Measuring Random Pulses with Unknown Time-Frequency and Power Parameters

Abstract

AbstractThe task of estimating the time of arrival and the dispersion of the pulse radio signal with an unknown band center of its random substructure is considered. By applying the maximum likelihood method, the two estimation algorithms are synthesized. The first algorithm called the quasi-likelihood one is designed for some expected value of the unknown band center that may not coincide with the real value in the general case. The second algorithm known as the maximum likelihood one estimates all the unknown time-frequency and power parameters of the pulse signal. The possibilities of the hardware implementation of the introduced algorithms are considered. In order to evaluate their efficiency, the analytical expressions for the characteristics of the resulting estimates are found through the local Markov approximation method. The losses in the accuracy of quasi-likelihood estimates of the time of arrival and the dispersion of the random pulse due to ignorance of the band center are determined. The gain in accuracy that is achieved when using the maximum likelihood algorithm instead of the quasi-likelihood one due to the adaptation to the band center is also demonstrated. It is then noted that the maximum likelihood algorithm has a more complex structure and requires more computational costs compared with the quasi-likelihood one. The conclusions are made about the possibility of an informed choice of one or another estimation algorithm in each specific case #CSOC1120.KeywordsRandom pulse signalMaximum likelihood methodRegular and discontinuous parametersLocal and additive local Markov approximation methodBias and variance of estimate