Efficient Nonlinear Bayesian Estimation based on Fourier Densities

Brunn, Dietrich; Sawo, Felix; Hanebeck, Uwe D.

doi:10.1109/mfi.2006.265642

Cited by 9 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[5] proposed to use the square root of density function instead of density function itself for calculation. In this way, the final approximated density is ensured to be non-negative.…”

Section: E Ensuring Non-negativitymentioning

confidence: 99%

“…Fourier series were first employed to estimate probability densities in [4]. Recently, [5] and [6] ensured the non-negativity of Fourier series by approximating the square root of the density instead of the density itself. The usage of Fourier series in nonlinear Bayesian filtering is also derived in [5] and [6].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, [5] and [6] ensured the non-negativity of Fourier series by approximating the square root of the density instead of the density itself. The usage of Fourier series in nonlinear Bayesian filtering is also derived in [5] and [6]. Using Fourier density approximation, the belief can be represented sufficiently by only a small number of Fourier coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the sum-product operations in BP algorithms can be more effectively calculated in Fourier domain since some convolution-like integral operations are more easily calculated than in space domain. Since the Fourier series are orthogonal expansions, the coefficients are derived independently and effectively [5]. In practice, this is done by efficient Fast Fourier Transform (FFT).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks

Wang

Obradović

et al. 2009

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

Abstract-Many distributed inference problems in wireless sensor networks can be represented by probabilistic graphical models, where belief propagation, an iterative message passing algorithm provides a promising solution. In order to make the algorithm efficient and accurate, messages which carry the belief information from one node to the others should be formulated in an appropriate format. This paper presents two belief propagation algorithms where non-linear and non-Gaussian beliefs are approximated by Fourier density approximations, which significantly reduces power consumptions in the belief computation and transmission. We use self-localization in wireless sensor networks as an example to illustrate the performance of this method.

show abstract

“…[5] proposed to use the square root of density function instead of density function itself for calculation. In this way, the final approximated density is ensured to be non-negative.…”

Section: E Ensuring Non-negativitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks

Wang

Obradović

et al. 2009

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

show abstract

“…The contribution of this paper is a full generalization of the approach we presented in [11] to the d-dimensional case. Particularly, the cumulative distribution, expected value and the covariance as well as the multidimensional Bayesian estimator are derived.…”

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

The Hitchhiker’s guide to nonlinear filtering

Kutschireiter

Surace

Pfister

2020

Journal of Mathematical Psychology

View full text Add to dashboard Cite

Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We start our review of the theory on nonlinear filtering from the simplest 'filtering' task we can think of, namely static Bayesian inference. From there we continue our journey through discrete-time models, which is usually encountered in machine learning, and generalize to and further emphasize continuous-time filtering theory. The idea of changing the probability measure connects and elucidates several aspects of the theory, such as the parallels between the discrete-and continuous-time problems and between different observation models. Furthermore, it gives insight into the construction of particle filtering algorithms. This tutorial is targeted at scientists and engineers and should serve as an introduction to the main ideas of nonlinear filtering, and as a segway to more advanced and specialized literature.

show abstract

Efficient Nonlinear Bayesian Estimation based on Fourier Densities

Cited by 9 publications

References 7 publications

Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks

Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks

Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

The Hitchhiker’s guide to nonlinear filtering

Contact Info

Product

Resources

About