APPROXIMATION APPROACH FOR NONLINEAR FILTERING PROBLEM WITH TIME-DEPENDENT NOISES .2. STABLE NONLINEAR FILTERS

This second part is devoted to the design of a stable nonlinear filter conditionally optimal in the minimum mean square (MMS) sense. The tec hnique used here is known as an inversion of a direct Lyapunov functio n method which suggests to find a filter in such way that a Lyapunov f unction, calculated along the filter trajectory, will change according to some prescribed law. Some properties of the stable filter are inve stigated. Connections of a stable MMS filter with an MMS filter propos ed in Part I is established. Stability of the proposed stable filter w ith 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 pr oposed stable filter.