Rao-Blackwellised particle methods for inference and identification

We consider the two related problems of state inference in nonlinear dynamical systems and nonlinear system identification. More precisely, based on noisy observations from some (in general) nonlin ...

[1]  T. Bayes.  An essay towards solving a problem in the doctrine of chances , 2003 .

[2]  Václav Šmídl,et al.  Forgetting in Marginalized Particle Filtering and its Relation to Forward Smoothing , 2011 .

[3]  Fredrik Lindsten,et al.  Identification of mixed linear/nonlinear state-space models , 2010, 49th IEEE Conference on Decision and Control (CDC).

[4]  Urban Forssell.  Properties and Usage of Closed-loop Identification Methods , 1997 .

[5]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..

[6]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[7]  I. Klein.  Planning for a Class of Sequential Control Problems , 1989 .

[8]  Jonas Callmer.  Topics in Localization and Mapping , 2011 .

[9]  P. Moral,et al.  On the stability of interacting processes with applications to filtering and genetic algorithms , 2001 .

[10]  Per Skoglar,et al.  Planning Methods for Aerial Exploration and Ground Target Tracking , 2009 .

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

[12]  Henrik Tidefelt.  Structural algorithms and perturbations in differential-algebraic equations , 2007 .

[13]  Václav Peterka,et al.  Bayesian system identification , 1979, Autom..

[14]  Andrew W. Moore,et al.  'N-Body' Problems in Statistical Learning , 2000, NIPS.

[15]  R. Douc,et al.  Limit theorems for weighted samples with applications to sequential Monte Carlo methods , 2008 .

[16]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[17]  M. Netto,et al.  A New Spline Algorithm for Non-Linear Filtering of Discrete Time Systems , 1978 .

[18]  Sumeetpal S. Singh,et al.  Forward Smoothing using Sequential Monte Carlo , 2010, 1012.5390.

[19]  T. McKelvey.  On State-Space Models in System Identification , 1994 .

[20]  Refik Soyer,et al.  Bayesian Methods for Nonlinear Classification and Regression , 2004, Technometrics.

[21]  H. Fortell.  Volterra and Algebraic Approaches to the Zero Dynamics , 1994 .

[22]  J. Sjöberg.  Some Results On Optimal Control for Nonlinear Descriptor Systems , 2006 .

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

[24]  P. Nordlund.  Sequential Monte Carlo Filters and Integrated Navigation , 2002 .

[25]  Larry S. Davis,et al.  Improved fast gauss transform and efficient kernel density estimation , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[26]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[27]  Fredrik Gustafsson,et al.  Particle Filters for Prediction of Chaos , 2003 .

[28]  Stephen M. Stigler,et al.  Thomas Bayes's Bayesian Inference , 1982 .

[29]  R. Douc,et al.  Optimality of the auxiliary particle filter , 2009 .

[30]  Ola Härkegård,et al.  Flight Control Design using Backstepping , 2001 .

[31]  Niclas Persson,et al.  Event Based Sampling with Application to Spectral Estimation , 2002 .

[32]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[33]  Frida Gunnarsson.  On Modeling and Control of Network Queue Dynamics , 2003 .

[34]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[35]  Krister Edström,et al.  Simulation of Mode Switching Systems Using Switched Bond Graphs , 1996 .

[36]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[37]  D. Blackwell.  Conditional Expectation and Unbiased Sequential Estimation , 1947 .

[38]  L. Ljung,et al.  Blind Identification of Wiener Models , 2011 .

[39]  Anders Skeppstedt.  Construction of composite models from large data-sets , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[40]  Daniel P. Huttenlocher,et al.  Efficient Graph-Based Image Segmentation , 2004, International Journal of Computer Vision.

[41]  P. Fearnhead,et al.  A sequential smoothing algorithm with linear computational cost. , 2010 .

[42]  A. Doucet,et al.  Monte Carlo Smoothing for Nonlinear Time Series , 2004, Journal of the American Statistical Association.

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

[44]  Jianjun Yin,et al.  The Marginal Rao-Blackwellized Particle Filter for Mixed Linear/Nonlinear State Space Models , 2007 .

[45]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[46]  Haikady N. Nagaraja,et al.  Inference in Hidden Markov Models , 2006, Technometrics.

[47]  Gert Malmberg.  A Study of Adaptive Control of Missiles , 1986 .

[48]  Mille Millnert,et al.  Vehicle size and orientation estimation using geometric fitting , 2001 .

[49]  Jan Palmqvist.  On Integrity Monitoring of Integrated Navigation Systems , 1997 .

[50]  Rikard Falkeborn.  Structure Exploitation in Semidefinite Programming for Control , 2010 .

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

[52]  Xiao-Li Hu,et al.  A General Convergence Result for Particle Filtering , 2011, IEEE Transactions on Signal Processing.

[53]  Thomas Bo Schön,et al.  An explicit variance reduction expression for the Rao-Blackwellised particle filter , 2011 .

[54]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[55]  Arnaud Doucet,et al.  Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation , 2009 .

[56]  Claes Olsson,et al.  Active Engine Vibration Isolation using Feedback Control , 2002 .

[57]  Simon J. Godsill,et al.  An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo , 2007, Proceedings of the IEEE.

[58]  A. Stenman.  Just-in-Time Models with Applications to Dynamical Systems , 1997 .

[59]  T. Andersson.  Concepts and Algorithms for Non-Linear System Identifiability , 1994 .

[60]  Brett Ninness,et al.  Bayesian system identification via Markov chain Monte Carlo techniques , 2010, Autom..

[61]  Thomas Bo Schön,et al.  Particle Filters for System Identification of State-Space Models Linear in Either Parameters or States , 2003 .

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

[63]  Christian Lundquist,et al.  Automotive Sensor Fusion for Situation Awareness , 2009 .

[64]  Torbjörn Wigren,et al.  Recursive prediction error identification using the nonlinear wiener model , 1993, Autom..

[65]  Thomas B. Schön,et al.  On computational methods for nonlinear estimation , 2003 .

[66]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[67]  Xiao-Li Hu,et al.  A Basic Convergence Result for Particle Filtering , 2008, IEEE Transactions on Signal Processing.

[68]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .

[69]  J. Sjöberg.  Regularization Issues in Neural Network Models of Dynamical Systems , 1993 .

[70]  Andreas Eidehall,et al.  An Automotive Lane Guidance System , 2004 .

[71]  Henrik Ohlsson,et al.  Geo-referencing for UAV navigation using environmental classification , 2010, 2010 IEEE International Conference on Robotics and Automation.

[72]  Fredrik Gustafsson,et al.  Statistical Sensor Fusion , 2013 .

[73]  José A. Romagnoli,et al.  Application of Wiener model predictive control (WMPC) to a pH neutralization experiment , 1999, IEEE Trans. Control. Syst. Technol..

[74]  R. Handel.  Uniform time average consistency of Monte Carlo particle filters , 2008, 0812.0350.

[75]  M. Jirstrand.  Algebraic Methods for Modeling and Design in Control , 1996 .

[76]  Ingela Lind.  Regressor Selection in System Identification using ANOVA , 2001 .

[77]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[78]  M. Eisen,et al.  Probability and its applications , 1975 .

[79]  Darrell Whitley,et al.  A genetic algorithm tutorial , 1994, Statistics and Computing.

[80]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[81]  Daniel Ankelhed,et al.  On low order controller synthesis using rational constraints , 2009 .

[82]  Thomas B. Schön,et al.  Marginalized particle filters for mixed linear/nonlinear state-space models , 2005, IEEE Transactions on Signal Processing.

[83]  A. Robinson.  A Comparison Between The Em And Subspace Identification Algorithms For Time-Invariant Linear Dynamic , 2000 .

[84]  F. Gustafsson.  Optimal Segmentation of Linear Regression Parameters , 1991 .

[85]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[86]  Thomas Bo Schön,et al.  Rao-Blackwellised particle smoothers for mixed linear / nonlinear state-space models , 2011 .

[87]  J. Gunnarsson.  On Modeling of Discrete Event Dynamic Systems : Using Symbolic Algebraic Methods , 1995 .

[88]  P. Fearnhead,et al.  Improved particle filter for nonlinear problems , 1999 .

[89]  K. Forsman.  Applications of Constructive Algebra to Control Problems , 1990 .

[90]  P. Fearnhead.  Using Random Quasi-Monte-Carlo Within Particle Filters, With Application to Financial Time Series , 2005 .

[91]  M. Loève.  Probability Theory II , 1978 .

[92]  M. J. Korenberg,et al.  The identification of nonlinear biological systems: Wiener and Hammerstein cascade models , 1986, Biological Cybernetics.

[93]  Måns Östring,et al.  Identification, Diagnosis, and Control of a Flexible Robot Arm , 2002 .

[94]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[95]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[96]  John P. Boyd,et al.  The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series , 2010, J. Comput. Phys..

[97]  R. Fisher.  001: On an Absolute Criterion for Fitting Frequency Curves. , 1912 .

[98]  K. Ståhl.  On the Frequency Domain Analysis of Nonlinear Systems , 1988 .

[99]  Jonas Gillberg,et al.  Methods for Frequency Domain Estimation of Continuous-Time Models , 2004 .

[100]  Kunio Takezawa.  Whiley Series in Probability and Statistics , 2005 .

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

[102]  Mats Viberg.  On the Adaptive Array Problem , 1987 .

[103]  Stig Moberg,et al.  Modeling and Control of Flexible Manipulators , 2007 .

[104]  Andrew W. Moore,et al.  Nonparametric Density Estimation: Toward Computational Tractability , 2003, SDM.

[105]  Simon J. Godsill,et al.  Monte Carlo smoothing with application to audio signal enhancement , 2002, IEEE Trans. Signal Process..

[106]  Jeroen D. Hol,et al.  Pose Estimation and Calibration Algorithms for Vision and Inertial Sensors , 2008 .

[107]  Christophe Andrieu,et al.  Particle methods for change detection, system identification, and control , 2004, Proceedings of the IEEE.

[108]  Arnaud Doucet,et al.  An overview of sequential Monte Carlo methods for parameter estimation in general state-space models , 2009 .

[109]  Johanna Wallén,et al.  On Kinematic Modelling and Iterative Learning Control of Industrial Robots , 2008 .

[110]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[111]  Rong Chen,et al.  A Theoretical Framework for Sequential Importance Sampling with Resampling , 2001, Sequential Monte Carlo Methods in Practice.

[112]  Pierre Del Moral,et al.  Discrete Filtering Using Branching and Interacting Particle Systems , 1998 .

[113]  Aurélien Garivier,et al.  Sequential Monte Carlo smoothing for general state space hidden Markov models , 2011, 1202.2945.

[114]  P. Moral.  Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications , 2004 .

[115]  Christian Lyzell,et al.  Initialization Methods for System Identification , 2009 .

[116]  Jakob Roll.  Robust Verification and Identification of Piecewise Affine Systems , 2001 .

[117]  L. Ljung,et al.  Wiener System Identification Using the Maximum Likelihood Method , 2010 .

[118]  M. Enqvist.  Some Results on Linear Models of Nonlinear Systems , 2003 .

[119]  David Törnqvist,et al.  Statistical Fault Detection with Applications to IMU Disturbances , 2006 .

[120]  Brett Ninness,et al.  Robust maximum-likelihood estimation of multivariable dynamic systems , 2005, Autom..

[121]  G. Hendeby,et al.  Fundamental Estimation and Detection Limits in Linear Non-Gaussian Systems , 2005 .

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

[123]  Rickard Karlsson,et al.  Simulation Based Methods for Target Tracking , 2002 .

[124]  A V Uglanov,et al.  FUBINI'S THEOREM FOR VECTOR-VALUED MEASURES , 1991 .

[125]  Fredrik Gustafsson,et al.  On Resampling Algorithms for Particle Filters , 2006, 2006 IEEE Nonlinear Statistical Signal Processing Workshop.

[126]  Erik Wernholt,et al.  On Multivariable and Nonlinear Identification of Industrial Robots , 2004 .

[127]  Thomas B. Schön,et al.  Particle Filter SLAM with High Dimensional Vehicle Model , 2009, J. Intell. Robotic Syst..

[128]  D. M. Titterington,et al.  Improved Particle Filters and Smoothing , 2001, Sequential Monte Carlo Methods in Practice.

[129]  L. Ljung,et al.  Clustering using sum-of-norms regularization: With application to particle filter output computation , 2011, 2011 IEEE Statistical Signal Processing Workshop (SSP).

[130]  Jonas Elbornsson,et al.  Equalization of Distortion in A/D Converters , 2001 .

[131]  R. Fisher.  014: On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. , 1921 .

[132]  Michael Isard,et al.  CONDENSATION—Conditional Density Propagation for Visual Tracking , 1998, International Journal of Computer Vision.

[133]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[134]  P. Billingsley,et al.  Probability and Measure , 1980 .

[135]  N. Chopin.  Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference , 2004, math/0508594.

[136]  S. Stigler.  Laplace's 1774 Memoir on Inverse Probability , 1986 .

[137]  B. Wahlberg.  On Model Simplification in System Identification , 1985 .

[138]  D. Lindgren.  Subspace Selection Techniques for Classification Problems , 2002 .

[139]  H. Kunsch.  Recursive Monte Carlo filters: Algorithms and theoretical analysis , 2006, math/0602211.

[140]  Lennart Ljung,et al.  Perspectives on system identification , 2010, Annu. Rev. Control..

[141]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[142]  Jonas Jansson.  Tracking and decision making for automotive collision avoidance , 2002 .

[143]  Wiro J. Niessen,et al.  Rao-Blackwellized Marginal Particle Filtering for Multiple Object Tracking in Molecular Bioimaging , 2007, IPMI.

[144]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[145]  Jimmy Olsson,et al.  Metropolising forward particle filtering backward sampling and Rao-Blackwellisation of Metropolised particle smoothers , 2010 .

[146]  G. Kitagawa.  A self-organizing state-space model , 1998 .

[147]  Simon J. Godsill,et al.  Monte Carlo filtering and smoothing with application to time-varying spectral estimation , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[148]  Donald B. Rubin,et al.  Comment : A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest : The SIR Algorithm , 1987 .

[149]  F. Gustafsson,et al.  Complexity analysis of the marginalized particle filter , 2005, IEEE Transactions on Signal Processing.

[150]  Henrik Ohlsson,et al.  Regression on Manifolds with Implications for System Identification , 2008 .

[151]  L. Greengard,et al.  A new version of the fast Gauss transform. , 1998 .

[152]  F. Gland,et al.  STABILITY AND UNIFORM APPROXIMATION OF NONLINEAR FILTERS USING THE HILBERT METRIC AND APPLICATION TO PARTICLE FILTERS1 , 2004 .

[153]  A. Doucet,et al.  A note on auxiliary particle filters , 2008 .

[154]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[155]  D. Mayne,et al.  Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering† , 1969 .

[156]  Fredrik Lindsten,et al.  Conflict Detection Metrics for Aircraft Sense and Avoid Systems , 2009 .

[157]  Håkan Hjalmarsson.  On Estimation of Model Quality in System Identification , 1990 .

[158]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[159]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[160]  Valur Einarsson.  On Verification of Switched Systems using Abstractions , 1998 .

[161]  O. Cappé,et al.  Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models , 2006, math/0609514.

[162]  Nando de Freitas,et al.  Fast particle smoothing: if I had a million particles , 2006, ICML.

[163]  R. Fildes.  Journal of the American Statistical Association : William S. Cleveland, Marylyn E. McGill and Robert McGill, The shape parameter for a two variable graph 83 (1988) 289-300 , 1989 .

[164]  Michel Verhaegen,et al.  Identifying MIMO Wiener systems using subspace model identification methods , 1996, Signal Process..

[165]  A. Doucet,et al.  Particle Markov chain Monte Carlo methods , 2010 .

[166]  R. B. Gopaluni.  Identification of Nonlinear Processes with known Model Structure Under Missing Observations , 2008 .

[167]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[168]  Karim Abed-Meraim,et al.  Blind system identification , 1997, Proc. IEEE.

[169]  P. Lindskog.  Algorithms and Tools for System Identification Using Prior Knowledge , 1994 .

[170]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[171]  Anna Hagenblad,et al.  Aspects of the Identification of Wiener Models , 1999 .

[172]  Anders Hald,et al.  On the history of maximum likelihood in relation to inverse probability and least squares , 1999 .

[173]  G. Hendeby,et al.  Performance and Implementation Aspects of Nonlinear Filtering , 2008 .

[174]  P. Moral,et al.  Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering , 2000 .

[175]  Michel Loève,et al.  Probability Theory I , 1977 .

[176]  Fredrik Tjärnström,et al.  Quality Estimation of Approximate Models , 2000 .

[177]  Leslie Greengard,et al.  The Fast Gauss Transform , 1991, SIAM J. Sci. Comput..

[178]  A. Doucet,et al.  Smoothing algorithms for state–space models , 2010 .

[179]  Magnus Larsson,et al.  On Modeling and Diagnosis of Discrete Event Dynamic Systems , 1997 .

[180]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[181]  D. Pierre.  Forward Smoothing Using Sequential Monte Carlo , 2009 .