A minimum variance filter for continuous discrete systems with additive-multiplicative noise

Abstract

In this paper, we extend the minimum variance filter, which is proposed in the literature for discrete state space systems with multiplicative noise, to continuous-discrete systems with multiplicative noise. The differential equations that describe the process are discretised using the Euler scheme at a higher sampling frequency than the measurement frequency. We test the performance of our new filter i.e. continuous discrete filter (CDF) on simulated numerical examples and compare the results with discrete discrete filter (DDF) which ignores the state behaviour in-between the measurement samples. The results show that the CDF outperforms the DDF in all the cases examined.