TY - GEN
T1 - A non asymptotical analysis of the optimal SIR algorithm vs. the fully adapted auxiliary particle filter
AU - Desbouvries, François
AU - Petetin, Yohan
AU - Monfrini, Emmanuel
PY - 2011/9/5
Y1 - 2011/9/5
N2 - Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques for estimating the a posteriori filtering probability density function (pdf) in a Hidden Markov Chain (HMC). These algorithms have been theoretically analysed from an asymptotical statistics perspective. In this paper we provide a non asymptotical, finite number of samples comparative analysis of two particular SMC algorithms : the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID), and the fully adapted APF (FA). Starting from a common set of N particles, we compute closed form expressions of the mean and variance of the empirical Monte Carlo (MC) estimators of a moment of the a posteriori filtering pdf. Both algorithms have the same mean, but in the case where resampling is used, the variance of the SIR algorithm always exceeds that of the FA algorithm.
AB - Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques for estimating the a posteriori filtering probability density function (pdf) in a Hidden Markov Chain (HMC). These algorithms have been theoretically analysed from an asymptotical statistics perspective. In this paper we provide a non asymptotical, finite number of samples comparative analysis of two particular SMC algorithms : the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID), and the fully adapted APF (FA). Starting from a common set of N particles, we compute closed form expressions of the mean and variance of the empirical Monte Carlo (MC) estimators of a moment of the a posteriori filtering pdf. Both algorithms have the same mean, but in the case where resampling is used, the variance of the SIR algorithm always exceeds that of the FA algorithm.
KW - Auxiliary Particle Filtering
KW - Sequential Monte Carlo
KW - non asymptotical analysis
U2 - 10.1109/SSP.2011.5967662
DO - 10.1109/SSP.2011.5967662
M3 - Conference contribution
AN - SCOPUS:80052210947
SN - 9781457705700
T3 - IEEE Workshop on Statistical Signal Processing Proceedings
SP - 213
EP - 216
BT - 2011 IEEE Statistical Signal Processing Workshop, SSP 2011
T2 - 2011 IEEE Statistical Signal Processing Workshop, SSP 2011
Y2 - 28 June 2011 through 30 June 2011
ER -