A fixed-complexity nonlinear estimation technique

The typical nonlinear estimation problem is solved by a quasi-linear technique, the extended Kalman filter (EKF). The EKF provides satisfactory results if first order approximations to the system equations are adequate. If they are not and the filtering time is long, substantial estimation errors may build up. To overcome this problem, various techniques have been developed, e.g., "second-order filters" and "polynomial filters" have been proposed1-3. In this paper, the nonlinear system and observation equations are linearized, the higher order terms in the Taylor series are treated as unknown time functions and these functions are estimated using a block sequential least squares technique. An extended observer is then used to solve for the linear perturbation from the nominal state and a second estimator is used to estimate the residual observer error.