Performance Assessment of Nonlinear State Filters

Nonlinear state filters of different approximations and capabilities have been developed in the last decade. The quality of different nonlinear filters, in terms of the mean squared error (MSE) of the estimates, depends on the approximations used in the filtering algorithm; however, there are no known methods for effectively evaluating the relative performance of these filters. A new method which measures the performance of different state filters against the theoretical posterior Cramér-Rao lower bound (PCRLB) is proposed. The complex high-dimensional integrals in PCRLB are approximated using sequential Monte-Carlo (SMC) methods. Efficacy of the proposed method is illustrated through a simulation example.