State estimation under non-Gaussian Levy noise: A modified Kalman filtering method

TL;DR

This paper introduces a modified Kalman filter designed to effectively estimate states in linear systems affected by non-Gaussian Le9vy noise, overcoming limitations of the traditional filter.

Contribution

A novel modified Kalman filtering approach tailored for systems with non-Gaussian Le9vy noise, addressing the challenge of infinite variance.

Findings

Effective state estimation with non-Gaussian Le9vy noise

Maintains reasonable computational cost

Simulation results validate the method

Abstract

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian L\'evy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian L\'evy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian L\'evy noise is devised. It works effectively with reasonable computational cost. Simulation results are presented to illustrate this non-Gaussian filtering method.