Progressive Bayesian estimation for nonlinear discrete-time systems:the filter step for scalar measurements and multidimensional states

Hanebeck, Uwe D.; Feiermann, O.

doi:10.1109/cdc.2003.1272490

Cited by 8 publications

(8 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For every number of components investigated, a full recalculation is performed [12]. The second approach adds new components one at a time and adjusts all components to guarantee optimality of the resulting approximation [13]. In both approaches, the complexity of the parameter adjustment grows quadratically with the number of components.…”

Section: A Motivationmentioning

confidence: 99%

See 1 more Smart Citation

Dirac mixture trees for fast suboptimal multi-dimensional density approximation

Klumpp

Hanebeck

2008

2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems

View full text Add to dashboard Cite

Abstract-We consider the problem of approximating an arbitrary multi-dimensional probability density function by means of a Dirac mixture density. Instead of an optimal solution based on minimizing a global distance measure between the true density and its approximation, a fast suboptimal anytime procedure is proposed, which is based on sequentially partitioning the state space and component placement by local optimization. The proposed procedure adaptively covers the entire state space with a gradually increasing resolution. It can be efficiently implemented by means of a pre-allocated tree structure in a straightforward manner. The resulting computational complexity is linear in the number of components and linear in the number of dimensions. This allows a large number of components to be handled, which is especially useful in high-dimensional state spaces.

show abstract

Section: A Motivationmentioning

confidence: 99%

“…Potential applications of the greedy approximation include the calculation of the density of a function of random variables, long-term prediction [13], state estimation of nonlinear stochastic systems [14], reachability analysis, numerical integration, and even the generation of pseudo-random numbers.…”

Section: A Motivationmentioning

confidence: 99%

Dirac mixture trees for fast suboptimal multi-dimensional density approximation

Klumpp

Hanebeck

2008

2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems

View full text Add to dashboard Cite

show abstract

“…For each recursive step, the number of mixture components increases so that the optimal analytical solution is not tractable. The algorithm proposed in [14] can optimally reduce the number of Gaussian components and get the suboptimal solution. Besides, particle filters are also used by some researchers to solve the similar problem.…”

Section: Bayesian Filtering For Simultaneous Localization and Biamentioning

confidence: 99%

Simultaneous Multi-Information Fusion and Parameter Estimation for Robust 3-D Indoor Positioning Systems

Wang¹,

Szabo²,

Bamberger³

et al. 2009

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

Abstract-Typical WLAN based indoor positioning systems take the received signal strength (RSS) as the major information source. Due to the complicated indoor environment, the RSS measurements are hard to model and too noisy to achieve a satisfactory 3-D accuracy in multi-floor scenarios. To enhance the performance of WLAN positioning systems, extra information sources could be integrated. In this paper, a Bayesian framework is applied to fuse multi-information sources and estimate the spatial and time varying parameters simultaneously and adaptively. An application of this framework, which fuses pressure measurements, a topological building map with RSS measurements, and simultaneously estimates the pressure sensor bias, is investigated. Our experiments indicate that the localization performance is more accurate and robust by using our approach.

show abstract

“…The algorithm proposed in [14] can optimally reduce the number of Gaussian components and get the suboptimal solution. Besides, particle filters are also used by some researchers to solve the similar problem.…”

Section: Bayesian Filtering For Simultaneous Localization and Biamentioning

confidence: 99%