Power allocation for state estimation over wireless channels using multiple sensors

This paper considers state estimation of scalar linear systems using analog 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 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. In the case of fading channels without channel state information a sub-optimal linear estimator is derived, and under optimal power allocation, numerical studies show that for non-zero mean channels its performance in the multi-access scheme is comparable to the case where full channel state information is available.