State Estimation Over Wireless Channels Using Multiple Sensors: Asymptotic Behaviour and Optimal Power Allocation

TL;DR

This paper analyzes the asymptotic behavior of state estimation in multi-sensor wireless systems, demonstrating error covariance decay with increasing sensors and proposing optimal power allocation strategies under various channel conditions.

Contribution

It introduces a comprehensive analysis of asymptotic error decay and develops optimal power allocation methods for multi-sensor wireless state estimation.

Findings

Estimation error covariance decays at a rate of 1/M with many sensors.

Optimal power allocation strategies are proposed for different channel knowledge scenarios.

Fading channels with channel state information are effectively managed using a greedy approach.

Abstract

This paper considers state estimation of linear systems using analog amplify and forwarding with multiple sensors, for both multiple access and orthogonal access schemes. Optimal state estimation can be achieved at the fusion center using a time varying Kalman filter. We show that in many situations, the estimation error covariance decays at a rate of $1/M$ when the number of sensors $M$ is large. We consider optimal allocation of transmission powers that 1) minimizes the sum power usage subject to an error covariance constraint and 2) minimizes the error covariance subject to a sum power constraint. In the case of fading channels with channel state information the optimization problems are solved using a greedy approach, while for fading channels without channel state information but with channel statistics available a sub-optimal linear estimator is derived.