A new filtering technique for a class of nonlinear systems

In this paper, a new nonlinear filtering technique (θ-D filter) is presented. This filter is derived by constructing the dual of a new nonlinear regulator control technique, θ-D approximation which involves approximate solution to the Hamilton-Jacobi-Bellman equation. The structure of this filter is similar to the state dependent riccati equation filter (SDREF). However, this method does not need time-consuming online computation of the algebraic Riccati equation at each sample time compared with the SDREF. By manipulating the perturbation terms both the asymptotic stability and optimality properties can be obtained. A simple pendulum problem is investigated to demonstrate the effectiveness of this new technique.