Enhancing noise robustness in discrete-time nonlinear observers

Moraal and Grizzle (1995) and Ciccarella et al. (1995) proposed two observers for discrete-time nonlinear systems. These observers are analyzed and it is demonstrated that in applications where measurement noise is present their performance may be inadequate. This deficiency is a consequence of the primary concern given to observer stability and rapidity of convergence and of the arbitrary manner by which the observer gains are selected. New versions of these observers are proposed which demonstrate improved noise rejection performance. The Moraal/Grizzle observer is improved by a minor modification of the gain. The observer of Ciccarella et al. is improved by eliminating a feedforward term which provides a measurement noise “passthrough” and by calculating the gains using the familiar Riccati equation