Linear Time-Varying Anisotropic Filtering and its Application to Nonlinear Systems State Estimation

The problem of optimal state estimation of linear discrete-time systems which outputs are measured with an additive white noise is addressed, in a anisotropy norm minimization setup. Such estimation problems are often encountered in target tracking problems where the target dynamics is not necessarily driven by white noise but rather driven by colored signals. The solution to the anisotropy filtering problem is obtained in terms of Difference Linear Matrix Inequalities which is derived using the Riccati equation associated with the anisotropic norm of linear-time-varying systems. The results are shown to be applicable to nonlinear systems state estimation using first order approximations or fuzzy representation. An simple but illustrative example is given to demonstrate the merits of the anisotropic filter.