Stochastic approximation based methods for computing the optimal thresholds in remote-state estimation with packet drops

Abstract

A remote-state estimation system consisting of a sensor and an estimator is considered. The sensor observes a scalar Gauss-Markov process and at each time determines whether or not to transmit the state of the process. The transmission takes place over a packet drop channel. Previous results have established that the optimal transmission strategies are threshold based and optimal estimation strategies are Kalman-like. We propose stochastic approximation algorithms to compute the optimal thresholds for two setups: a Keifer-Wolfowitz based algorithm for the case when there is a cost associated with each transmission and a Robbins-Monro based algorithm for the case when there is a constraint on the expected number of transmissions. The results are verified by comparing against existing results for the no packet drop case.