The Modified Gain Extended Kalman Filter and Parameter Identification in Linear Systems

For a special class of systems, a general formulation and stochastic stability analysis of a new nonlinear filter, called the modified gain extended Kalman filter (MGEKF), is presented. Used as an observer, it is globally exponentially convergent. In the stochastic environment a nominal nonrealizable filter algorithm is developed for which global stochastic stability is proven. With respect to this nominal filter algorithm, conditions are obtained such that the effective deviations of the realizable filter are not destabilizing. In an appropriate coordinate frame, the parameter identification problem of a linear system is shown to be a member of this special class. For the example problems, the MGEKF shows superior convergence characteristics without evidence of instability.