Convolution particle filtering for parameter estimation in general state-space models

The state-space modeling of partially observed dynamic systems generally requires estimates of unknown parameters. From a practical point of view, it is relevant in such filtering contexts to simultaneously estimate the unknown states and parameters. Efficient simulation-based methods using convolution particle filters are proposed. The regularization properties of these filters is well suited, given the context of parameter estimation. Firstly the usual non Bayesian statistical estimates are considered: the conditional least squares estimate (CLSE) and the maximum likelihood estimate (MLE). Secondly, in a Bayesian context, a Monte Carlo type method is presented. Finally we present a simulated case study

[1]  N. Gordon A hybrid bootstrap filter for target tracking in clutter , 1997 .

[2]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[3]  M. West Approximating posterior distributions by mixtures , 1993 .

[4]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[5]  James Ting-Ho Lo,et al.  Synthetic approach to optimal filtering , 1994, IEEE Trans. Neural Networks.

[6]  Luc Devroye,et al.  Combinatorial methods in density estimation , 2001, Springer series in statistics.

[7]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[8]  G. Kitagawa Non-Gaussian State—Space Modeling of Nonstationary Time Series , 1987 .

[9]  T. Brehard,et al.  Hierarchical particle filter for bearings-only tracking , 2007, IEEE Transactions on Aerospace and Electronic Systems.

[10]  W. Gilks,et al.  Following a moving target—Monte Carlo inference for dynamic Bayesian models , 2001 .

[11]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[12]  Paul I. Nelson,et al.  On Conditional Least Squares Estimation for Stochastic Processes , 1978 .

[13]  Laurent Miclo,et al.  A Moran particle system approximation of Feynman-Kac formulae , 2000 .

[14]  Jean-Pierre Vila,et al.  Nonlinear filtering in discrete time : A particle convolution approach , 2006 .

[15]  T. Higuchi Monte carlo filter using the genetic algorithm operators , 1997 .

[16]  Christian Musso,et al.  Improving Regularised Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[17]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[18]  L. Mevel,et al.  Recursive maximum likelihood estimation for structural health monitoring: tangent filter implementations , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[19]  V. Aidala,et al.  Utilization of modified polar coordinates for bearings-only tracking , 1983 .

[20]  Charles J. Geyer,et al.  Estimation and Optimization of Functions , 1996 .

[21]  Hans R. Künsch,et al.  Approximating and Maximising the Likelihood for a General State-Space Model , 2001, Sequential Monte Carlo Methods in Practice.

[22]  Pierre Del Moral,et al.  Feynman-Kac formulae , 2004 .

[23]  H. Tong Non-linear time series. A dynamical system approach , 1990 .

[24]  P. Protter,et al.  The Monte-Carlo method for filtering with discrete-time observations , 2001 .

[25]  Branko Ristic,et al.  Bearings-Only Tracking of Manoeuvring Targets Using Particle Filters , 2004, EURASIP J. Adv. Signal Process..

[26]  G. Kitagawa Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[27]  Michael A. West,et al.  Combined Parameter and State Estimation in Simulation-Based Filtering , 2001, Sequential Monte Carlo Methods in Practice.

[28]  Pierre Del Moral Feynman-Kac and Interacting Particle Recipes , 2004 .

[29]  M. Schervish Theory of Statistics , 1995 .

[30]  G. Storvik Particle filters in state space models with the presence of unknown static parameters YYYY No org found YYY , 2000 .

[31]  F. LeGland,et al.  A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals , 2003 .

[32]  Dominic S. Lee,et al.  A particle algorithm for sequential Bayesian parameter estimation and model selection , 2002, IEEE Trans. Signal Process..

[33]  A. Doucet,et al.  Parameter estimation in general state-space models using particle methods , 2003 .

[34]  Eric Moulines,et al.  Inference in hidden Markov models , 2010, Springer series in statistics.