Robust Estimation and Detection in Ad Hoc and Sensor Networks

Interest in robust detection and estimation in the presence of lying nodes has assumed importance in a number of applications. In this paper we motivate the robust detection and estimation problem using recent results for cooperative sensing in cognitive radios and multi-object tracking in sensor networks. As a first step, we formulate an abstract version of the problem that is solved under different assumptions. We use expectation maximization (EM) framework to successfully weed out the lying nodes. We consider different types of lying behavior. In the simplistic case of liars behaving the same over all observations. In the more complex cases, the lying behavior of the users changes over time. The solution to the problem of detection in the presence of lying nodes has been developed from two view points. In the first case we consider the binary variable being detected as a latent variable, and in the second case we consider the binary variable as a parameter. The results under the two schemes are presented and compared. In all of the cases considered in this paper, we show that the factors that maximally impact the estimation/decision process are the mean of the liars, the variance of the channel, and the number of observations