Nonlinear set-theoretic position estimation of cellular phones

Horn, Joachim; Hanebeck, Uwe D.; Riegel, Konrad; Heesche, Kai; Hauptmann, Werner

doi:10.23919/ecc.2003.7085093

Cited by 6 publications

(2 citation statements)

References 19 publications

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“…The key idea is to find an appropriate approximation for probability density functions, which allows an efficient implementation of the Bayesian estimator. Very popular are the extended Kalman filter, particle filters [4], and set based methods [5]. They all have in common that they are efficient, scale well with an increasing number of dimensions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

Brunn¹,

Sawo²,

Hanebeck³

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-Efficiently implementing nonlinear Bayesian estimators is still an unsolved problem, especially for the multidimensional case. A trade-off between estimation quality and demand on computational resources has to be found. Using multidimensional Fourier series as representation for probability density functions, so called Fourier densities, is proposed. To ensure non-negativity, the approximation is performed indirectly via Ψ-densities, of which the absolute square represent the Fourier density. It is shown that Ψ-densities can be determined using the efficient fast Fourier transform algorithm and their coefficients have an ordering with respect to the Hellinger metric. Furthermore, the multidimensional Bayesian estimator based on Fourier densities is derived in closed form. That allows an efficient realization of the Bayesian estimator where the demands on computational resources are adjustable.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

Brunn¹,

Sawo²,

Hanebeck³

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…In applications, the incorporation of motion often transforms a poorly posed problem and makes it possible to estimate the state effectively. In [6], Hanebeck makes no use of dynamics, and further work in [7] and [8] also deals only with static systems. The main problem with incorporating dynamics into this framework is due to the fact that the chosen embedding renders the measurement equations linear but does not necessarily do so for the state update and, even worse, can make linear dynamics become nonlinear.…”

Section: Incorporating Motionmentioning

confidence: 99%

Extensive Representations and Algorithms for Nonlinear Filtering and Estimation

Stump

Grocholsky

Kumar

Springer Tracts in Advanced Robotics

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Summary. Most estimation problems in robotics are difficult because of (a) the nonlinearity in observation models; and (b) the lack of suitable probabilistic models for the process and observation noise. In this paper we develop a set-valued approach to estimation that overcomes both these limitations and illustrates the application to localization of multiple, mobile sensor platforms with range sensors.

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