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

Research output: Thesis › Doctoral Thesis › Collection of Articles

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**Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems.** / Kokkala, Juho.

Research output: Thesis › Doctoral Thesis › Collection of Articles

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*Particle and Sigma-Point Methods for State and Parameter Estimation in Nonlinear Dynamic Systems*. Aalto University.

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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 -

ID: 19021122