A new technique for nonlinear estimation

A new nonlinear filter referred to as the state-dependent Riccati equation filter (SDREF) is presented. The SDREF is derived by constructing the dual of a little known nonlinear regulator control design technique which involves the solution of a state-dependent Riccati equation (SDRE) and which has been appropriately called the SDRE control method. The resulting SDREF has the same structure as the continuous steady-state linear Kalman filter. In contrast to the linearized Kalman filter (LKF) and the extended Kalman filter (EKF) which are based on linearization, the SDREF is based on a parameterization that brings the nonlinear system to a linear structure having state-dependent coefficients (SDC). In a deterministic setting, before stochastic uncertainties are introduced, the SDC parameterization fully captures the nonlinearities of the system, It was shown in Cloutier et al. (1996) that, in the multivariable case, the SDC parameterization is not unique and that the SDC parameterization itself can be parameterized. This latter parameterization creates extra degrees of freedom that are not available in traditional filtering methods. These additional degrees of freedom can be used to either enhance filter performance, avoid singularities, or avoid loss of observability. The main intent of this paper is to introduce the new nonlinear filter and to illustrate the behaviorial differences and similarities between the new filter, the LKF, and the EKF using a simple pendulum problem.