A map wavelet-based particle filter for estimating chaotic states with uncertain parameters and unknown measurement noises

In this paper, we develop a Maximum-A-Posterior wavelet-based particle filter (MAP-WPF) and apply it to estimating the states and parameters of the chaotic systems with uncertain parameters and unknown parameters. To implement the proposed method, the covariance of the observation sequence is estimated using the wavelet transform, and the proper weights of particles are obtained accordingly. In addition, we obtain the parameters by the Maximum-A-Posterior (MAP) method to converge at the true parameters. Therefore, the MAP-WPF can effectively alleviate the sample degeneracy problem which is common in the standard particle filter (PF). Numerical simulations of Logistic map indicate the effectiveness of our proposed method which produces significant accuracy improvement than the PF.