A Modified Kalman Filter Under Non-Gaussian Levy Noise

This article presents a modified Kalman filter for linear systems with non-Gaussian Levy noise. The article consists of five parts. The first part reviews the origin and development of the Kalman filter. The second part presents some related concepts and preliminary knowledge. The third part reviews the iterative formulas of the conventional Kalman filter with Gaussian white noise. As non-Gaussian Levy noise exists widely in practice and has infinite variance, it is desirable to study the Kalman filtering problems under non-gaussian Levy noise.of infinite variance. To this end, a modified Kalman filter is developed in Part five. The modified Kalman filter is verified by numerical simulation. The fifth part presents the effect of the state estimation using the conventional Kalman filter to Gaussian noise, the effect of the state estimation using the conventional Kalman filter to non-Gaussian Levy noise and the good effect of the state estimation using the modified Kalman filter to non-Gaussian Levy noise.The article uses the linear minimum variance estimation theory to derive the conventional Kalman filter and the modified Kalman filter. Simulations are carried out by using Matlab. We also use the figures to visualize the measurement value, the state estimation value, the measurement error and state position error.