Independent Resampling Sequential Monte Carlo Algorithms

• Published in: IEEE transactions on signal processing Vol. 65; no. 20; pp. 5318 - 5333
• Main Authors: Lamberti, Roland, Petetin, Yohan, Desbouvries, Francois, Septier, Francois
• Format: Journal Article
• Language: English
• Published: IEEE 15.10.2017; Institute of Electrical and Electronics Engineers
• Subjects: Approximation algorithms; auxiliary particle filter; Computational modeling; Engineering Sciences; importance sampling; Manganese; Monte Carlo methods; Particle filters; Probability density function; resampling; Sequential Monte Carlo algorithms; Signal and Image processing; Signal processing algorithms; Auxiliary particle filter; Particle filters; Sequential Monte Carlo algorithms; Resampling; Importance sampling
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2017.2726971

Sequential Monte Carlo algorithms, or particle filters, are Bayesian filtering algorithms, which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on importance sampling with a bootstrap resampling step, which aims at struggling against weight degeneracy. However, in some situations (informative measurements, high-dimensional model), the resampling step can prove inefficient. In this paper, we revisit the fundamental resampling mechanism, which leads us back to Rubin's static resampling mechanism. We propose an alternative rejuvenation scheme in which the resampled particles share the same marginal distribution as in the classical setup, but are now independent. This set of independent particles provides a new alternative to compute a moment of the target distribution and the resulting estimate is analyzed through a CLT. We next adapt our results to the dynamic case and propose a particle filtering algorithm based on independent resampling. This algorithm can be seen as a particular auxiliary particle filter algorithm with a relevant choice of the first-stage weights and instrumental distributions. Finally, we validate our results via simulations, which carefully take into account the computational budget.