On fusion of information from multiple sensors in the presence of analog erasure links

Consider multiple sensors that transmit data over analog erasure links to an estimation center. The sensors have access to distinct entries of the output vector of a linear and time-invariant plant, and the estimation center is intended to produce state estimates. If the estimation center can transmit noiseless acknowledgements back to the sensors at every time step, optimal algorithms to calculate the information to be transmitted by the sensors and to fuse the data at the estimation center have recently been identified. However, optimal algorithms are not known for the case when acknowledgements are not available. In this paper, we present an algorithm for the intermediate case when acknowledgements can be stochastically erased. Although no claims about optimality are made, the estimation error covariance achieved by the algorithm is a continuous function of the erasure probabilities at the links from the sensors to the estimation center, and at the links over which acknowledgements are transmitted. Thus, the performance improves continuously between the two extreme cases of no acknowledgements, and perfect noiseless acknowledgements being available. Moreover, with the proposed algorithm, there is no loss of stability region even if noiseless acknowledgements are no longer available.