Rao-Blackwellised Particle Filtering Implementation for Dynamic Conditionally Gaussian Models

In this article, we present a method called Rao-Blackwellised Particle Filtering for Dynamic Conditionally Gaussian Models, implemented as a MATLAB program for Gaussian model-based particle filtering (RBPF). This approach is widely used for estimating states in nonlinear and non-Gaussian systems. The algorithm employs particle filtering to estimate system states and uses Monte Carlo averaging of the posterior distribution to estimate expected state values. The implementation leverages Rao-Blackwellization to reduce computational complexity by analytically marginalizing out linear Gaussian components while using particles for nonlinear parts. Key MATLAB functions include systematic resampling, Kalman filter updates for Gaussian components, and importance sampling for particle propagation. This method demonstrates high accuracy and robustness, making it suitable for various applications such as target tracking, autonomous navigation, and robotics. We provide detailed theoretical foundations and practical implementation approaches, accompanied by MATLAB code that includes: - Particle initialization and propagation routines - Conditional Kalman filter implementations for Gaussian subsystems - Effective sample size calculation for resampling triggers - Weight computation and normalization procedures The code structure follows modular design principles, allowing users to easily adapt the filter to specific system dynamics and observation models. We include comprehensive comments and configuration parameters to facilitate understanding and application of this powerful filtering technique.