Envelope only TDOA estimation for sensor network self calibration

Self localization of nodes in wireless sensor networks (WSN) attracts wide interest in the past few years. The main challenge is to adopt calibration algorithms to the low-power/ low-bandwidth/ low-cost constrains on each sensor in the network. In this paper we present a novel approach, in which position-known anchors transmit special calibration signals simultaneously. Each node measures only the received signal strength (RSSI), i.e. envelope of the sum of received signals, and estimates time difference of arrivals (TDOA) of the signals. Two or more TDOA measurements allow the node to estimate its own position in the WSN. Based on an analysis of the appropriate Cramer Rao Lower Bound (CRLB) on the TDOA estimates, we suggest the choice of calibrating signals which provide optimal performance. The theoretical results are supported by simulations of the Maximum Likelihood (ML) estimators and numerical evaluation of the CRLB for a specific scenario of interest.