Adaptive Sparse-grid Gauss-Hermite Filter

TL;DR

The paper introduces an adaptive sparse-grid Gauss-Hermite filter (ASGHF) that reduces computational load while maintaining accuracy in nonlinear filtering by adaptively allocating points based on nonlinearity levels.

Contribution

It proposes a novel adaptive sparse-grid quadrature method for nonlinear filtering that adjusts points dynamically to optimize accuracy and computational efficiency.

Findings

ASGHF achieves similar accuracy to existing filters with fewer computations.

The method allows controlled accuracy improvements with limited additional computational cost.

ASGHF enables online estimation near full efficiency within a predefined computational budget.

Abstract

In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid Gauss-Hermite filter (SGHF) and Gauss-Hermite filter (GHF) with a considerable reduction in computational load. Further, in the conventional GHF and SGHF, any increase in the accuracy level may result in an unacceptably high increase in the computational burden. However, in ASGHF, a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter. This enables the online estimator to operate near full efficiency with a predefined computational budget.