Fusion Estimation for WSNs Using Dimension-Reduction Method

Abstract

In Chaps. 2, 3, and 4, energy-efficient fusion estimation methods are presented by slowing down the transmission rates of measurements/local estimates and the estimation rate. In this chapter, a dimension-reduction method will be introduced for energy-efficient fusion estimation. To satisfy finite communication bandwidth and save energies consumed in communication, different dimensionality reduction approaches have been proposed in [1–7] to solve the fusion estimation problem, and the main idea of these approaches is that all the components of a vector signal are weighted and added to realize the objective of dimension reduction. Note that one should resort to the feedback information from a fusion center to obtain the compression matrices [3]. Different from the existing methods, this chapter presents the idea of directly choosing a part of components of local estimates to reduce the dimension of the local estimates to be transmitted to a fusion center. Specifically, when a local estimate is available at each sensor, only a part of the elements of the local estimate is selected and transmitted to the fusion center to save energy and meet the network bandwidth constraint. After the fusion center receives the local estimate with reduced dimension, a compensation strategy is proposed to reconstruct the local estimate and design the local unbiased estimator and improve the fusion estimation precision. Based on the optimal fusion estimation algorithm weighted by matrices, a recursive distributed fusion estimator is designed in the linear minimum variance sense. The gain matrix of the designed fusion estimator can be computed off-line as it does not need to know whether each component is sent or not at a particular time. Since the performance of the fusion estimator is dependent on the local estimate components selecting probabilities, some sufficient conditions, which are related to the selecting probabilities and system parameters, are derived such that the mean square error (MSE) of the fusion estimator is bounded. For linear time-invariant systems, some sufficient conditions are presented for the convergence of the fusion estimators.