Abstract:

This second part is devoted to the design of a stable nonlinear filter conditionally optimal in the minimum mean square (MMS) sense. The technique used here is known as an inversion of a direct Lyapunov function method which suggests to find a filter in such a way that a Lyapunov function, calculated along the filter trajectory, will change according to some prescribed law. Some properties of the stable filter are investigated. Connections of a stable MMS filter with an MMS filter proposed in Part I is established. Stability of the proposed stable filter with respect to misspecification of the model error statistics as well as the parameter uncertainty will be also examined. Numerical examples and simulation study are given to illustrate the efficiency of the proposed stable filter.