Asymptotic CRB for Satellite based Localization

We present novel lower bounds on the localization error using a network of satellites randomly deployed on a sphere around Earth. The land terminal (LT) estimates its location using the received signals from the satellites, taking advantage of both time difference of arrival (TDOA) and received signal strength (RSS) information. Our new analysis approach characterizes the localization performance by its asymptotic behavior as the number of satellites gets large. Using the law of large numbers, we derive closed-form expressions for the asymptotic Cramer Rao bound (CRB) from which we draw useful insights. The resulting expressions depend solely on the network statistics and are not a function of a particular network configuration. We show that the results are relevant for realistic finite numbers of satellites and give a good prediction to the localization accuracy. We also show the relative importance of TDOA vs. RSS in different system bandwidths.