Online estimation of a time-varying delay based on a univariate cross-ambiguity function analysis

This paper presents a method to estimate a linearly time-varying delay between two continuous signals. The joint estimation of the time delay and Doppler shift by analyzing the cross-ambiguity function is state of the art, however, this method has high computational demands as it relies on a bi-variate search. It is shown that, by using previous estimation results to initialize the analysis, a similar result can already be obtained with a univariate search, as is then sufficient to search for the variation of the delay since the last measurement. Perfect tracking is obtained with proper initialization, and for the case of incorrect initialization, convergence can be guaranteed and even influenced with a tuning parameter. A theoretical analysis and a numerical example illustrate the performance of the proposed method.