Robust Estimation and Detection

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 problem using recent results for cooperative sensing in Cognitive Radios. Issues in robust estimation are motivated by the problem of deploying a sensor network for tracking vehicles. As a first step, we formulate an abstracted version of problem that is solved under different assumptions. In the simplistic case of liars behaving the same over all observations, we use the EM algorithm to successfully weed out lying nodes. The solution has been developed from two view points; in the first we consider the binary variable being detected as a latent variable and in the other case we consider the binary variable as a parameter. The results under the two schemes are presented and compared. Next we use the EM algorithm to deal with cases where the users may vary their lying behavior over time. In all we show that the factors that maximally impact our estimate/decision are the mean of the liars, the variance of the channel and the number of observations.