Advanced Maximum Likelihood Time Delay Estimation for Weak Signal

Abstract — In this paper, we propose a robust maximum like-lihood (RML) approach for delay and amplitude estimation of weak GPS signals in multipath and interference environments such as that encountered in indoor applications. First, to formu-late the problem we exploit the fact that during the acquisition period the propagation delay causes only a circular shift to the spreading C/A code vector. This allows the decomposition of the received data vector into a constant component plus an undesired signals component. Then, a sample mean model is developed using a moving average over long time durations to reduce the effect of undesired zero-mean signals to one of a colored Gaussian noise. The developed model has an anti-jam structure which relies on the exploitation of a temporal structure property of the GPS signal, namely the replication of the C/A-code. An efficient temporal whitening technique is derived from the sample covariance matrix and applied to suppress the colored noise effect. The ML time-delay estimation of the superimposed multipath parameters becomes tractable and results in an efficient algorithm by adopting a sequential procedure. I