Maximum Likelihood Estimate of the Arrival Time of Ultra-Wideband Quasi-Radio Signal with Unknown Amplitude and Phase

Abstract

The maximum likelihood algorithm for estimating the arrival time of ultra-wideband quasi-radio signal with unknown amplitude and phase has been synthesized. The duration of the specified signal can amount to several periods or a fraction of harmonic oscillation period. The realization of maximum likelihood algorithm (ML) for estimating the arrival time of ultra-wideband quasi-radio signal is shown to be appreciably more complex than the realization of ML algorithm for estimating the arrival time of narrowband radio signal. The probability of reliable estimate, bias and scattering of ML estimate of the arrival time of ultra-wideband quasi-radio signal have been found with due regard for anomalous errors making it possible to investigate its threshold properties. The computer methods of statistical simulation were used to determine the performance efficiency of the synthesized algorithm of ML estimate and the limits of the application scope of obtained asymptotically exact (with the rise of signal-to-noise ratio) formulas for the characteristics of time arrival estimate of ultra-wideband quasi-radio signal with unknown amplitude and phase.