Core Implementation of Basic RBPF Particle Filter

The Rao-Blackwellized Particle Filter (RBPF) is a hybrid filtering method that combines sampling techniques with analytical computation, effectively addressing state estimation problems in nonlinear non-Gaussian systems. This algorithm finds extensive applications in target tracking and navigation fields, making it particularly suitable for beginners to understand the core concepts of probabilistic estimation.

The basic implementation typically consists of the following modules: First, initialize a set of random particles where each particle carries a state hypothesis and corresponding weight. In the prediction phase, particle states are propagated through motion models to simulate system dynamics. During the observation update phase, sensor data is utilized to adjust particle weights, embodying the "survival of the fittest" principle. The key innovation of RBPF lies in performing analytical computation for partial states rather than full sampling, significantly reducing computational complexity. Implementation-wise, this involves creating separate structures for sampled states (like discrete modes) and analytically tractable states (typically Gaussian components).

Typical application scenarios include robot localization (such as pose estimation in SLAM) and vehicle trajectory tracking. During implementation, special attention must be paid to particle degeneracy issues, commonly addressed through resampling strategies like systematic or stratified resampling to maintain particle diversity. For beginners, it's recommended to start with 2D planar tracking scenarios to gradually understand key concepts including probability distribution modeling and importance sampling. Code implementation typically involves defining particle structures with state vectors and weights, implementing motion model propagation using system equations, and designing observation likelihood functions based on sensor models.