Application of the SPOC form to Estimation and Identification of Nonlinear Systems

Abstract

Problems of state estimation and the optimal-best linear approximation of continuous time-variant non-linear system are formulated. A solution is proposed by generalization of the State and Parameters Observability Canonical form - SPOC to parameters varying systems. The SPOC representation of linear parameter varying systems enables application of tools from the existing estimation theories for linear time-varying systems to state estimation and identification of nonlinear systems. The solution is explicit, in closed form and gives recursive formulas of the optimal filter. The performance of the proposed algorithm is demonstrated for parameters varying parameters by simulations.