Rao－Blackwellised粒子滤波器(RBPF)
1. Rao-Blackwellisation is a general technique for improving the accuracyof sampling methods by analytically marginalizing some variables andonly sampling the remainder. In its simplest form, consider the problemof estimating the expectation E , where x is a joint product oftwo variables r,z.Using direct Monte-Carlo sampling, we obtain the estimator:
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lternatively, a Rao-Blackwellised estimator can be derived by samplingonly the variable r, with the other variable z, being integrated outanalytically:
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where
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For our convenience, r will be referred to as the Rao-Blackwellising variable. The Rao-Blackwellised estimator \hat{f}_{RB} is generally more accurate than \hat{f} for the same number of samples N.
From :http://www.djp3.net/codexcaelestis/archives/2004/07/what_exactly_is.html
2. 在高维状态空间中采样时,PF的效率很低。对某些状态空间模型，状态向量的一部分在其余部分的条件下的后验分布可以用解析方法求得，例如某些状态是条件线性高斯模型，可用Kalman滤波器得到条件后验分布，对另外部分状态用PF，从而得到一种混合滤波器，降低了PF采样空间的维数，RBPF样本的重要性权的方差远远低于SIR方法的权的方差，为使用粒子滤波器解决SLAM问题提供了理论基础。而Montemerlo等人在2002年首次将Rao-Blackwellised粒子滤波器应用到机器人SLAM中，并取名为FastSLAM算法。该算法将SLAM问题分解成机器人定位问题和基于位姿估计的环境特征位置估计问题，用粒子滤波算法做整个路径的位姿估计，用EKF估计环境特征的位置，每一个EKF对应一个环境特征。该方法融合EKF和概率方法的优点，既降低了计算的复杂度，又具有较好的鲁棒性。
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