Collaborative Sequential Detection of Gaussian Models from Observed Data and The Value of Information Exchanged

We consider the problem of detecting which Gaussian model generates an observed time series data. We consider as possible generative models two linear systems driven by white Gaussian noise with Gaussian initial conditions. We also consider two collaborating observers. The observers observe a function of the state of the systems. Using these observations, the aim is to find which one of the two Gaussian models has generated the observations. For each observer we formulate a sequential hypothesis testing problem. Each observer computes its own likelihood ratio based on its own observations.Using the likelihood ratio, each observer performs sequential probability ratio test (SPRT) to arrive at its decision on the hypothesis. Taking into account the random and asymmetric stopping times of the two observers, we present a consensus algorithm which guarantees asymptotic convergence to the true hypothesis. The consensus algorithm involves exchange of information, i.e., the decision of the observers. Through simulations, the “value” of the information exchanged, probability of error and average time to consensus are computed.