Maximum Likelihood recursive state estimation using the Expectation Maximization algorithm
A Maximum Likelihood recursive state estimator is derived for non-linear state–space models. The estimator iteratively combines a particle filter to generate the predicted/filtered state densities and the Expectation Maximization algorithm to compute the maximum likelihood filtered state estimate. A...
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| Vydané v: | Automatica (Oxford) Ročník 144; s. 110482 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
01.10.2022
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | A Maximum Likelihood recursive state estimator is derived for non-linear state–space models. The estimator iteratively combines a particle filter to generate the predicted/filtered state densities and the Expectation Maximization algorithm to compute the maximum likelihood filtered state estimate. Algorithms for maximum likelihood state filtering, prediction and smoothing are derived. The convergence properties of these algorithms, which are inherited from the Expectation Maximization algorithm and the particle filter, are examined in two examples. For nonlinear state–space systems with linear measurements and additive Gaussian noises, it is shown that the filtering and prediction algorithms reduce to gradient-free optimization in a form of a fixed-point iteration. It is also shown that, with randomized reinitialization, which is feasible because of the simplicity of the algorithm, these methods are able to converge to the Maximum Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as well as those of disjoint support. |
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| AbstractList | A Maximum Likelihood recursive state estimator is derived for non-linear state–space models. The estimator iteratively combines a particle filter to generate the predicted/filtered state densities and the Expectation Maximization algorithm to compute the maximum likelihood filtered state estimate. Algorithms for maximum likelihood state filtering, prediction and smoothing are derived. The convergence properties of these algorithms, which are inherited from the Expectation Maximization algorithm and the particle filter, are examined in two examples. For nonlinear state–space systems with linear measurements and additive Gaussian noises, it is shown that the filtering and prediction algorithms reduce to gradient-free optimization in a form of a fixed-point iteration. It is also shown that, with randomized reinitialization, which is feasible because of the simplicity of the algorithm, these methods are able to converge to the Maximum Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as well as those of disjoint support. |
| ArticleNumber | 110482 |
| Author | Bitmead, Robert R. Ramadan, Mohammad S. |
| Author_xml | – sequence: 1 givenname: Mohammad S. surname: Ramadan fullname: Ramadan, Mohammad S. email: msramada@eng.ucsd.edu organization: Department of Mechanical & Aerospace Engineering, University of California, San Diego, La Jolla CA 92093-0411, USA – sequence: 2 givenname: Robert R. surname: Bitmead fullname: Bitmead, Robert R. email: rbitmead@eng.ucsd.edu organization: Department of Mechanical & Aerospace Engineering, University of California, San Diego, La Jolla CA 92093-0411, USA |
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| Cites_doi | 10.1080/01621459.1990.10474930 10.1023/A:1008935410038 10.1016/j.automatica.2010.10.013 10.1214/18-BA1099 10.1214/14-STS511 10.1016/j.dsp.2013.11.006 10.1109/TIT.2020.3047761 10.1214/aos/1176346060 10.1093/restud/rds040 10.1093/biomet/asq062 10.2514/3.3166 10.1111/j.2517-6161.1977.tb01600.x 10.1145/2414416.2414418 10.1109/TAC.2016.2624698 10.1093/biomet/80.2.267 10.1109/79.543975 10.1080/01621459.1999.10474153 10.1111/j.2517-6161.1995.tb02037.x 10.1016/j.jeconom.2011.07.006 |
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| Keywords | Expectation Maximization Maximum Likelihood State estimation Particle filter |
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| References | Le Corff, Fort (b6) 2013; 23 Mihaylova, Carmi, Septier, Gning, Pang, Godsill (b12) 2014; 25 Doucet, Godsill, Andrieu (b3) 2000; 10 Li, Scharth (b8) 2020 Dempster, Laird, Rubin (b2) 1977; 39 Vankov, Guindani, Ensor (b20) 2019; 14 Malik, Pitt (b10) 2011; 165 Septier, Pang, Godsill, Carmi (b18) 2009 Lange (b5) 1995; 57 Li, Liu, Chen (b7) 2016; 62 Poyiadjis, Doucet, Singh (b15) 2011; 98 Schön, Wills, Ninness (b17) 2011; 47 Rauch, Tung, Striebel (b16) 1965; 3 DeJong, Liesenfeld, Moura, Richard, Dharmarajan (b1) 2013; 80 Pitt, Shephard (b14) 1999; 94 Kantas, Doucet, Singh, Maciejowski, Chopin (b4) 2015; 30 Tadić, Doucet (b19) 2020; 67 Moon (b13) 1996; 13 Wei, Tanner (b21) 1990; 85 Lindholm, Lindsten (b9) 2018 Wu (b22) 1983; 11 Meng, Rubin (b11) 1993; 80 Lindholm (10.1016/j.automatica.2022.110482_b9) 2018 Malik (10.1016/j.automatica.2022.110482_b10) 2011; 165 Wu (10.1016/j.automatica.2022.110482_b22) 1983; 11 Li (10.1016/j.automatica.2022.110482_b8) 2020 Septier (10.1016/j.automatica.2022.110482_b18) 2009 Moon (10.1016/j.automatica.2022.110482_b13) 1996; 13 Li (10.1016/j.automatica.2022.110482_b7) 2016; 62 Wei (10.1016/j.automatica.2022.110482_b21) 1990; 85 Doucet (10.1016/j.automatica.2022.110482_b3) 2000; 10 Pitt (10.1016/j.automatica.2022.110482_b14) 1999; 94 DeJong (10.1016/j.automatica.2022.110482_b1) 2013; 80 Le Corff (10.1016/j.automatica.2022.110482_b6) 2013; 23 Vankov (10.1016/j.automatica.2022.110482_b20) 2019; 14 Meng (10.1016/j.automatica.2022.110482_b11) 1993; 80 Tadić (10.1016/j.automatica.2022.110482_b19) 2020; 67 Poyiadjis (10.1016/j.automatica.2022.110482_b15) 2011; 98 Rauch (10.1016/j.automatica.2022.110482_b16) 1965; 3 Dempster (10.1016/j.automatica.2022.110482_b2) 1977; 39 Kantas (10.1016/j.automatica.2022.110482_b4) 2015; 30 Schön (10.1016/j.automatica.2022.110482_b17) 2011; 47 Mihaylova (10.1016/j.automatica.2022.110482_b12) 2014; 25 Lange (10.1016/j.automatica.2022.110482_b5) 1995; 57 |
| References_xml | – volume: 30 start-page: 328 year: 2015 end-page: 351 ident: b4 article-title: On particle methods for parameter estimation in state-space models publication-title: Statistical Science – volume: 25 start-page: 1 year: 2014 end-page: 16 ident: b12 article-title: Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking publication-title: Digital Signal Processing – volume: 98 start-page: 65 year: 2011 end-page: 80 ident: b15 article-title: Particle approximations of the score and observed information matrix in state space models with application to parameter estimation publication-title: Biometrika – volume: 3 start-page: 1445 year: 1965 end-page: 1450 ident: b16 article-title: Maximum likelihood estimates of linear dynamic systems publication-title: American Institute of Aeronautics and Astronautics – volume: 165 start-page: 190 year: 2011 end-page: 209 ident: b10 article-title: Particle filters for continuous likelihood evaluation and maximisation publication-title: Journal of Econometrics – volume: 80 start-page: 538 year: 2013 end-page: 567 ident: b1 article-title: Efficient likelihood evaluation of state-space representations publication-title: Review of Economic Studies – volume: 14 start-page: 29 year: 2019 end-page: 52 ident: b20 article-title: Filtering and estimation for a class of stochastic volatility models with intractable likelihoods publication-title: Bayesian Analysis – volume: 10 start-page: 197 year: 2000 end-page: 208 ident: b3 article-title: On sequential Monte Carlo sampling methods for Bayesian filtering publication-title: Statistics and Computing – volume: 67 start-page: 1825 year: 2020 end-page: 1848 ident: b19 article-title: Asymptotic properties of recursive particle maximum likelihood estimation publication-title: IEEE Transactions on Information Theory – volume: 80 start-page: 267 year: 1993 end-page: 278 ident: b11 article-title: Maximum likelihood estimation via the ECM algorithm: A general framework publication-title: Biometrika – volume: 11 start-page: 95 year: 1983 end-page: 103 ident: b22 article-title: On the convergence properties of the EM algorithm publication-title: The Annals of Statistics – volume: 62 start-page: 4639 year: 2016 end-page: 4646 ident: b7 article-title: An auxiliary particle filtering algorithm with inequality constraints publication-title: IEEE Transactions on Automatic Control – year: 2018 ident: b9 article-title: Learning dynamical systems with particle stochastic approximation EM – volume: 39 start-page: 1 year: 1977 end-page: 22 ident: b2 article-title: Maximum likelihood from incomplete data via the EM algorithm publication-title: Journal of the Royal Statistical Society. Series B. Statistical Methodology – volume: 57 start-page: 425 year: 1995 end-page: 437 ident: b5 article-title: A gradient algorithm locally equivalent to the EM algorithm publication-title: Journal of the Royal Statistical Society. Series B. Statistical Methodology – volume: 13 start-page: 47 year: 1996 end-page: 60 ident: b13 article-title: The expectation-maximization algorithm publication-title: IEEE Signal Processing Magazine – volume: 85 start-page: 699 year: 1990 end-page: 704 ident: b21 article-title: A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms publication-title: Journal of the American Statistical Association – volume: 94 start-page: 590 year: 1999 end-page: 599 ident: b14 article-title: Filtering via simulation: Auxiliary particle filters publication-title: Journal of the American Statistical Association – start-page: 1 year: 2009 end-page: 11 ident: b18 article-title: Tracking of coordinated groups using marginalised MCMC-based particle algorithm publication-title: 2009 IEEE aerospace conference – volume: 23 start-page: 1 year: 2013 end-page: 22 ident: b6 article-title: Convergence of a particle-based approximation of the block online expectation maximization algorithm publication-title: ACM Transactions on Modeling and Computer Simulation (TOMACS) – volume: 47 start-page: 39 year: 2011 end-page: 49 ident: b17 article-title: System identification of nonlinear state-space models publication-title: Automatica – start-page: 1 year: 2020 end-page: 17 ident: b8 article-title: Leverage, asymmetry, and heavy tails in the high-dimensional factor stochastic volatility model publication-title: Journal of Business & Economic Statistics – volume: 85 start-page: 699 issue: 411 year: 1990 ident: 10.1016/j.automatica.2022.110482_b21 article-title: A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms publication-title: Journal of the American Statistical Association doi: 10.1080/01621459.1990.10474930 – volume: 10 start-page: 197 issue: 3 year: 2000 ident: 10.1016/j.automatica.2022.110482_b3 article-title: On sequential Monte Carlo sampling methods for Bayesian filtering publication-title: Statistics and Computing doi: 10.1023/A:1008935410038 – volume: 47 start-page: 39 issue: 1 year: 2011 ident: 10.1016/j.automatica.2022.110482_b17 article-title: System identification of nonlinear state-space models publication-title: Automatica doi: 10.1016/j.automatica.2010.10.013 – start-page: 1 year: 2009 ident: 10.1016/j.automatica.2022.110482_b18 article-title: Tracking of coordinated groups using marginalised MCMC-based particle algorithm – year: 2018 ident: 10.1016/j.automatica.2022.110482_b9 – start-page: 1 year: 2020 ident: 10.1016/j.automatica.2022.110482_b8 article-title: Leverage, asymmetry, and heavy tails in the high-dimensional factor stochastic volatility model publication-title: Journal of Business & Economic Statistics – volume: 14 start-page: 29 issue: 1 year: 2019 ident: 10.1016/j.automatica.2022.110482_b20 article-title: Filtering and estimation for a class of stochastic volatility models with intractable likelihoods publication-title: Bayesian Analysis doi: 10.1214/18-BA1099 – volume: 30 start-page: 328 issue: 3 year: 2015 ident: 10.1016/j.automatica.2022.110482_b4 article-title: On particle methods for parameter estimation in state-space models publication-title: Statistical Science doi: 10.1214/14-STS511 – volume: 25 start-page: 1 year: 2014 ident: 10.1016/j.automatica.2022.110482_b12 article-title: Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking publication-title: Digital Signal Processing doi: 10.1016/j.dsp.2013.11.006 – volume: 67 start-page: 1825 issue: 3 year: 2020 ident: 10.1016/j.automatica.2022.110482_b19 article-title: Asymptotic properties of recursive particle maximum likelihood estimation publication-title: IEEE Transactions on Information Theory doi: 10.1109/TIT.2020.3047761 – volume: 11 start-page: 95 issue: 1 year: 1983 ident: 10.1016/j.automatica.2022.110482_b22 article-title: On the convergence properties of the EM algorithm publication-title: The Annals of Statistics doi: 10.1214/aos/1176346060 – volume: 80 start-page: 538 issue: 2 year: 2013 ident: 10.1016/j.automatica.2022.110482_b1 article-title: Efficient likelihood evaluation of state-space representations publication-title: Review of Economic Studies doi: 10.1093/restud/rds040 – volume: 98 start-page: 65 issue: 1 year: 2011 ident: 10.1016/j.automatica.2022.110482_b15 article-title: Particle approximations of the score and observed information matrix in state space models with application to parameter estimation publication-title: Biometrika doi: 10.1093/biomet/asq062 – volume: 3 start-page: 1445 issue: 8 year: 1965 ident: 10.1016/j.automatica.2022.110482_b16 article-title: Maximum likelihood estimates of linear dynamic systems publication-title: American Institute of Aeronautics and Astronautics doi: 10.2514/3.3166 – volume: 39 start-page: 1 issue: 1 year: 1977 ident: 10.1016/j.automatica.2022.110482_b2 article-title: Maximum likelihood from incomplete data via the EM algorithm publication-title: Journal of the Royal Statistical Society. Series B. Statistical Methodology doi: 10.1111/j.2517-6161.1977.tb01600.x – volume: 23 start-page: 1 issue: 1 year: 2013 ident: 10.1016/j.automatica.2022.110482_b6 article-title: Convergence of a particle-based approximation of the block online expectation maximization algorithm publication-title: ACM Transactions on Modeling and Computer Simulation (TOMACS) doi: 10.1145/2414416.2414418 – volume: 62 start-page: 4639 issue: 9 year: 2016 ident: 10.1016/j.automatica.2022.110482_b7 article-title: An auxiliary particle filtering algorithm with inequality constraints publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2016.2624698 – volume: 80 start-page: 267 issue: 2 year: 1993 ident: 10.1016/j.automatica.2022.110482_b11 article-title: Maximum likelihood estimation via the ECM algorithm: A general framework publication-title: Biometrika doi: 10.1093/biomet/80.2.267 – volume: 13 start-page: 47 issue: 6 year: 1996 ident: 10.1016/j.automatica.2022.110482_b13 article-title: The expectation-maximization algorithm publication-title: IEEE Signal Processing Magazine doi: 10.1109/79.543975 – volume: 94 start-page: 590 issue: 446 year: 1999 ident: 10.1016/j.automatica.2022.110482_b14 article-title: Filtering via simulation: Auxiliary particle filters publication-title: Journal of the American Statistical Association doi: 10.1080/01621459.1999.10474153 – volume: 57 start-page: 425 issue: 2 year: 1995 ident: 10.1016/j.automatica.2022.110482_b5 article-title: A gradient algorithm locally equivalent to the EM algorithm publication-title: Journal of the Royal Statistical Society. Series B. Statistical Methodology doi: 10.1111/j.2517-6161.1995.tb02037.x – volume: 165 start-page: 190 issue: 2 year: 2011 ident: 10.1016/j.automatica.2022.110482_b10 article-title: Particle filters for continuous likelihood evaluation and maximisation publication-title: Journal of Econometrics doi: 10.1016/j.jeconom.2011.07.006 |
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