Comparison of Discrete and Continuous State Estimation with Focus on Active Flux Scheme

Abstract

This paper deals with the state estimation of non-linear stochastic dynamic systems, both continuous and discrete in time, with an emphasis on a numerical solution to the Bayesian relations by the point-mass filters. The filters for discrete-discrete and continuous-discrete state-space models are reviewed and a new highly accurate and fast active flux method is introduced and adapted for a continuous filter design. A wide set of the point-mass filters is compared in a numerical study together with a set of the particle filters.

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

“…For an arbitrary grid movement, the time update cannot be written as a convolution. That is why the ePMF uses a specific grid movement [12] ξ…”

“…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.…”

“…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…”

“…The extension to n x dimensions can be found in our previous paper [12]. The proposed solution is a combination of n x one-dimensional solutions, based on the Kronecker product.…”

“…In our previous paper [12] we have focused on the reduction of the computational complexity of the time-update and proposed an efficient point-mass predictor, (ePMFp) which simplified the big O complexity from O(N 2 ) to O(N log(N )) for systems with linear dynamics, where N is the number of grid points.…”