We address distributed detection in wireless sensor networks, in which a number of spatially distributed sensors monitor the presence or absence of a common event and report their binary decisions to a fusion center (FC) through dedicated binary symmetric channels (BSCs). Both the sensing channels and the reporting channels vary over time, so the detection performance of the sensors and the error probabilities of the BSCs change between consecutive sensing periods and are unknown to the FC. Under these conditions, the likelihood ratio test (LRT) is not implementable.In this work, we derive an online algorithm that enables the FC to blindly estimate and track the operating points of the sensors based on the binary decisions received through the BSCs. The algorithm also estimates the prior probability of the event to be detected. Based on these estimates, we propose an adaptive fusion rule that allows for online detection at the FC. The overall computational cost per sensing period is linear in the number of sensors. Numerical results show that the proposed fusion rule performs close to the clairvoyant LRT in realistic scenarios, and it outperforms the optimal counting rule.
This paper presents an optimal risk sensitive filter for a class of discrete-time linear singular systems. Unlike the standard Kalman filter (KF), which minimizes the mean squared estimation error and is sensitive to model uncertainty, the proposed filter employs an exponential quadratic cost criterion that penalizes large estimation errors more heavily, which is intended to improve robustness against modeling inaccuracies. By employing the Weierstrass canonical form (WCF), the singular system is transformed into an equivalent augmented state-space representation, which facilitates the derivation of explicit recursive equations. Based on this framework, a closed-form optimal risk sensitive (RS) filtering algorithm, referred to as the risk sensitive Kalman filter (RSKF), is developed for estimating states of singular systems. It is also shown that the proposed framework reduces to the standard KF for singular systems as a special case when the RS parameter vanishes, and recovers the standard RS filter when the singular matrix of the original system reduces to the identity matrix. Sufficient conditions for the uniform boundedness of the estimation error covariance under model uncertainty are established, and numerical results on uncertain singular systems further illustrate that the proposed filter achieves improved estimation accuracy compared with the standard KF in the presence of model uncertainty.
