A new nonlinear filter referred to as the state-dependent Riccatiequation filter (SDREF) is presented. The SDREF is derived byconstructing the dual of a little known nonlinear regulator controldesign technique which involves the solution of a state-dependentRiccati equation (SDRE) and which has been appropriately called the SDREcontrol method. The resulting SDREF has the same structure as thecontinuous steady-state linear Kalman filter. In contrast to thelinearized Kalman filter (LKF) and the extended Kalman filter (EKF)which are based on linearization, the SDREF is based on aparameterization that brings the nonlinear system to a linear structurehaving state-dependent coefficients (SDC). In a deterministic setting,before stochastic uncertainties are introduced, the SDC parameterizationfully captures the nonlinearities of the system, It was shown inCloutier et al. (1996) that, in the multivariable case, the SDCparameterization is not unique and that the SDC parameterization itselfcan be parameterized. This latter parameterization creates extra degreesof freedom that are not available in traditional filtering methods.These additional degrees of freedom can be used to either enhance filterperformance, avoid singularities, or avoid loss of observability. Themain intent of this paper is to introduce the new nonlinear filter andto illustrate the behaviorial differences and similarities between thenew filter, the LKF, and the EKF using a simple pendulum problem
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