Covariance-Based Transmission Power Control for Estimation over Wireless Sensor Networks

Abstract

In this study, we would like to design a transmission power control mechanism for minimizing the transmit power of a wireless sensor node subject to a constraint on the quality of estimation at a remote estimator. In particular, we measure the estimation distortion by a mean square error function, and model the transmit power as a function of the packet success rate using the IEEE 802.15.4 standard which was formed for the specification of low-data-rate and low-power wireless communication. We formulate the problem with an infinite horizon discounted cost function. We show that there is a separation between the designs of the optimal estimator and optimal transmit power policy. Then, we use dynamic programming to characterize the optimal transmit power policy in terms of the estimation error covariance. Finally, we propose approximate value iteration as an approximation algorithm to calculate a near-optimal transmit power policy.

Transmission Power Control for Remote State Estimation in Industrial Wireless Sensor Networks

“…Initially, the trade-off between transmission power and packet loss for remote state estimation of a single-sensor has been studied in [5]- [10]. Solutions are presented for a noiseless sensor [5], and for noisy measurements where the transmission power policy is computed offline [6]- [8], online [9], and in combination with an energy harvester [10].…”

“…where Θ k,ℓ ≻ 0 is a weighting matrix and xk,ℓ is the best state estimate given the information set I k,ℓ . As shown in [8], the conditional expected value of the state is the minimizer of the mean square error for the system in ( 15) and ( 16) over the one-step delay packet-erasure channel with arrival process specified by (6). Hence, we can obtain…”

“…to reformulate the estimation error [8]. Hence, the optimal transmit power schedule is obtained by solving the following optimization problem…”