Confidence partitioning sampling filtering

The confidence partitioning sampling filter (CPSF) method proposed in this paper is a novel approach for solving the generic nonlinear filtering problem. First, the confidence probability space (CPS) is defined, which restricts the state transition in a bounded and closed state space in the recursive Bayesian filtering. In the posterior CPS, the weighted grid samples, represented the posterior PDF, are obtained by using the partitioning sampling technique (PST). Each weighted grid sample is treated as an impulse function. The approximate expression of the posterior PDF, as key for the PST implementation, is obtained by using the properties of the impulse function in the integral operation. By executing the selection of the CPS and the PST step repeatedly, the CPSF framework is formed to achieve the approximation of the recursive Bayesian filtering. Second, the difficulty of the CPSF framework implementation lies in obtaining the real posterior CPS. Therefore, the space intersection (SI) method is suggested to obtain the approximate posterior CPS. On this basis, the SI_CPSF algorithm, as an executable algorithm, is formed to solve the generic nonlinear filtering problem. Third, the approximate error between the CPSF framework and the recursive Bayesian filter is analyzed theoretically. The consistency of the CPSF framework to the recursive Bayesian filter is proved. Finally, the performances of the SI_CPSF algorithm, including robustness, accuracy and efficiency, are evaluated using four representative simulation experiments. The simulation results showed that SI_CSPF requires far less samples than particle filter (PF) under the same accuracy. Its computation is on average one order of magnitude less than that of the PF. The robustness of the proposed algorithm is also evaluated in the simulations.