Adaptive Gaussian mixture filter for Markovian jump nonlinear systems with colored measurement noises. (September 2018) - Yang, Yanbo; Liang, Yan; Pan, Quan; Qin, Yuemei; Wang, Xiaoxu
Abstract: This paper considers the state estimation of discrete-time Markovian jump nonlinear systems with colored measurement noises obeying a nonlinear autoregressive process of order n, which is motivated by tracking the maneuvering target under electronic countermeasures with high speed sampling or persistent perturbations. In order to remove the measurement noises correlation, the left zero divisor is explored to reconstruct a new measurement equation via difference approach, with the help of applying statistical linear regression to the colored measurement noise model. Then, a novel hypothesis set constituted of all possible values of multi-step Markov jumping parameters is defined and the posterior probability density of the state is derived recursively. By using Gaussian mixtures to approximate the posterior probability densities, an adaptive Gaussian mixture filter for the considered system is proposed, where the Gaussian components with small weights are pruned adaptively through measuring the Alpha (or Beta) divergence for the original and approximated Gaussian mixtures, to achieve a tradeoff between the estimation accuracy and running time. A maneuvering target tracking accompanied by range gate pull-off with different colored measurement noises cases is simulated to validate the proposed method. Highlights: The state estimation is considered for Markovian jump nonlinear systems with colored measurement noises. The colored measurement noise is obeyed a nonlinear autoregressive process of order n . A new measurement equation is reconstructed by applying the statistical linear regression to the colored noise model. The recursive posterior probability density of the state is derived and a novel adaptive Gaussian mixture filter is proposed. The Gaussian components with small weights are pruned adaptively by using the family of Alpha (Beta) divergence measure.