Second, the theoretical covariance matrix of CMNF errors meets the real values. First, the obtained estimates are unbiased. The CMNF estimates have the following advantageous features. ![]() The proposed filter postulates recurrent “prediction–correction” form with some predefined basic prediction and correction terms, and then they are optimally fused. 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.
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