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Adaptive particle filter with fixed empirical density quality

IFAC Proceedings Volumes 2008年第2期41卷 6484-6489页

作者： Ondřej Straka Miroslav Šimandl Department of Cybernetics and Research Centre: Data - Algorithms - Decision Faculty of Applied Sciences University of West Bohemia Univerzitní 8 306 14 Plzeň Czech Republic

The paper deals with the particle filter in state estimation of a discrete-time nonlinear non-Gaussian system. The goal of the paper is to design a sample size adaptation technique to guarantee the quality of an empirical probability density function (pdf) which approximates a target filtering pdf. The quality is measured by inaccuracy (cross-information) between the empirical pdf and the filtering pdf. It is shown that for increasing sample size the inaccuracy converges to the Shannon differential entropy (SDE) of the filtering pdf. The proposed technique adapts the sample size to keep a difference between the inaccuracy and the SDE within prespecified bounds with a pre-specified probability. The particle filter with the proposed sample size adaptation technique is illustrated in a numerical example.

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Framework for implementing and testing nonlinear filters

Framework for implementing and testing nonlinear filters

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作者： Flídr, Miroslav Duník, Jindřich Straka, Ondřej Švácha, Jaroslav Šimandl, Miroslav Department of Cybernetics and Research Centre Data - Algorithms - Decision Making University of West Bohemia In Pilsen Univerzitní 8 30614 Plzeň Czech Republic

ISBN: (纸本)9783902661074

The aim of this paper is to present a software framework facilitating implementation, testing and use of various nonlinear estimation methods. This framework is designed to offer an easy to use tool for state estimation of discrete time dynamic stochastic systems. Besides implementation of various local and global state estimation methods it contains procedures for system design and simulation. Its strength is in the fact that it provides means that help students get acquainted with nonlinear state estimation problem and to be able to test features of various estimation methods. Another considerable advantage of proposed framework is its high modularity and extensibility. The paper briefly describes nonlinear estimation problem and its general solution using the Bayesian approach leading to the Bayesian recursive relations. Then it presents key features of the software framework designed in MATLAB environment that supports straightforward implementation of estimation methods based on the Bayesian approach. The strengths of the framework are demonstrated on implementation of the Divided difference filter 1st order. Copyright © 2006 IFAC.

关键词： Stochastic systems

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Nonlinear filtering toolbox for continuous stochastic systems with discrete measurements

Nonlinear filtering toolbox for continuous stochastic system...

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作者： Švácha, Jaroslav Šimandl, Miroslav Straka, Ondřej Flídr, Miroslav Research Centre Data Algorithms and Decision Making Department of Cybernetics University of West Bohemia In Pilsen Univerzitní 8 306 14 Plzeň Czech Republic

ISBN: (纸本)9783902661074

The paper deals with a problem of state estimation for nonlinear continuous stochastic systems with discrete-time measurements. A general recursive solution of the estimation problem given by the Bayesian rule and by the Fokker-Planck equation is described. Local estimation methods employing analytical approach to solution and global estimation methods employing analytical, numerical and simulation approaches are discussed. A software package for state estimation of continuous stochastic systems with discrete-time measurements is developed and described. It serves for system design, system simulation, estimator setup and state estimation. The package is designed to embody easily user defined estimators and thus it is suitable for estimator testing and quality comparison of different estimators. Usage of the nonlinear filtering software package is illustrated in a numerical example. Copyright © 2006 IFAC.

关键词： Stochastic systems

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FRAMEWORK FOR IMPLEMENTING AND TESTING NONLINEAR FILTERS

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IFAC Proceedings Volumes 2006年第6期39卷 117-122页

作者： Miroslav Flídr Jindrich Duník Ondrej Straka Jaroslav Ŝvácha Miroslav Ŝimandl Cybernetics & Research Centre Data - Algorithms - Decision Making University of West Bohemia in Pilsen Univerzitní8 30614 Plzen Czech Republic

关键词： stochastic systems nonlinear state and parameter estimation Bayesian recursive relations nonlinear filters software framework

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DESIGN OF DERIVATIVE-FREE SMOOTHERS AND PREDICTORS

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IFAC Proceedings Volumes 2006年第1期39卷 1240-1245页

作者： Miroslav Šimandl Jindřich Duník Department of Cybernetics & Research Centre Data-Algorithms-Decision Making University of West Bohemia in Pilsen Univerzitní 8 30614 Plzeň Czech Republic

Local state estimation approaches for nonlinear stochastic systems are treated. The unscented transformation and the Stirling's polynomial interpolation, used in the design of the derivative-free Kalman filters, are briefly discussed. These approximation techniques are exploited to the design of the derivative-free smoothers and predictors. Some aspects of the different types of the derivative-free smoothers are analysed. The estimation qualities of the proposed estimators are illustrated in a numerical example.

关键词： stochastic systems nonlinear systems state estimation Kalman filtering estimation theory

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NONLINEAR FILTERING TOOLBOX FOR CONTINUOUS STOCHASTIC SYSTEMS WITH DISCRETE MEASUREMENTS

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IFAC Proceedings Volumes 2006年第6期39卷 422-427页

作者： Jaroslav Ŝvácha Miroslav Ŝimandl Ondrej Straka Miroslav Flídr Cybernetics Research Centre Data Algorithms and Decision Making University of West Bohemia in Pilsen Univerzitní 8 306 14 Plzen Czech Republic

关键词： stochastic systems state estimation nonlinear filters continuous time systems estimation algorithms software tools

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PARTICLE FILTER ADAPTATION BASED ON EFFICIENT SAMPLE SIZE

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IFAC Proceedings Volumes 2006年第1期39卷 991-996页

作者： Ondřej Straka Miroslav Šimandl Department of Cybernetics and Research Centre: Data - Algorithms - Decision University of West Bohemia in Pilsen Univerzitní 8 306 14 Plzeň Czech Republic

The paper deals with the particle filter in state estimation of a discrete-time nonlinear nongaussian system. The aim of the paper is to design a sample size adaptation technique to guarantee an estimate quality. The proposed sample size adaptation technique considers an unadapted particle filter with a fixed number of samples that would be drawn directly from the filtering probability density function and modifies the sample size of the adapted particle filter to keep the particle filters estimate quality identical. The adaptation technique is based on the effective sample size and utilizes the sampling probability density function and an implicit form of the filtering probability density function. Application of the particle filter with the sample size adaptation technique is illustrated in a numerical example.

关键词： state estimation nonlinear systems Monte Carlo method particle filter sample size effective sample size

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Bicriterial dual control with multiple linearization

Bicriterial dual control with multiple linearization

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作者： Flídr, Miroslav Šimandl, Miroslav Department of Cybernetics Research Centre: Data - Algorithms - Decision University of West Bohemia in Pilsen Univerzitní 8 30614 Plzeň Czech Republic

ISBN: (纸本)008045108X

A suboptimal dual controller for discrete stochastic systems with unknown parameters based on the bicriterial approach is proposed and discussed. It is supposed that all the random quantities are non-Gaussian. This assumption induces that a global estimation method has to be used. The Gaussian sum method with multiple linearization technique was chosen and applied in the bicriterial control approach. The probing part of the control law is determined for each local node of estimated probability density function separately and respects accuracy of each local estimate inherent in the estimated probability density function. A comparison of the proposed modified bicriterial controller and the bicriterial controller which uses global point estimate only is shown in some numerical examples. Copyright © 2005 IFAC.

关键词： Stochastic systems

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Sigma point Gaussian sum filter design using square root unscented filters

Sigma point Gaussian sum filter design using square root uns...

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作者： Šimandl, Miroslav Duník, Jindřich Department of Cybernetics Research Centre: Data - Algorithms - Decision University of West Bohemia in Pilsen Univerzitń 8 306 14 Plzeň Czech Republic

ISBN: (纸本)008045108X

Local and global estimation approaches are discussed, above all the Unscented Kalman Filter and the Gaussian Sum Filter. The square root modifica- tion of the Unscented Kalman Filter is derived and it is used in the Gaussian Sum Filter framework. The new Sigma Point Gaussian Sum Filter is designed and some aspects of the filter are presented. Estimation quality and computational demands of the filter are illustrated in a numerical example. Copyright © 2005 IFAC.

关键词： Stochastic systems

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Using the bhattacharyya distance in functional sampling density of particle filter

Using the bhattacharyya distance in functional sampling dens...

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作者： Straka, Ondřej Šimandl, Miroslav Department of Cybernetics Research Centre: Data - Algorithms - Decision University of West Bohemia in Pilsen Univerzitní 8 306 14 Plzeń Czech Republic

ISBN: (纸本)008045108X

The particle filter for nonlinear state estimation of discrete time dynamic stochastic systems is treated. The functional sampling density of the particle filter strongly affecting estimate quality is studied. The density is given by weighted mixture of the transition probability density functions. The weights are calculated using distance of two reference variable probability density functions representing prior and measurement information. The aim is to find a suitable distance that does not suffer from problems with its numerical computation and that can be computed for a large set of systems analytically. It seems that the Bhattacharyya distance is feasible for evaluation of such a distance. Quality and computational demands of the functional particle filter with primary weights computed using the Bhattacharyya distance are illustrated in a numerical example. Copyright © 2005 IFAC.

关键词： Monte Carlo methods

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