Linear-minimum-mean-square-error observer for multi-rate sensor fusion with missing measurements

This note presents the problem of designing the linear-minimum-mean-square-error observer for a class of multi-rate sensor fusion systems with missing measurements. Under the casuality constraint because of the multi-rate nature, the covariances of the equivalent noises in the estimation error system are obtained via multi-rate recursive computation. Through minimising the traces of the covariances of the estimation errors, the optimal observer is obtained. Fortunately, all the observer parameters can be calculated off-line. A numerical example is given to show the effectiveness of the proposed observer.