Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems

Juho Kokkala

Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems

Julkaisun otsikon käännös: Partikkeli- ja sigmapistemenetelmiä epälineaaristen dynaamisten systeemien tila- ja parametriestimointiin

Juho Kokkala

Neurotieteen ja lääketieteellisen tekniikan laitos

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Dynaamisten systeemien tila-avaruusmalleilla mallinnetaan ajassa eteneviä ilmiöitä, joista saadaan epätarkkoja havaintoja. Näitä malleja voidaan soveltaa esimerkiksi liikkuvan kohteen seuraamiseen. Tila-avaruusmalli kuvaa todennäköisyysjakaumina miten systeemin tila riippuu aiemmasta tilasta ja miten kunkin ajanhetken mittaus riippuu tilasta. Tila-avaruusmallin suodatustehtävässä lasketaan tilan todennäköisyysjakauma kullakin ajanhetkellä ottaen huomioon kaikki siihen mennessä saadut mittaukset. Silotustehtävässä puolestaan nämä jakaumat päivitetään ottamaan huomioon myös myöhemmät mittaukset. Suodatus- ja silotustehtävää ei voi ratkaista analyyttisesti suljetussa muodossa kuin tietyissä erikoistapauksissa. Tässä väitöskirjassa käytetään sigmapiste- ja partikkelipohjaisia suodatus- ja silotusmenetelmiä. Sigmapistemenetelmät perustuvat suotimen ja silottimen todennäköisyysjakaumien approksimointiin gaussisilla jakaumilla ja eräiden integraalien approksimointiin numeerisilla integrointisäännöillä. Partikkelisuotimissa ja -silottimissa puolestaan käytetään satunnaisotoksia. Tietyillä ehdoilla partikkelisuotimet ja -silottimet suppenevat suodatus- ja silotustehtävän täsmällisiin ratkaisuihin, kun otoskoko lähestyy ääretöntä. Tämän väitöskirjan tutkimuskohteet ovat importanssijakaumien kehittäminen partikkelisuodinalgoritmeihin, tila-avaruusmallien parametrien estimointimenetelmien kehittäminen sekä sovellus eläinpopulaation koon arviointiin. Väitöskirjassa ehdotetaan split-gaussista importanssijakaumaa partikkelisuotimiin ja verrataan sitä muihin importanssijakaumiin. Aikariippuville Poisson-regressiomalleille osoitetaan, että eräs split-gaussinen importanssijakauma takaa partikkelisuotimen suppenemisen - toisin kuin gaussiseen approksimaatioon perustuva importanssijakauma. Väitöskirjassa kehitetään monen kohteen seurantatehtäviin parametriestimointialgoritmi, joka perustuu partikkelipohjaisten Markov-ketju- Monte Carlo -algoritmien ja rao-black-wellisoidun Monte Carlo -data-assosiaation yhdistämiseen. Tällä menetelmällä voidaan samanaikaisesti estimoida mallin parametrit ja kohteiden liikkuminen sekä kohteiden lukumäärä. Menetelmää sovelletaan karhupopulaation koon arviointiin kenttähavaintojen perusteella. Väitöskirjassa tutkitaan parametriestimointia myös additiivis-gaussisissa epälineaarisissa dynaamisissa systeemeissä. Työssä vertaillaan suoraa suurimman uskottavuuden menetelmää ja expectation-maximization -algoritmia käyttäen partikkeli- ja sigmapiste-menetelmiä.

Julkaisun otsikon käännös	Partikkeli- ja sigmapistemenetelmiä epälineaaristen dynaamisten systeemien tila- ja parametriestimointiin
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Lampinen, Jouko, Vastuuprofessori Särkkä, Simo, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-6663-9
Sähköinen ISBN	978-952-60-6664-6
Tila	Julkaistu - 2016
OKM-julkaisutyyppi	G5 Tohtorinväitöskirja (artikkeli)

Tutkimusalat

bayesilainen suodatus ja silotus
tila-avaruusmallit
dynaamiset systeemit
partikkelisuotimet
sigmapistesuotimet

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-6664-6Lisenssi: Määrittelemätön

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@phdthesis{dc986c8d9e3f416bb4d304ff7963bfbf,

title = "Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems",

abstract = "State-space models of dynamic systems are used to model phenomena, which evolve over time, and are observed only through noisy or incomplete measurements. An example is tracking a moving target based on sensor measurements. A state-space model consists of a probabilistic specification of the evolution of a latent state, conditional on the previous values, and a probabilistic specification of how the observations depend on the latent states. Typically, we are interested in the filtering and smoothing problems, and parameter estimation. In filtering, one computes the probability distribution of the current latent state, taking into account all observations obtained so far. Smoothing refers to updating the probability distributions of the latent states on the previous times based on new observations obtained after those times. Both filtering and smoothing problems are analytically intractable except in some special cases. In this thesis, sigma-point and particle based filtering and smoothing methods are used. Sigma-point filters and smoothers are based on approximating the filters and smoothers by Gaussian density approximations and then further approximating certain integrals by numerical cubature rules. Particle filters and smoothers in turn use random samples to approximate the probability distributions and, under certain conditions, converge to exact filters and smoothers when the number of samples tends to infinity. The research topics of this thesis are to develop new importance distributions for particle filters, to develop methods for static parameter estimation, and an application to animal population size estimation. A split-Gaussian importance distribution is proposed for particle filters and compared to alternatives. In addition, in a certain time-varying Poisson regression model, it is shown that a split-Gaussian modification to a Gaussian approximation based importance distribution guarantees convergence of the particle filter when the pure Gaussian approximation does not. A parameter estimation method for multiple target tracking models is developed based on combining recently proposed particle Markov chain Monte Carlo algorithms with the Rao-Blackwellized Monte Carlo data association algorithm. This method allows for joint estimation of the target movements and the parameters of the models, as well as the number of targets. The method is applied to estimating bear population size based on a database of field signs. Additionally, parameter estimation in nonlinear systems with additive Gaussian noise is discussed using both direct likelihood maximization and expectation-maximization (EM), and both particle and sigma-point algorithms for the smoothing problem arising in EM.",

keywords = "Bayesian filtering and smoothing, state-space models, dynamic systems, particle filters, sigma-point filters, bayesilainen suodatus ja silotus, tila-avaruusmallit, dynaamiset systeemit, partikkelisuotimet, sigmapistesuotimet, Bayesian filtering and smoothing, state-space models, dynamic systems, particle filters, sigma-point filters",

author = "Juho Kokkala",

year = "2016",

language = "English",

isbn = "978-952-60-6663-9",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "30",

address = "Finland",

school = "Aalto University",

}

TY - THES

T1 - Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems

AU - Kokkala, Juho

PY - 2016

Y1 - 2016

N2 - State-space models of dynamic systems are used to model phenomena, which evolve over time, and are observed only through noisy or incomplete measurements. An example is tracking a moving target based on sensor measurements. A state-space model consists of a probabilistic specification of the evolution of a latent state, conditional on the previous values, and a probabilistic specification of how the observations depend on the latent states. Typically, we are interested in the filtering and smoothing problems, and parameter estimation. In filtering, one computes the probability distribution of the current latent state, taking into account all observations obtained so far. Smoothing refers to updating the probability distributions of the latent states on the previous times based on new observations obtained after those times. Both filtering and smoothing problems are analytically intractable except in some special cases. In this thesis, sigma-point and particle based filtering and smoothing methods are used. Sigma-point filters and smoothers are based on approximating the filters and smoothers by Gaussian density approximations and then further approximating certain integrals by numerical cubature rules. Particle filters and smoothers in turn use random samples to approximate the probability distributions and, under certain conditions, converge to exact filters and smoothers when the number of samples tends to infinity. The research topics of this thesis are to develop new importance distributions for particle filters, to develop methods for static parameter estimation, and an application to animal population size estimation. A split-Gaussian importance distribution is proposed for particle filters and compared to alternatives. In addition, in a certain time-varying Poisson regression model, it is shown that a split-Gaussian modification to a Gaussian approximation based importance distribution guarantees convergence of the particle filter when the pure Gaussian approximation does not. A parameter estimation method for multiple target tracking models is developed based on combining recently proposed particle Markov chain Monte Carlo algorithms with the Rao-Blackwellized Monte Carlo data association algorithm. This method allows for joint estimation of the target movements and the parameters of the models, as well as the number of targets. The method is applied to estimating bear population size based on a database of field signs. Additionally, parameter estimation in nonlinear systems with additive Gaussian noise is discussed using both direct likelihood maximization and expectation-maximization (EM), and both particle and sigma-point algorithms for the smoothing problem arising in EM.

AB - State-space models of dynamic systems are used to model phenomena, which evolve over time, and are observed only through noisy or incomplete measurements. An example is tracking a moving target based on sensor measurements. A state-space model consists of a probabilistic specification of the evolution of a latent state, conditional on the previous values, and a probabilistic specification of how the observations depend on the latent states. Typically, we are interested in the filtering and smoothing problems, and parameter estimation. In filtering, one computes the probability distribution of the current latent state, taking into account all observations obtained so far. Smoothing refers to updating the probability distributions of the latent states on the previous times based on new observations obtained after those times. Both filtering and smoothing problems are analytically intractable except in some special cases. In this thesis, sigma-point and particle based filtering and smoothing methods are used. Sigma-point filters and smoothers are based on approximating the filters and smoothers by Gaussian density approximations and then further approximating certain integrals by numerical cubature rules. Particle filters and smoothers in turn use random samples to approximate the probability distributions and, under certain conditions, converge to exact filters and smoothers when the number of samples tends to infinity. The research topics of this thesis are to develop new importance distributions for particle filters, to develop methods for static parameter estimation, and an application to animal population size estimation. A split-Gaussian importance distribution is proposed for particle filters and compared to alternatives. In addition, in a certain time-varying Poisson regression model, it is shown that a split-Gaussian modification to a Gaussian approximation based importance distribution guarantees convergence of the particle filter when the pure Gaussian approximation does not. A parameter estimation method for multiple target tracking models is developed based on combining recently proposed particle Markov chain Monte Carlo algorithms with the Rao-Blackwellized Monte Carlo data association algorithm. This method allows for joint estimation of the target movements and the parameters of the models, as well as the number of targets. The method is applied to estimating bear population size based on a database of field signs. Additionally, parameter estimation in nonlinear systems with additive Gaussian noise is discussed using both direct likelihood maximization and expectation-maximization (EM), and both particle and sigma-point algorithms for the smoothing problem arising in EM.

KW - Bayesian filtering and smoothing

KW - state-space models

KW - dynamic systems

KW - particle filters

KW - sigma-point filters

KW - bayesilainen suodatus ja silotus

KW - tila-avaruusmallit

KW - dynaamiset systeemit

KW - partikkelisuotimet

KW - sigmapistesuotimet

KW - Bayesian filtering and smoothing

KW - state-space models

KW - dynamic systems

KW - particle filters

KW - sigma-point filters

M3 - Doctoral Thesis

SN - 978-952-60-6663-9

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems

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