Continuous Nonlinear State Prediction by Finite Volume Method on Logically Rectangular Grids

Matoušek, Jakub; Brandner, Marek; Duník, Jindřich

doi:10.1109/cdc45484.2021.9683293

Cited by 2 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the grid movement (19), (20), the TPM matrix rows contain the same unique values of the Gaussian transition kernel with mean ξ (:,j) k+1 for j-th row, therefore the predictive weights can be calculated by n x dimensional convolution with zero padding as ). Matrices with ∼ overhead are transformed from computational space generally to tensors in the physical space as shown in Figure 1 for 2 dimensions with Gaussian noise (i.e.…”

Section: A Fast Fourier Transform Based Solutionmentioning

confidence: 99%

“…As the eigenvalues λ t k are time-varying because of the grid movement (19), (20), and the eigenvectors are timeinvariant (i.e., constant), the decomposition (26) can be treated as…”

Section: B Fast Sine Transform Based Solutionmentioning

confidence: 99%

“…Unfortunately, the filtering grid (i.e. predictive grid from last step k − 1 to this step k) has generally a rhomboid size, because of (19), and (20). This means that a computationally expensive MATLAB® function scatteredInterpolant has to be used.…”

Section: A Grid Movement Compensation Applicationmentioning

confidence: 99%

See 2 more Smart Citations

Design of Efficient Point-Mass Filter with Application in Terrain Aided Navigation

Matoušek¹,

Duník²,

Brandner³

2023

Preprint

View full text Add to dashboard Cite

This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-pointbased point-mass filter (PMF), which is the most computationally demanding part of the PMF algorithm. A novel efficient PMF (ePMF) estimator, unifying continuous and discrete, approaches is proposed, designed, and discussed. By numerical illustrations, it is shown, that the proposed ePMF can lead to a time complexity reduction that exceeds 99.9% without compromising accuracy. The MATLAB® code of the ePMF is released with this paper.

show abstract

Section: A Fast Fourier Transform Based Solutionmentioning

confidence: 99%

“…As the eigenvalues λ t k are time-varying because of the grid movement (19), (20), and the eigenvectors are timeinvariant (i.e., constant), the decomposition (26) can be treated as…”

Section: B Fast Sine Transform Based Solutionmentioning

confidence: 99%