Gaussian Model-Based RBPF (Rao-Blackwellised Particle Filter) Implementation

Rao-Blackwellised Particle Filter (RBPF) is an efficient state estimation algorithm that combines particle filtering with analytical integration, particularly suitable for Dynamic Conditionally Gaussian Models. Core Algorithm Concept RBPF utilizes Rao-Blackwellisation technique to decompose the state space into two components: Nonlinear part is approximated through particle filtering (PF) Linear Gaussian part is analytically solved using Kalman filtering (KF) This hybrid strategy significantly reduces the required number of particles while improving estimation accuracy. Key Implementation Steps in MATLAB Particle Initialization: Generate initial particle set according to prior distribution, where each particle contains nonlinear states and corresponding Gaussian distribution parameters (mean and variance). In code, this involves creating a particle structure array with fields for nonlinear states and Kalman filter parameters. Importance Sampling: Generate new particles through proposal distribution (such as state transition model) and update nonlinear components. Implementation requires careful design of the proposal function to ensure effective sampling efficiency. Kalman Update: For each particle, analytically update the state mean and covariance of the linear Gaussian part using Kalman filter equations. This step involves matrix operations for prediction and update phases within each particle's KF instance. Resampling: Perform systematic resampling based on particle weights to avoid degeneracy issues. MATLAB implementation can use built-in functions like datasample or custom multinomial/categorical resampling algorithms. State Estimation: Combine nonlinear states and Gaussian parameters from the particle set to produce final estimates. Typically achieved by weighted averaging of particle states and parameters. Application Scenarios Target tracking (e.g., robot localization) Financial time series analysis Complex sensor fusion systems Advantages and Limitations Advantages: Higher computational efficiency and smaller variance compared to standard PF; capability to handle non-Gaussian noise and nonlinear models compared to pure KF. Limitations: Still affected by particle count; high-dimensional nonlinear parts may require large numbers of particles. Implementation Notes: Optimize MATLAB matrix operations for real-time performance, and recommend starting with simplified models to validate algorithm logic before scaling to complex applications. Consider using vectorized operations and preallocation for efficiency.