Optimal Data Incest Removal in Bayesian Decentralized Estimation Over a Sensor Network

A fundamental issue in Bayesian decentralized estimation over a sensor network is the inadvertent multiple re-use of data also known as data incest. We show the relationship between data incest and the network topology by using a graph theoretical formulation. A novel necessary and sufficient condition based on the topology of the network is derived so that data incest management can be optimally achieved. This approach requires large storage capabilities at the sensor level. In the case of an arbitrary network, if the necessary and sufficient condition for data incest does not hold then finding a sub-optimal strategy requires solving a 0-1 integer optimization problem where the dimension of the vector to optimize increases with time. Numerical results illustrate the effectiveness of our approach.