Power efficient state estimation using multiple sensors

This paper considers state estimation of scalar linear systems using analog amplify and forwarding with multiple sensors, under a multiple access communication scheme. Optimal state estimation can be achieved using a Kalman filter. We show that in many situations, the error covariance decays at a rate of 1/M when the number of sensors M is large. Optimal allocation of transmission powers subject to constraints on the error covariance or sum power is also considered.