Rate-constrained robust estimation for unreliable sensor networks

We consider the problem of rate-constrained robust estimation of noisy sensor measurements in an unreliable sensor network. Noisy measurements of some physical process (e.g., temperature) made by individual sensors need to be communicated to a central observer over unreliable channels. Limited power resources of the sensors place a strong limit on the resolution with which the noisy sensor readings can be transmitted. Both, the sensors and the communication links can breakdown. However, the central observer is guaranteed to reliably receive readings from a certain minimum number of sensors. The goal of the central observer is to estimate the observed physical process from the received transmissions where a specified distortion metric provides an objective measure of estimation quality. In this work, we present an information-theoretic achievable rate-distortion region for this problem when the sensor measurement noise statistics are symmetric with respect to the sensors. Our results are optimal when the physical process and sensor noise are independent, i.i.d. Gaussian, and the sensor network is only as reliable as guaranteed.