Density Difference Grid Design in a Point-Mass Filter

Matoušek, Jakub; Duník, Jindřich; Straka, Ondřej

doi:10.3390/en13164080

Cited by 6 publications

(4 citation statements)

References 30 publications

(62 reference statements)

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“…Suitable algorithms for TRN include the grid resolution/support adaption algorithm considering noise magnitude [ 19 ], and the grid support adaption algorithm using mutual information [ 20 ]. The density specific grid design algorithm that assumes two different grids [ 21 ] and the density difference grid design algorithm based on the differentiation of the PDF in a sparse grid [ 22 ] have been presented recently for general estimation problems.…”

Section: Pmf With Reliable Time Propagationmentioning

confidence: 99%

“…Most of the studies have been conducted for the purpose of improving TRN performance, but the results are applicable to general estimation problems. Numerous research results for efficient grid design or reselection have been presented to improve PMF performance, and there are the Anticipative Grid Design (AGD) algorithm and the Boundary-based Grid Design (BGD) algorithm [ 18 ], the grid resolution and support design algorithm considering a noise level in TRN [ 19 ], the grid support design algorithm using mutual information [ 20 ], the density specific grid design algorithm assuming two different grids [ 21 ], and the density difference grid design algorithm based on the differentiation of the PDF in a sparse grid [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

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Reliable Time Propagation Algorithms for PMF and RBPMF

Sung

Lee

2021

Sensors

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This paper addresses the reliable time propagation algorithms for Point Mass Filter (PMF) and Rao–Blackwellized PMF (RBPMF) for the nonlinear estimaton problem. The conventional PMF and RBPMF process the probability diffusion for the time propagation with the direct sampled-values of the process noise. However, if the grid interval is not dense enough, it fails to represent the statistical characteristics of the noise accurately so the performance might deteriorate. To overcome that problem, we propose time propagation convolution algorithms adopting Moment Matched Gaussian Kernel (MMGK) on regular grids through mass linear interpolation. To extend the dimension of the MMGK that can accurately describe the noise moments up to the kernel length, we propose the extended MMGK based on the outer tensor product. The proposed time propagation algorithms using one common kernel through the mass linear interpolation not only improve the performance of the filter but also significantly reduce the computational load. The performance improvement and the computational load reduction of the proposed algorithms are verified through numerical simulations for various nonlinear models.

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Section: Pmf With Reliable Time Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reliable Time Propagation Algorithms for PMF and RBPMF

Sung

Lee

2021

Sensors

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“…• Density Difference Grid Design in a Point-Mass Filter by Jakub Matoušek, Jindřich Duník and Ondřej Straka [10].…”

Section: Contributions' Descriptionmentioning

confidence: 99%

Advanced Control Design and Fault Diagnosis

Simani

Zattoni

2021

Energies

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This document provides the motivations and a brief introduction to the Special Issue entitled “Advanced Control Design and Fault Diagnosis”, which aims at presenting several solutions to the advanced control design and fault diagnosis systems. These methodologies can be considered in the general framework of advanced control, fault diagnosis and fault tolerant control systems, which are also able to improve the safety of the system under monitoring. The focuses of the current research in this field addressed in this Special Issue are also presented with emphasis on the practical application to simulated and realistic examples, which should provide an overall picture of current and future developments in this area. The works of this Special Issue represent suitably extended contributions selected by the proponents from the ACD2019—the 15th European Workshop on Advanced Control and Diagnosis, which was organised in Bologna, Italy on November 21st–22nd.

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“…If we denote the part of our state describing the orientation with

and the part describing its translation with

, then we can rewrite our joint density as a product of the conditional density

and the marginalized density for the periodic part

. Splitting the state up into a part that is well suited for estimation using the Kalman filter and another part for which a nonlinear filter should be applied is a technique that has become popular for PFs as Rao–Blackwellization [ 16 ] and has also found application in other filters such as the point mass filter [ 17 ]. This technique was also the foundation for the grid-based filter for SE(2) [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

The State Space Subdivision Filter for Estimation on SE(2)

Pfaff

Hanebeck

2021

Sensors

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The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

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Density Difference Grid Design in a Point-Mass Filter

Cited by 6 publications

References 30 publications

Reliable Time Propagation Algorithms for PMF and RBPMF

Reliable Time Propagation Algorithms for PMF and RBPMF

Advanced Control Design and Fault Diagnosis

The State Space Subdivision Filter for Estimation on SE(2)

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