An Optimal Filtering Algorithm for Systems With Multiplicative/Additive Noises

In this letter, we propose a new optimal filtering algorithm for systems with multiplicative noise process under correlated additive noises. Different from the traditional derivation method of constructing innovation process, we derive the new algorithm based on the well-known projection theorem, which is simple in principle, convenient for recursive estimation and flexible for application. The new recursive filter is superior to the conventional Kalman filter in flexibility and applicability.