Estimation of the TOA performance of Loran-C

Loran-C is a navigational aid that relies on the ability to make correct estimates of the Times of Arrival (TOAs) of signals received over a noisy radio channel. How good is the performance of Loran-C in this respect? Is it close to optimal? Are there perhaps better estimation techniques available than we currently employ? In this paper we use Estimation Theory to find the optimal limit of the accuracy of TOA estimates, for a given signalto-noise ratio (SNR). Specifically, we compute the Cramer-Rao Lower Bound (CRLB) which specifies the absolute minimum error variance that can be achieved by an unbiased estimator. From the CRLB we can estimate the best repeatable accuracy that can be attained using a set of TOAs. We compute here the CRLBs for the TOA of a Loran-C signal with both Additive White Gaussian Noise (AWGN) and Additive Coloured Gaussian Noise (ACGN). We then employ the Maximum Likelihood Estimator (MLE) and compare its results with that of CRLB. Simulation results show that the MLE approaches the minimum variance obtained by CRLB for SNR values of practical and reliable Loran-C operation.