@article{Zoubir2010,
title = {Analysis of a Sequential Monte Carlo Method for Optimization in Dynamical Systems},
author = {Zoubir, A. and Viberg, M. and Yang, B. and Miguez, Joaquin},
url = {http://www.sciencedirect.com/science/article/pii/S0165168409004708},
year = {2010},
date = {2010-01-01},
journal = {Signal Processing},
volume = {90},
number = {5},
pages = {1609--1622},
abstract = {We investigate a recently proposed sequential Monte Carlo methodology for recursively tracking the minima of a cost function that evolves with time. These methods, subsequently referred to as sequential Monte Carlo minimization (SMCM) procedures, have an algorithmic structure similar to particle filters: they involve the generation of random paths in the space of the signal of interest (SoI), the stochastic selection of the fittest paths and the ranking of the survivors according to their cost. In this paper, we propose an extension of the original SMCM methodology (that makes it applicable to a broader class of cost functions) and introduce an asymptotic-convergence analysis. Our analytical results are based on simple induction arguments and show how the SoI-estimates computed by a SMCM algorithm converge, in probability, to a sequence of minimizers of the cost function. We illustrate these results by means of two computer simulation examples.},
keywords = {Dynamic optimization, Nonlinear dynamics, Nonlinear tracking, Sequential Monte Carlo, Stochastic optimization},
pubstate = {published},
tppubtype = {article}
}

We investigate a recently proposed sequential Monte Carlo methodology for recursively tracking the minima of a cost function that evolves with time. These methods, subsequently referred to as sequential Monte Carlo minimization (SMCM) procedures, have an algorithmic structure similar to particle filters: they involve the generation of random paths in the space of the signal of interest (SoI), the stochastic selection of the fittest paths and the ranking of the survivors according to their cost. In this paper, we propose an extension of the original SMCM methodology (that makes it applicable to a broader class of cost functions) and introduce an asymptotic-convergence analysis. Our analytical results are based on simple induction arguments and show how the SoI-estimates computed by a SMCM algorithm converge, in probability, to a sequence of minimizers of the cost function. We illustrate these results by means of two computer simulation examples.

@inproceedings{Maiz2009,
title = {Particle Filtering in the Presence of Outliers},
author = {Maiz, Cristina S. and Miguez, Joaquin and Djuric, Petar M.},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278645},
isbn = {978-1-4244-2709-3},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},
pages = {33--36},
publisher = {IEEE},
address = {Cardiff},
abstract = {Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different from the assumed model of the data. Therefore, when handled in the same way as regular observations, outliers may drastically degrade the performance of the particle filter. To address this problem, we introduce an auxiliary particle filtering scheme that incorporates an outlier detection step. We propose to implement it by means of a test involving statistics of the predictive distributions of the observations. Specifically, we investigate the use of a proposed statistic called spatial depth that can easily be applied to multidimensional random variates. The performance of the resulting algorithm is assessed by computer simulations of target tracking based on signal-power observations.},
keywords = {computer simulations, Degradation, Filtering, multidimensional random variates, Multidimensional signal processing, Multidimensional systems, Nonlinear tracking, Outlier detection, predictive distributions, Signal processing, signal processing tools, signal-power observations, spatial depth, statistical analysis, statistical distributions, statistics, Target tracking, Testing},
pubstate = {published},
tppubtype = {inproceedings}
}

Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different from the assumed model of the data. Therefore, when handled in the same way as regular observations, outliers may drastically degrade the performance of the particle filter. To address this problem, we introduce an auxiliary particle filtering scheme that incorporates an outlier detection step. We propose to implement it by means of a test involving statistics of the predictive distributions of the observations. Specifically, we investigate the use of a proposed statistic called spatial depth that can easily be applied to multidimensional random variates. The performance of the resulting algorithm is assessed by computer simulations of target tracking based on signal-power observations.