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Feynman-Kac measures and Interacting Particle systems :

Selected applications on Filtering, Systems, & Advanced Signal Processing

(see also : selected studies, publications & MLSS 08 Lecture notes, 2011-Sino-French Summer Institute (lecture 1, lecture 2, and lecture 3) & other application areas)

This webpage presents a selected series of articles related to particle filters and some of their application domains, including

Robotics
Image Processing
Audio Signals
Tracking, positioning
GPS/INS Integration
Fluids Mechanics, data assimilation, and forecasting
Optical tomography
Multiple target tracking
The list is far from being exhaustive, and it is partially biased towards my work on stochastic particle algorithms. More references and links to this subject can be added on demand. This webpage also contains some articles on the particle filter methodology, and the performance analysis of these algorithms.

Software BiiPS

The software BIIPS is a general software developed by the INRIA team ALEA for bayesian inference with interacting particle systems, a.k.a. Sequential Monte Carlo methods. A demonstration of the BiiPS software for estimating the stochastic volatility of financial data can be found in

BIIPS : Bayesian inference with interacting Particle Systems in Finance,

INRIA project manager : F. Caron, Design and developement engineer : A. Todeschini, Project contributors : P. Del Moral & P. Legrand, Logo designer : Timothée Del Moral.

Particle filtering, some projects websites

Advanced Learning Evolutionary Algorithms (ALEA project, Centre INRIA Bordeaux Sud-Ouest)
Applications of Interacting Particle Systems to Statistics (IRISA, INRIA Rennes)
Sequential Learning (SEQUEL project, INRIA Futurs Lille)
Sequential Monte Carlo homepage, particle filtering (Elena Punskaya , Department of Engineering, Cambridge University)
Sequential Monte Carlo Methods & Particle Filters Resources (Arnaud Doucet , Department of Statistics, Oxford University)

Trends in Systems and Signals (Annual Review in Control, Status report IFAC 2006, Coordinating Committee)

Some Videos in YouTube

Robotics	Nao particle filter	Tracking soccer players	Pacman particle filter	Ping Pong	Rubiks cube	Mario particle filter	Indoor tracking
Slam 1	Slam 2	Pattern recognition	Odor source localization	Real time tracking	Multiple touch tracking	Robot navigation	People tracking
People tracking 1	People tracking 2	Active tracking	Visual tracking	Multiple target tracking	Multiple lane tracking	Tracking a car	Multiple lane tracking

Recent tutorials & Surveys

Pierre Del Moral, Peng Hu, Liming Wu
On the concentration properties of Interacting particle processes HAL-INRIA RR-7677 (2011),
Foundations and Trends in Machine Learning, Vol. 3, No. 3 - 4, 225-389 (2012). (online article, 167 pages)
Particle Methods: An introduction with applications (Pierre Del Moral, Arnaud Doucet) HAL-INRIA RR-6991 [50p] (2009).
2008 Machine Learning Summer School, Springer LNCS/LNAI Tutorial book no. 6368 (2010-2011).
Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering
(Del Moral P., Miclo L.) Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor.
Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).
A Mean Field Theory of Nonlinear Filtering (P. Del Moral, F. Patras, & S. Rubenthaler)
The Oxford Handbook of Nonlinear Filtering, Oxford University Press, 2011
A Tutorial on Particle Filtering and Smoothing: Fifteen years later (A. Doucet, A. Johansen, 2008)
An overview of existing methods and recent advances in sequential Monte Carlo (Olivier Cappe, Simon J. Godsill and Eric Moulines)
Filtering Methods (Andras Fulop, ESSEC Business School, Paris)

A series of recent tutorials presenting this interacting particle methodology in a more general framework are provided below
- Horizon Maths, Les maths se devoilent aux industriels; Fondation Science Maths de Paris, Tour AREVA, dec. 2011.
  (programme) ( lecture notes (in french) & the presentation video (in french) )
- Sino-French Summer Institute 2011.Beijing, China, June 13-25, 2011. ((lecture note 1), (lecture note 2), and (lecture note 3))
- INRIA Workshop on Statistical Learning Institut Henri Poincaré Paris, December 5-6, 2011 ( (lecture notes) )
- Isaac Newton Institute for Mathematical Sciences, Workshop on filtering. June 2010 (lecture notes) & (presentation video)
- University of Cambridge, Statistics Laboratory seminar, Feb. 2010. (lecture notes)
- 10th Machine Learning summer school, September 1-15th, 2008. (lecture notes)
- Opening workshop, Sequential Monte Carlo Methods, SAMSI, Duke Univ. September 7-10th, 2008. (lecture notes)
Ph.D. thesis
Modélisation probabiliste des écoulements atmosphériques turbulents afin d'en filtrer la mesure par approche particulaire (Christophe Baehr, Ph.D. thesis, Paul Sabatier University, 2008)
Rao-Blackwellised particle methods for inference and identification (Fredrik Lindsten, Ph.D. thesis , Linkoping studies in science and technology 2011)
Some statistical topics on sequential data assimilation (Lui Chiu Sing Gilbert Ph.D. thesis The University of Hong Kong 2008)
Observations bruitees d?une diffusion Estimation, filtrage, applications (Benjamin Favetto, Ph. D. Univ. Paris Descartes 2010)
Grey-Box Modelling for Nonlinear Systems (Jan Hauth, Ph.D. thesis 2008)
Prevision locale de faible visibilite (Ph.D; Samuel Remy, Univ. Paul Sabatier, Toulouse 2009)

Robotics
Particle filtering in Robotics (Dieter Fox, Mobile Robotics Research Labratory, Washington University)
Real Time Particle Filters (C. Kwok, D. Fox, M. Meila, Washington University)
Multi-robot Simultaneaous Localization and Mapping using Particle Filters (A. Howard; NASA Jet Propulsion Lab.)
Particle Filters for Rover Fault Diagnosis (V. Verma, G. Gordon, S; Simmons, S. Thrun; Stanford Univ. and Carnegie Mellon Univ.)

Image Processing
Interacting and Annealing Particle Filters: Mathematics and a Recipe for Applications (Jurgen Gall, Jurgen Potthoff, Christoph Schnorr-Bodo Rosenhahn, Hans-Peter Seidel, 2007)
2D Action Recognition Serves 3D Human Pose Estimation (Jurgen Gall, Angela Yao, and Luc Van Gool, Computer Vision Laboratory, ETH Zurich, Switzerland)
Visual tracking using Particle Filters (Peter Torma and Csaba Szepesvari, Budapest University)
Color-Based Fingertip Tracking Using Modified Dynamic Model Particle Filtering Method (Ting Zhu, Ph.D., The Ohio State University 2011 )
Automated detection and time lapse analysis of dendritic spines in laser scanning microscopy images(Jie Cheng, Ph.D. thesis Northeastern University, 2009)
Particle filters in body motion tracking (J. Gall, J. Potthoff and C. Schnoerr; Max Planck Institute and Mannheim Univ.)
Particle Belief Propagation (Alexander Ihler, David McAllester, 2009)
Real Time Pedestrian Tracking using Thermal Infrared Imagery (Jianfu Li, Weiguo Gong; Chongqing University 2010)
Combining Local Search, Neural Networks and Particle Filters to Achieve Fast and Reliable Contour Tracking P. Torma and C. Szepesvari; Budapest Univ.
Interacting and Annealing Particle Filters: Mathematics and a Recipe for Applications (J. Gall, J. Potthoff, B. Rosenhan, H.P. Seidel and C. Schnoerr; Max Planck Institute and Mannheim Univ.)
Tracking, Image processing (Michael Isard, Engineering Science Department, Oxford University)
Filtre Conditionnel pour le Suivi de Point dans des Sequences d'Images (E. Arnaud, E. Memin, B. Cernuschi-Frias; IRISA INRIA Rennes and Buenos Aires Univ.)
A Rao-Blawellized Particle Filter for Eigen Tracking (Z. Khan, T. Balch, F. Dellaert; Georgia Institute of Technology College of Computing)
An MCMC Based Particle Filter for Tracking Multiple Interacting Targets (Z. Khan, T. Balch, F. Dellaert; Georgia Institute of Technology College of Computing)

Audio Signal
Méhodes Monte Carlo Séquentielles Pour l'Analyse Spectrale Bayesienne. (M. Davy and P. Del Moral and A. Doucet; CNRS, Nice Sophia Antopolis Univ., UBC Vancouver )
A Particle Filter for Model Based Audio Source Separation (C. Andrieu, S.J. Godsill; Cambridge Univ. )
Particle Methods for Bayesian Modeling and Enhancement of Speech Signals (J. Vermaak, C. Andrieu, A. Doucet, S.J. Godsill; Cambridge Univ. )
Language-based feedback control using Monte Carlo Sensing (Sean B. Andersson, Dimitrios Hristu-Varsakelis, 2005)

Tracking, positioning
Tracking Mobile Phones in Urban Areas (Christer Akerblom, Chalmers and Goteborg University)
Statistical Data Fusion for Hybrid Localization of Mobile Terminals (Carsten Fritsche PhD. thesis, Darmstadt University 2011)
Monte Carlo methods for signal processing in wireless sensor networks (Mahesh Vemula, PhD. thesis, Stony Brook 2007)
Sensor fusion, positioning, navigation, tracking (Fredrik Gustafsson, Control and Communication division - Linkoping University)
Particle Filter Theory and Practice with Positioning Applications (Fredrik Gustafsson, Control and Communication division - Linkoping University, 2010)
Inferring high-level behavior from low-level sensors (D.J. Patterson, L. Liao, D. Fox, H. Kautz; Washington Univ.)
A Kalman-Particle Kernel Filter and its Application to Terrain Navigation (Dinh-Tuan Pham, Karim Dahia, Chalmers and Christian Musso, 2003)
Suivi de Trajectoires Temps-Frequence par Filtrage Particulaire (C. Dubois, M. Davy; Nantes Univ.)
Simulation-based optimal sensor scheduling with application to observer trajectory planning (Sumeetpal S. Singh, Nikolaos Kantas, Ba-Ngu Vob, Arnaud Doucet, Robin J. Evans, 2006)
Nouvelles methodes en filtrage particulaire Application au recalage de navigation inertielle par mesures altimetriques (Karim Dahia, Ph.D. thesis, Univ. J. Fourier 2005)
Approximate Nonlinear Filtering and its Application in Navigation (B. Azimi-Sadjadiyz and P.S. Krishnaprasad 2002)
Etude statistique du probleme de la trajectographie passive (B. Landelle, Ph. D. thesis, Orsay Univ. 2009)
The Value of Observation for Monitoring Dynamic Systems (Eyal Even-Dar, Sham M. Kakade, Yishay Mansour)
Filtering, Objects tracking (Michael Koutizin, PINTS, Mathematics of Information Technology and Complex Systems, Alberta University)
Tracking Multiple Objects with Particle Filtering (C. Hue, J.P. Le Cadre, P. Perez, IRISA-INRIA Rennes)
Change detection for nonlinear systems; a particle filtering approach (B. Azimi-Sadjadi, P.S. Krishnaprasad, Univ. Maryland)
Particle filtering of RADAR Video Signals for pointwise targets (J.C. Noyer, G. Salut LAAS-CNRS Toulouse)
Particle resolution and non-linear signal : processing with RADAR/SONAR applications Del Moral P., J.C. Noyer, G. Rigal, Salut G.(LAAS-CNRS Toulouse)
Optimal Policies Search for Sensor Management : Application to the ESA Radar (Th. Brehard, E. Duflos Ph. Vanheeghe, P.A. Coquelin, INRIA 2009)
Particle Filtering of Radar Signals for Non-Cooperating Target Imaging M.A. Chamon Salut G. (INPE Brasil and LAAS-CNRS Toulouse)
Particle Methods in Filtering and Finance R. Carmona (Princeton-Bendheim Center for Finance)
A Particle Filtering Approach to Change Detection for Nonlinear Systems (B. Azimi-Sadjadi, P.S. Krishnaprasad; Maryland Univ.)

GPS/INS Integration
Approximate nonlinear filtering and its applications to GPS B. Azimi-Sadjani and P.S. Krishnaprasad (Maryland Univ. 2000)
A Novel Data Fusion Approach in an Integrated GPS/INS System using Adaptive Fuzzy Particle Filter (A. Asadian, B. Moshiri, A.K. Sedigh; Dpt. Electrical Engineering Tehran Univ)
Fusion de Capteurs Potentiellement Defaillants par Filtrage Particulaire. Application au Positionnement par GPS d'un Vehicule Terrestre (F. Caron, M. Davy, E. Duflos, Ph. Vanheeghe; LAGIS CNRS Lille)
Optimal nonlinear filtering in GPS/INS integration Carvalho H., Del Moral P., Monin A., Salut G. (LAAS-CNRS Toulouse)

Fluids Mechanics, data assimilation, forecasting
Some issues and results on the EnKF and Particle Filters for meteorological models (C. Baehr, O. Pannekoucke, Meteo France Toulouse)
A Stochastic Filtering Technique for Fluid Flow Velocity Fields Tracking (A. Cuzol, E. Memin, 2009)
Filtering complex turbulent systems (Andrew J. Majda, John Harlim; Center for Atmosphere and Ocean Sciences, Courant Institute, and North Carolina University)
Suivi de mouvement fluide par filtrage stochastique (A. Cuzol, E. Memin, IRISA)
Filtrage des vitesses d'un fluide. Estimation particulaire par modele markovien conditionnel vs modele a priori (C. Baehr, Meteo France Toulouse)
Modelisation et Filtrage non-lineaire des mesures discretes sur un fluide turbulent. Application au debruitage des mesures du vent atmospherique (C. Baehr, Meteo France Toulouse, 2008)
Prevision locale de faible visibilite (Ph.D; Samuel Remy, Univ. Paul Sabatier, Toulouse 2009)
Stochastic modeling and filtering of discrete measurements for a turbulent field. Application to measurements of atmospheric wind. (Ch. Baehr, Meteo-France-CNRS; International Journal of Modern Physics B 2008)

Optical tomography
Solutions for diffuse optical tomography using the Feynman-Kac formula and interacting particle method (Nannan Cao, Mathias Ortner, and Arye Nehorai, Department of Electrical and Systems Engineering, Washington University)

Multiple target tracking
On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering (Fr. Caron, P. Del Moral M. Pace, Ba-Ngu Vo, Stoch. An. and Appl. 2011)
Particle approximations of a class of branching distribution flows arising in multi-target tracking(Francois Caron, Pierre Del Moral, Arnaud Doucet, and Michele Pace) (HAL-INRIA RR-7233 (2010)) [29p], SIAM J. Control Optim. 49, pp. 1766-1792 (2011).
On the Conditional Distributions of Spatial Point Processes(Francois Caron, Pierre Del Moral, Arnaud Doucet, and Michele Pace) (HAL-INRIA RR-7232) Adv. in Appl. Probab. Volume 43, Number 2, 301-307. (2011).
Bayesian Filtering with Random Finite Set Observations (Ba-Tuong Vo, Ba-Ngu Vo, and Antonio Cantoni 2008)
Auxiliary Particle Implementation of the Probability Hypothesis Density Filter (Nick Whiteley, Sumeetpal Singh Simon Godsill)
Sequential Monte Carlo methods for Multi-target Filtering with Random Finite Sets (Ba-Ngu Vo, Sumeetpal Singh, and Arnaud Doucet 2005)
Multiple Target Tracking With Constrained Motion Using Particle Filtering Methods (Ioannis Kyriakides, Ph.D. thesis, Univ. Arizona 2005)
Integration du contexte par reseaux bayesiens pour la detection et le suivi multi-cibles (Bassem Jida, Ph.D. thesis, Univ. du Littoral 2008)

Particle filters, methodology
Sequential Monte Carlo Methods for Bayesian Filtering (Andreas Storksen Stordal, Ph.D. thesis 2008)
Particle filtering within adaptive Metropolis-Hastings sampling (Ralph S. Silva, Paolo Giordani, Robert Kohn, Michael K. Pitt, 2009 )
Iterated Filters (Edward L. Ionides, Anindya Bhadra, and Aaron King, The University of Michigan 2009)
Particle Filter-based Policy Gradient in POMDPs (Pierre-Arnaud Coquelin, Romain Deguest, Remi Munos, CMAP et INRIA Lille)
Computation of information rates by particle filters (Justin Dauwels, Hans-Andrea Loeliger, IEEE Trans. Info. th. 2008 )
Framework for online sur-imposed event detection by sequential Monte Carlo methods (O. Urfalioglu, Ercan E. Kuruoglu, and A. Enis Cetin Ankara and Pisa Univ. )
Change Detection in Partially Observed Nonlinear Dynamic Systems with Unknown Change Parameters (Namrata Vaswani, University of Maryland)
Learning and Filtering via simulation: smoothly jittered particle Filters (Thomas Flury, Neil Shephard 2009)
Nonlinear filtering in discrete time : A particle convolution approach (Vivien Rossi and Jean-Pierre Vila)
Inference and Estimation in Probabilistic Time-Series Models (Isaac Newton Institute, June 2008)
On Adaptive Resampling Procedures for Sequential Monte Carlo Methods (joint work with Arnaud Doucet, Ajay Jasra)
Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC (Paul Fearnhead Department of Mathematics and Statistics Lancaster University)
Particle Filters for State and Parameter Estimation of Cox Process (Omiros Papaspiliopoulos, Miguel A. G. Belmonte, and Michael K. Pitt, University of Warwick)
Smoothing algorithms for state-space models (Mark Briers, Arnaud Doucet, Simon Maskell 2010)
Efficient Filtering in State-Space Representations (David N. DeJong, Roman Liesenfeld, Hariharan Dharmarajan, Jean-Francois Richard, 2008)
Particle Filters for Partially Observed Diffusions (Paul Fearnhead, Omiros Papaspiliopoulos, and Gareth O. Roberts, 2008)
Nonlinear filtering for stochastic systems with fixed delay: approximation by a modified Milstein scheme (Antonella Calzolari, Patrick Florchinger, and Giovanna Nappo)
A Maximum Entropy Method for Particle Filtering (Gregory L. Eyink, and Sangil Kimy, University, Baltimore and University of Arizona)
Variance Reduction for Particle Filters of Systems with Time Scale Separation (Dror Givon, Panagiotis Stinis, and Jonathan Weare, 2008)
Generalized particle filters with Gaussian mixture (D. Crisan, K. Li, Imperial College 2011)
Filtrage non lineaire en temps discret par convolution de particules (Vivien Rossi, Jean-Pierre Vila, 2003)
Introducing the Laplace approximation in particle filtering (Ch. Musso, P.B. Quang, Fr. Le Gland, 2011)
Filtrage Particulaire (in french) (F. Le Gland; IRISA INRIA Rennes)
A sequential Particle Algorithm that keeps the Particle System Alive (F. Le Gland and N. Oudjane, IRISA INRIA Rennes, et EDF Division Rercherche et Developpement)
Niching in Monte Carlo Filtering Algorithms (A. Bienvenue, M. Joannides, J. Berard, E. Fontenas, O. Francois; Grenoble and Lyon Univ.)
Stochastic Particle Methods for Linear Tangent Filtering Equations (F. Cerou, F. Le Gland, N. Newton; IRISA INRIA Rennes and Essex Univ.).
Adapting the sample size in Particle Filters Through KLD-Sampling (D. Fox, Washinton Univ.)
Particle Filters for Partially Observed Diffusions (P. Fernhead, O. Papaspiliopoulos, G.0. Roberts; Lancaster Univ.)
On Sequential Monte Carlo Sampling of Discretely Observed Stochastic Differential Equations (Simo Sarkka, Helsinki Univ.)
Comparison of Resampling Schemes for Particle Filtering (A. Douc, E. Moulines, O. Cappe; Ecole Polytechnique, CNRS and ENST Paris)
Using Systematic Sampling for Approximating Feynman-Kac Solutions by Monte Carlo by Monte Carlo Methods (I. Gentil, B. Remillard; Dauphine Univ. Paris and HEC Montreal)
Particle approximation improvement of the joint smoothing distribution with on-the-fly variance estimation (Cyrille Dubarry, Randal Douc, TELECOM SudParis 2011).
Inference for Partially Observed Point Process Models (J.S. Martin, A. Jasra, E. McCoy).
A Branching Particle Approximation to the Filtering Problem with Counting Process Observations (Jie Xiong, Yong Zeng, 2006).
Optimal Filtering for Partially Observed Point Processes using Trans dimensional Sequential Monte Carlo (A. Doucet,L. Montesano, A. Jasra, UBC Univ., Vancouver, Zaragoza Univ., and Imperial College London)
Filtre Particulaire Parallele (V. Teuliere, O. Brun; LAAS-CNRS Toulouse)
Efficient Likelihood Evaluation of State-Space Representations(David N. DeJong, Hariharan Dharmarajan, Roman Liesenfeld, Guilherme Moura, and Jean-Francois Richard, 2009)
Nearly Smooth Particle Filters for Likelihood Estimation with Multivariate Latent Variables(Anthony Lee, slides 2009)

Particle filters, performance analysis
Nonlinear Filtering : Interacting Particle Resolution.( Del Moral P., Markov Processes and Related Fields, vol. 2, no; 4, pp. 555-580, 1996)
Pierre Del Moral, Peng Hu, Liming Wu. On the concentration properties of Interacting particle processes
HAL-INRIA RR-7677 (2011) [122p], To appear in Foundations and Trends in Machine Learning (2011-2012).
Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering
(Del Moral P., Miclo L.) Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor. Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).
On the stability of interacting processes with applications to filtering and genetic algorithms (Del Moral P., Guionnet A. Annales de l'Institut Henri Poincaré, Vol. 37, No. 2, 155-194 (2001)).
An Analysis of Regularized Interacting Particle Methods for Nonlinear Filtering (F. Le Gland, C. Musso, N. Oudjane; IRISA INRIA Rennes, and ONERA)
Monte Carlo Smoothing for Nonlinear Time Series (Simon J. Godsill, Arnaud Doucet, and Mike West 2004)
A Robustification Approach to Stability and to Uniform Particle Approximation of Nonlinear Filters : the Example of Pseudo?Mixing Signals (F. Le Gland, N. Oudjane; IRISA INRIA Rennes 2002)
A Uniformly Convergent Adaptive Particle Filter (A. Papavasiliou, Columbia Univ.)
Rates for branching particle approximations of continuous-discrete filters (M.A. Kouritzin, W. Sun; Alberta Univ.)
Using Systematic Sampling for Approximating Feynman-Kac Solutions by Monte Carlo by Monte Carlo Methods (I. Gentil, B. Remillard; Dauphine Univ. Paris and HEC Montreal)
Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications Del Moral P., Springer New York; Springer Heidelberg,
Series: Probability and its Applications, [585 pages] (April 2004).
Generalized Annealed Particle Filter Mathematical Framework, Algorithms and Applications (Jurgen Gall, 2005)
On the stability of the discrete time filter and the uniform convergence of its approximations (K. Heine, Ph.D. thesis, Tempere University 2007)
On Adaptive Resampling Procedures for Sequential Monte Carlo Methods (joint work with Arnaud Doucet, Ajay Jasra, Statistics and Computing (2011))
Uniform time average consistency of Monte Carlo particle filters (R. Van Handel, Princeton Univ. 2009)
Basic Convergence Results for Particle Filtering Methods: Theory for the Users (Xiao-Li Hu, Thomas B. Schon, Lennart Ljung, 2009)
Optimality of the auxiliary particle filter (R. Douc, E. Moulines, J. Olsson 2009)
A non asymptotic variance theorem for unnormalized Feynman-Kac particle models Fr. Cerou, P. Del Moral, A. Guyader HAL-INRIA RR-6716 (2008) . Annales de l'Institut Henri Poincare Probab. Statist. Volume 47, Number 3, 629-649 (2011).
Strong consistency of Bayesian estimator under discrete observations and unknown transition density (A. Kohatsu-Higa, N. Vayatis, K.Yasuda, 2010)
Stability properties of some particle filters (N. Whiteley, Univ. Bristol 2011)