Rao-Blackwellised粒子滤波器（RBPF）是一种提高采样方法精度的技术，通过解析边缘化某些变量来优化估计。在高维状态空间中，RBPF通过结合解析方法和粒子滤波降低采样维度，常用于解决如SLAM等复杂问题。FastSLAM算法是RBPF在机器人定位和环境建模中的应用，结合了EKF和粒子滤波的优势，提供了一种高效且鲁棒的解决方案。
1. Rao-Blackwellisation is a general technique for improving the accuracy of sampling methods by analytically marginalizing some variables and only sampling the remainder. In its simplest form, consider the problem of estimating the expectation E [f(x)], where x is a joint product of two variables r,z.
Using direct Monte-Carlo sampling, we obtain the estimator:
lternatively, a Rao-Blackwellised estimator can be derived by sampling only the variable r, with the other variable z, being integrated out analytically:
where
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