An Opportunistic Sensor Scheduling Solution to Remote State Estimation Over Multiple Channels

We consider a sensor scheduling problem where the sensors have multiple choices of communication channel to send their local measurements to a remote state estimator for state estimation. Specifically, the sensors can transmit high-precision data packets over an expensive channel or low-precision data packets, which are quantized in several bits, over some cheap channels. The expensive channel, though being able to deliver more accurate data which leads to good estimation quality at the remote estimator, can only be used scarcely due to its high cost (e.g., high energy consumption). On the other hand, the cheap channel, though having a small cost, delivers less accurate data which inevitably deteriorates the remote estimation quality. In this work we propose a new framework in which the sensors switch between the two channels to achieve a better tradeoff among the communication cost, the estimation performance and the computational complexity, where the two-channel case can be easily extended to a multiple-channel case. We propose an opportunistic sensor schedule which reduces the communication cost by randomly switching among the expensive and cheap channels, and in the meantime maintains low computational complexity while introducing data quantization into the estimation problem. We present a minimum mean square error (MMSE) estimator in a closed-form under the proposed opportunistic sensor schedule. We also formulate an optimization problem to search the best opportunistic schedule with a linear quantizer. Furthermore, we show that the MMSE estimator in the limiting case becomes the standard Kalman filter.