Adaptive Kalman Filter for Linear Systems with Additive and Multiplicative Noises
preprintposted on 2021-05-14, 11:40 authored by Xingkai YuXingkai Yu
This manuscript investigates adaptive Kalman filter problem of of linear systems with multiplicative and additive noises. The main contributions are stated in two aspects. Firstly, compared with the estimation problem of linear systems with additive noises, we propose an algorithm that is applicable to the linear systems with both additive and multiplicative noises. To solve the technical issue raised by the multiplicative noise, a variational Bayesian approach is proposed. Moreover, the proposed approach is capable of estimating the multiplicative and additive measurement noise covariances as a whole, while the existing algorithms often operate in a separate way. Secondly, in contrast with existing literature, where the covariance of the multiplicative noise is assumed to be fixed and known, we focus on the situation that the covariances of both additive and multiplicative noises are time-varying and unknown. Towards this end, a novel adaptive Kalman filter is proposed to jointly estimate the covariances of multiplicative and additive noises based on projection formula and a VB approach.