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For regular particle filter algorithm or Sequential Monte Carlo (SMC)methods, the initial weights are traditionally dependent on the proposeddistribution, the posterior distribution at the current timestamp in thesampled sequence, and the target is the posterior distribution of the previoustimestamp. This is technically correct, but leads to algorithms which usuallyhave practical issues with degeneracy, where all particles eventually collapseonto a single particle. In this paper, we propose and evaluate using $k$ meansclustering to attack and even take advantage of this degeneracy. Specifically,we propose a Stochastic SMC algorithm which initializes the set of $k$ means,providing the initial centers chosen from the collapsed particles. To fightagainst degeneracy, we adjust the regular SMC weights, mediated by clusterproportions, and then correct them to retain the same expectation as before. Weexperimentally demonstrate that our approach has better performance thanvanilla algorithms.

$k$-means: Fighting against Degeneracy in Sequential Monte Carlo with an Application to Tracking