Fundamental limits of remote estimation of autoregressive Markov processes under communication constraints
For researchers in networked control and estimation, this provides theoretical limits and optimal strategies for remote estimation with communication constraints, though the results are for specific Markov processes and noiseless channels.
This paper characterizes the fundamental trade-off between communication cost and estimation accuracy for remote estimation of Markov processes (symmetric countable state Markov or Gauss-Markov) under noiseless but costly communication. It derives the minimum achievable cost (communication plus estimation error) for discounted and average cost setups, and the minimum estimation error under a constraint on average transmissions.
The fundamental limits of remote estimation of Markov processes under communication constraints are presented. The remote estimation system consists of a sensor and an estimator. The sensor observes a discrete-time Markov process, which is a symmetric countable state Markov source or a Gauss-Markov process. At each time, the sensor either transmits the current state of the Markov process or does not transmit at all. Communication is noiseless but costly. The estimator estimates the Markov process based on the transmitted observations. In such a system, there is a trade-off between communication cost and estimation accuracy. Two fundamental limits of this trade-off are characterized for infinite horizon discounted cost and average cost setups. First, when each transmission is costly, we characterize the minimum achievable cost of communication plus estimation error. Second, when there is a constraint on the average number of transmissions, we characterize the minimum achievable estimation error. Transmission and estimation strategies that achieve these fundamental limits are also identified.