Quasi-likelihood estimation of the arrival time of an ultra-wideband quasi-radio signal with unknown amplitude and initial phase

The problem of estimating the time of arrival of a signal is relevant in the fields of radio and hydrolocation, radio astronomy, remote observation and sensing, etc. The useful signal is often described by a quasi-deterministic function of time, which can be regular or discontinuous. In recent years, problems of processing ultra-wideband signals have been of significant interest. Among the many UWB signals, it is customary to distinguish a separate class of ultra-wideband quasi-radio signals, the structure of which is similar to the structure of narrowband radio signals, but the condition of relative narrowband for which may not be met. Algorithms for estimating the arrival time of regular ultra-wideband quasi-radio signals have been studied in the existing literature. In this case, the synthesis and analysis of an algorithm for quasi-plausible estimation of the arrival time of a discontinuous signal of finite duration and arbitrary shape is of practical interest. The purpose of the work is to synthesize and analyze a quasi-likelihood algorithm for estimating the time of arrival of a discontinuous ultra-wideband quasi-radio signal with an unknown amplitude and initial phase against a background of white Gaussian noise. In this work, closed asymptotically exact expressions for the bias and scattering of the estimate are obtained, which make it possible to study the effectiveness of the synthesized algorithm, as well as compare its effectiveness with special cases of signal models - narrowband and wideband radio and video signals. The results of the study make it possible to determine losses in the accuracy of estimation the signal arrival time due to a priori ignorance of the initial phase and shape of the modulating function of the signal. Depending on the required accuracy of estimate the time of arrival of an ultra-wideband quasi-radio signal, it is possible to optimize the parameters of the transmitted signals and determine the limits of applicability of the designed radio system.