Conditionally-Minimax Nonlinear Filtering for Continuous-Discrete Stochastic Observation Systems: Comparative Study in Target Tracking

The paper presents an algorithm of the Conditionally-Minimax Nonlinear Filtering (CMNF) of the stochastic differential system state given indirect noisy discrete-time observations. The filter has a two-step "prediction-correction" form with fixed basic prediction and correction terms, which are jointly processed in the optimal way. The obtained estimates are unbiased and the theoretical covariance matrix of CMNF errors, which may be calculated a priori, meets the real a posteriori values. The key feature of the CMNF algorithm is a possibility to choose the preliminary observation transformation, basic prediction and correction functions for a particular case of the observation system, which allows to improve the estimation accuracy significantly. All the features of CMNF are demonstrated by the maneuvering target tracking model in comparison with the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) estimates.

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