Multi-rate fusion estimation for multi-sensor systems over Gilbert-Elliott channels

The distributed fusion estimation problem is discussed in this paper for a class of multi-rate multi-sensor systems. The measurements are assumed to be transmitted from the sensor to estimator over the Gilbert-Elliott channels governed by a two-state Markov chain due to the unreliable wireless network. Moreover, the probabilistic packet losses are considered in the Gilbert-Elliott channels, which is described by a random variable. The underlying system is measured by multiple sensors, where the sampling periods of sensors are integer multiples of the updating periods for system states. The above-mentioned multi-rate system is converted into a general single-rate one by the state iterative approach, and then a general system is put forward to characterize the dynamics from both the plant and transmission channels. Subsequently, the local estimators are devised to ensure the upper bounds of the estimation error covariances, and the estimator parameters are determined properly to minimize the derived upper bounds. In addition, the local estimates are fused by the covariance intersection method, and the corresponding consistency of the proposed fusion estimator is presented. Finally, a numerical example is given to illustrate the validity of the developed fusion estimation scheme.