Approximating Posterior Cramér–Rao Bounds for Nonlinear Filtering Problems Using Gaussian Mixture Models

The posterior Cramér-Rao bound (PCRB) is a fundamental tool to assess the accuracy limit of Bayesian estimation problem. In this article, we propose novel framework compute PCRB for general nonlinear filtering problem with additive white Gaussian noise. It uses mixture model represent and propagate uncertainty contained in state vector Gauss-Hermite quadrature rule mathematical expectations vector-valued functions variable. detailed pseudocodes both small large component covariance cases are also presented. Three numerical experiments conducted. All results show that proposed method has high it more efficient than plain Monte Carlo integration approach case.