The eXogenous Kalman Filter (XKF)

It is well known that the time-varying Kalman Filter (KF) is globally exponentially stable and optimal in the sense of minimum variance under some conditions. However, nonlinear approximations such as the extended KF linearizes the system about the estimated state trajectories, leading in general to loss of both global stability and optimality. Nonlinear observers tend to have strong, often global, stability properties. They are, however, often designed without optimality objectives considering the presence of unknown measurement errors and process disturbances. We study the cascade of a global nonlinear observer with the linearized KF, where the estimate from the nonlinear observer is an exogenous signal only used for generating a linearized model to the KF. It is shown that the two-stage nonlinear estimator inherits the global stability property of the nonlinear observer, and simulations indicate that local optimality properties similar to a perfectly linearized KF can be achieved. This two-stage estimator is called an eXogeneous KF (XKF).