A Solution to Estimation Fusion for Multirate Measurements with Delays

This paper presents the distributed estimation fusion algorithms for a class of multirate multisensor systems with measurement delays. Different sensors uniformly sample measurements with different sampling rates and time delays. First, a new state-space model at the measurement sampling points is constructed and the original time delayed system is transformed to a delay-free one with correlated noises in limited time intervals to obtain the real-time estimation. Based on the new state-space model, the optimal local filter at the measurement sampling points is obtained for each single-sensor subsystem, and then the local estimator at the state update points is derived by using the predictor based on the filter at the measurement sampling points. Then, the estimation error cross-covariance matrices between any two local estimators are derived. Finally, the real-time distributed fusion estimator at the state update points is obtained based on the optimal fusion criterion weighed by matrices in the linear unbiased minimum variance sense. Besides, to avoid the correlation between system and measurement noises in the developed state-space model, a simple alternative but nonreal-time estimation fusion algorithm is also presented by employing dummy measurements. A numerical example is given to illustrate the effectiveness of the proposed algorithms.