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Bayesian Estimation and Tracking: A Practical Guide by Anton J. Haug

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16.2 Resampling and Regularization (Move) for SIS Particle Filters

The SIS sample degeneracy problem can be moderated by a process called resampling. The basic idea of resampling is to eliminate state space particles with small weights by replacing them with replicated values of particles with larger weights. For this process, the weights are treated as a one-dimensional discrete probability distribution and the inverse transform method [1, 2] is used to resample the particles associated with the inverse of the cumulative distribution of the weights.

However, this leads to a new problem, a loss of diversity among the particles, since the resultant sample set will contain many repeated particles for any given weight. This problem has been labeled in the literature as sample impoverishment. In severe cases, all particles migrate to one sample point. To rectify the sample impoverishment due to resampling, after each resampling process a kernel density estimate of the particle density can be used to resample the particles a second time. In this process, each new particle (Monte Carlo sample) is selected from the resampled particles based on a draw from a uniform distribution and then the sample point is moved a small amount based on a draw from the local kernel. This process tends to concentrate the particles in the region of highest probability and separates them in a random fashion. This method of reducing sample impoverishment is called regularization [3] and constitutes the move ...

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