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Estimation of Nonlinear Dynamic Systems: Theory and Applications
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 998
Series
Keyword [en]
Nonlinear estimation, system identification, Kalman filter, particle filter, marginalized particle filter, expectation maximization, automotive applications
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-7124ISBN: 91-85497-03-7 (print)OAI: oai:DiVA.org:liu-7124DiVA: diva2:22197
Public defence
2006-02-02, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2009-06-04
List of papers
1. Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models
Open this publication in new window or tab >>Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models
2005 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 7, 2279-2289 p.Article in journal (Refereed) Published
Abstract [en]

The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2005
Keyword
Kalman filter, Marginalization, Navigation systems, Nonlinear systems, Particle filter, State estimation
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-11749 (URN)10.1109/TSP.2005.849151 (DOI)
Available from: 2008-05-07 Created: 2008-05-07 Last updated: 2017-12-13Bibliographically approved
2. Complexity Analysis of the Marginalized Particle Filter
Open this publication in new window or tab >>Complexity Analysis of the Marginalized Particle Filter
2005 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 11, 4408-4411 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the computational complexity of the marginalized particle filter is analyzed and a general method to perform this analysis is given. The key is the introduction of the equivalent flop measure. In an extensive Monte Carlo simulation, different computational aspects are studied and compared with the derived theoretical results.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2005
Keyword
Complexity analysis, Kalman filter, Equivalent flop, Marginalized particle filter, Nonlinear estimation
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-11751 (URN)10.1109/TSP.2005.857061 (DOI)
Available from: 2008-05-07 Created: 2008-05-07 Last updated: 2017-12-13
3. A Modeling and Filtering Framework for Linear Differential-Algebraic Equations
Open this publication in new window or tab >>A Modeling and Filtering Framework for Linear Differential-Algebraic Equations
2003 (English)In: Proceedings of the 42th IEEE Conference on Decision and Control, 2003, 892-897 vol.1 p.Conference paper, Published paper (Refereed)
Abstract [en]

General approaches to modeling, for instance using object-oriented software, lead to differential-algebraic equations (DAE). As the name reveals, it is a combination of differential and algebraic equations. For state estimation using observed system inputs and outputs in a stochastic framework similar to Kalman filtering, we need to augment the DAE with stochastic disturbances ("process noise"), whose covariance matrix becomes the tuning parameter. We will determine the subspace of possible causal disturbances based on the linear DAE model. This subspace determines all degrees of freedom in the filter design, and a Kalman filter algorithm is given. We illustrate the design on a system with two interconnected rotating masses.

Keyword
Implicit systems, Descriptor systems, Singular systems, White noise, Noise, Discretization, Kalman filters
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13917 (URN)10.1109/CDC.2003.1272679 (DOI)000189434100154 ()0-7803-7924-1 (ISBN)
Conference
42nd IEEE Conference on Decision and Control, Maui, HI, USA, December, 2003
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-11-27
4. A Note on State Estimation as a Convex Optimization Problem
Open this publication in new window or tab >>A Note on State Estimation as a Convex Optimization Problem
2003 (English)In: Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003, Vol. 6, no 6-10, 61-64 vol.6 p.Conference paper, Published paper (Refereed)
Abstract [en]

The Kalman filter computes the maximum a posteriori (MAP) estimate of the states for linear state space models with Gaussian noise. We interpret the Kalman filter as the solution to a convex optimization problem, and show that we can generalize the MAP state estimator to any noise with a log-concave density function and any combination of linear equality and convex inequality constraints on the states. We illustrate the principle on a hidden Markov model, where the state vector contains probabilities that are positive and sum to one.

Keyword
State estimation, Kalman filter, Convex optimization, Hidden Markov Models
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13918 (URN)10.1109/ICASSP.2003.1201618 (DOI)0-7803-7663-3 (ISBN)
Conference
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, China, April, 2003
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-11-27
5. Particle Filters for System Identification of State-Space Models Linear in Either Parameters or States
Open this publication in new window or tab >>Particle Filters for System Identification of State-Space Models Linear in Either Parameters or States
2003 (English)In: Proceedings of the 13th IFAC Symposium on System Identification, 2003, 1251-1256 vol.1 p.Conference paper, Published paper (Refereed)
Abstract [en]

The potential use of the marginalized particle filter for nonlinear system identification is investigated. The particle filter itself offers a general tool for estimating unknown parameters in non-linear models of moderate complexity, and the basic trick is to model the parameters as a random walk (so called roughening noise) with decaying variance. We derive algorithms for systems which are non-linear in either the parameters or the states, but not both generally. In these cases, marginalization applies to the linear part, which firstly significantly widens the scope of the particle filter to more complex systems, and secondly decreases the variance in the linear parameters/states for fixed filter complexity. This second property is illustrated on an example of chaotic model. The particular case of freely parametrized linear state space models, common in subspace identification approaches, is bi-linear in states and parameters, and thus both cases above are satisfied. One can then choose which one to marginalize.

Keyword
System identification, Nonlinear estimation, Recursive estimation, Particle filters, Kalman filters, Bayesian estimation
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13919 (URN)978-0080437095 (ISBN)
Conference
13th IFAC Symposium on System Identification, Rotterdam, The Netherlands, August, 2003
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-11-27
6. Maximum Likelihood Nonlinear System Estimation
Open this publication in new window or tab >>Maximum Likelihood Nonlinear System Estimation
2006 (English)In: Proceedings of the 14th IFAC Symposium on System Identification, Newcastle, Australia, 2006, 1003-1008 p.Conference paper, Published 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.

Keyword
Nonlinear systems, System identification, Maximum likelihood, Expectation maximisation algorithm, Particle smoother
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13920 (URN)10.3182/20060329-3-AU-2901.00160 (DOI)978-3-902661-02-9 (ISBN)
Conference
14th IFAC Symposium on System Identification, Newcastle, Australia, March, 2006
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-04-07
7. Integrated Navigation of Cameras for Augmented Reality
Open this publication in new window or tab >>Integrated Navigation of Cameras for Augmented Reality
2005 (English)In: Proceedings of the 16th IFAC World Congress, 2005, 187-187 p.Conference paper, Published paper (Refereed)
Abstract [en]

In augmented reality, the position and orientation of the camera must be estimated very accurately. This paper will propose a filtering approach, similar to integrated navigation in aircraft, which is based on inertial measurements as primary sensor on which dead-reckoning can be based, and features in the image as supporting information to stabilize the dead-reckoning. The image features are considered to be sensor signals in a Kalman filter framework.

Keyword
Sensor fusion, Kalman filter, Inertial navigation, Augmented reality, Computer vision, Feature extraction
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13921 (URN)10.3182/20050703-6-CZ-1902.00188 (DOI)978-3-902661-75-3 (ISBN)
Conference
16th IFAC World Congress, Prague, Czech Republic, July, 2005
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-03-23
8. The Marginalized Particle Filter in Practice
Open this publication in new window or tab >>The Marginalized Particle Filter in Practice
2006 (English)In: Proceedings of the 2006 IEEE Aerospace Conference, 2006Conference paper, Published paper (Refereed)
Abstract [en]

The marginalized particle filter is a powerful combination of the particle filter and the Kalman filter, which can be used when the underlying model contains a linear sub-structure, subject to Gaussian noise. This paper will illustrate several positioning and target tracking applications, solved using the marginalized particle filter. Furthermore, we analyze several properties of practical importance, such as its computational complexity and how to cope with quantization effects.

Keyword
Gaussian noise, Adaptive Kalman filters, Computational complexity, Particle filtering (numerical methods), Position control, Quantisation (signal), Target tracking, Linear sub-structure, Marginalized particle filter, Positioning, Quantization effects
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13922 (URN)10.1109/AERO.2006.1655922 (DOI)9780780395459 (ISBN)
Conference
2006 IEEE Aerospace Conference, Big Sky, MT, USA, March, 2006
Funder
Vinnova
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-04-07
9. Lane Departure Detection for Improved Road Geometry Estimation
Open this publication in new window or tab >>Lane Departure Detection for Improved Road Geometry Estimation
2006 (English)In: Proceedings of the 2006 IEEE Intelligent Vehicle Symposium, 2006, 546-551 p.Conference paper, Published paper (Refereed)
Abstract [en]

An essential part of future collision avoidance systems is to be able to predict road curvature. This can be based on vision data, but the lateral movement of leading vehicles can also be used to support road geometry estimation. This paper presents a method for detecting lane departures, including lane changes, of leading vehicles. This information is used to adapt the dynamic models used in the estimation algorithm in order to accommodate for the fact that a lane departure is in progress. The goal is to improve the accuracy of the road geometry estimates, which is affected by the motion of leading vehicles. The significantly improved performance is demonstrated using sensor data from authentic traffic environments.

Keyword
Automotive tracking, Change detection, State estimation, Kalman filter, CUSUM-test
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-13923 (URN)10.1109/IVS.2006.1689685 (DOI)
Conference
2006 IEEE Intelligent Vehicle Symposium, Tokyo, Japan, June, 2006
Available from: 2006-09-04 Created: 2006-09-04 Last updated: 2013-02-26

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