Sequential estimation by combined cost-reference particle and Kalman filtering

Cost-reference particle filtering (CRPF) is a methodology for recursive estimation of hidden states of dynamic systems. It is used for tracking nonlinear states when probabilistic assumptions about the state and observations noises are not made. Recently, we have proposed a CRPF algorithm for systems with conditionally linear states that combines the use of Kalman filtering for the linear states and CRPF for the nonlinear states. We have shown that this combined method yields improved results over the standard CRPF. In this paper, we further extend that approach by relaxing some of the assumptions about the noises in the system. As a result, the only statistical assumption that remains is that the noises are stationary and zero mean. We demonstrate the performance of the proposed method by computer simulations and compare it with standard CRPF, standard particle filtering (SPF), and marginalized particle filtering (MPF).