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Maximum Likelihood Nonlinear System Estimation
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
University of Newcastle, Australia.
University of Newcastle, Australia.
2006 (English)In: Proceedings of the 14th IFAC Symposium on System Identification, Newcastle, Australia, 2006, 1003-1008 p.Conference paper (Refereed)
Abstract [en]

This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed in the interests of statistical efficiency, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of so-called "particle smoothing" methods to compute required conditional expectations via a Monte Carlo approach. A simulation example demonstrates the efficacy of these techniques.

Place, publisher, year, edition, pages
2006. 1003-1008 p.
Keyword [en]
Nonlinear systems, System identification, Maximum likelihood, Expectation maximisation algorithm, Particle smoother
National Category
Engineering and Technology Control Engineering
URN: urn:nbn:se:liu:diva-13920DOI: 10.3182/20060329-3-AU-2901.00160ISBN: 978-3-902661-02-9OAI: diva2:22193
14th IFAC Symposium on System Identification, Newcastle, Australia, March, 2006
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-04-07
In thesis
1. Estimation of Nonlinear Dynamic Systems: Theory and Applications
Open this publication in new window or tab >>Estimation of Nonlinear Dynamic Systems: Theory and Applications
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with estimation of states and parameters in nonlinear and non-Gaussian dynamic systems. Sequential Monte Carlo methods are mainly used to this end. These methods rely on models of the underlying system, motivating some developments of the model concept. One of the main reasons for the interest in nonlinear estimation is that problems of this kind arise naturally in many important applications. Several applications of nonlinear estimation are studied.

The models most commonly used for estimation are based on stochastic difference equations, referred to as state-space models. This thesis is mainly concerned with models of this kind. However, there will be a brief digression from this, in the treatment of the mathematically more intricate differential-algebraic equations. Here, the purpose is to write these equations in a form suitable for statistical signal processing.

The nonlinear state estimation problem is addressed using sequential Monte Carlo methods, commonly referred to as particle methods. When there is a linear sub-structure inherent in the underlying model, this can be exploited by the powerful combination of the particle filter and the Kalman filter, presented by the marginalized particle filter. This algorithm is also known as the Rao-Blackwellized particle filter and it is thoroughly derived and explained in conjunction with a rather general class of mixed linear/nonlinear state-space models. Models of this type are often used in studying positioning and target tracking applications. This is illustrated using several examples from the automotive and the aircraft industry. Furthermore, the computational complexity of the marginalized particle filter is analyzed.

The parameter estimation problem is addressed for a relatively general class of mixed linear/nonlinear state-space models. The expectation maximization algorithm is used to calculate parameter estimates from batch data. In devising this algorithm, the need to solve a nonlinear smoothing problem arises, which is handled using a particle smoother. The use of the marginalized particle filter for recursive parameterestimation is also investigated.

The applications considered are the camera positioning problem arising from augmented reality and sensor fusion problems originating from automotive active safety systems. The use of vision measurements in the estimation problem is central to both applications. In augmented reality, the estimates of the camera’s position and orientation are imperative in the process of overlaying computer generated objects onto the live video stream. The objective in the sensor fusion problems arising in automotive safety systems is to provide information about the host vehicle and its surroundings, such as the position of other vehicles and the road geometry. Information of this kind is crucial for many systems, such as adaptive cruise control, collision avoidance and lane guidance.

Place, publisher, year, edition, pages
Institutionen för systemteknik, 2006
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 998
Nonlinear estimation, system identification, Kalman filter, particle filter, marginalized particle filter, expectation maximization, automotive applications
National Category
Control Engineering
urn:nbn:se:liu:diva-7124 (URN)91-85497-03-7 (ISBN)
Public defence
2006-02-02, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2009-06-04

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