Minimum-Variance State and Fault Estimation for Multirate Systems With Dynamical Bias

This brief is concerned with the joint state and fault estimation problem for a class of multi-rate systems with dynamical bias. To reflect real practice, the multi-rate sampling is considered which allows the sensor sampling rate and the state update rate to be different. The sensor is subject to the sensor fault that changes according to a dynamic equation. Instead of applying the traditional lifting technique, we introduce a time-varying delay into the measurement equation so as to transform the multi-rate systems into single-rate ones. The aim of this brief is to develop a joint state and fault estimation algorithm with minimized estimation error covariance. The recursion of the estimation error covariance is first derived, and appropriate estimator gains are then characterized that minimizes the estimation error covariance. A simulation example on the DC servo system is given to confirm the usefulness of the developed recursive state and fault estimation algorithm.