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Efficiency evaluation for algorithms of measurement of phase difference and time difference of arrival of RF signals received by two spaced receivers

Keywords:

T.P. Potapova – Head of Sector, JSC «Kaluga Scientific Research Radio Engineering Institute»
E-mail: ptp7@yandex.ru


Accuracy of measurement (estimation) of phase difference and time difference of arrival between the received unknown signals by two spaced receiving channels defines accuracy characteristics of position finding devices of corresponding types.
The objective of the paper is to design a near-optimal algorithm for measurement of a relative phase and time shift of an unknown radiotechnical signal in a two-channel system; to obtain by means of math modeling the estimation variance against Cramer-Rao lower bound.
To identify potential accuracies for measurement of difference characteristics of a signal, in this paper we review the task of efficient estimation of the initial phase and delay time of the signal by the method of maximum likelihood. We give functional diagrams of devices that perform optimal measurement of these parameters relatively to a known reference wave, as well as analytical expressions for lower bounds of variances of estimations obtained. Maximum likelihood estimation of phase difference and arrival time difference of a signal in a two-channel system can be obtained as difference of maximum likelihood estimations of corresponding parameters in each channel. In this case measurements maintain the Gaussian law and measurement variances double.
For the case when the reference (emitted) signal is unknown, difference parameter estimation can be obtained with the help of the algorithm that performs optimal measurement of correspondent parameter, if one of received realizations is taken as reference signal. As the results of math modeling show, accuracy of such estimation will approach to potential accuracy of optimal estimation with increase of signal-to-noise ratio; this is proved by the diagrams that show dependence of estimation variances on signal-to-noise ratio. Preliminary filtering of the signal taken as reference signal considerably approximates the measurements to optimal values.

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