Age of Information and Remote Estimation

In this chapter, we discuss the relationship between age of information and signal estimation error in real-time signal sampling and reconstruction. Consider a remote estimation system, where samples of a scalar Gauss-Markov signal are taken at a source node and forwarded to a remote estimator through a channel that is modeled as a queue. The estimator reconstructs an estimate of the real-time signal value from causally received samples. The optimal sampling policy for minimizing the mean square estimation error is presented, in which a new sample is taken once the instantaneous estimation error exceeds a predetermined threshold. When the sampler has no knowledge of current and history signal values, the optimal sampling problem reduces to a problem for minimizing a nonlinear Age of Information (AoI) metric. In the AoI-optimal sampling policy, a new sample is taken once the expected estimation error exceeds a threshold. The threshold can be computed by low-complexity algorithms, and the insights behind these algorithms are provided. These optimal sampling results were established (i) for general service time distributions of the queueing server, (ii) for both stable and unstable scalar Gauss-Markov signals, and (iii) for sampling problems both with and without a sampling rate constraint.(1)