A.A. Skripkin1, V.A. Shcherbachev2

1,2 JSC «All-Russian Scientific Research Institute «Gradient» (Rostov-on-Don, Russia)

1 alexyscrypkin@rostov.ru, 2 vove64@mail.ru

Some communication, radionavigation and radioastronomy problems are related with received signal frequency estimation. Often the problems are reduced to frequency estimation [1, 2] of sinusoid signal damaged by additive white Gaussian noise (AWGN). Top-priority significance has computational efficiency with practical implementation of some known optimal or near optimal frequency estimation algorithms [1−3].

For example [1], it has been created cisoid (damaged by additive white Gaussian noise) frequency estimation algorithm. The frequency estimation algorithm has been realized by least square optimal weighing of phasedifference statistic. It has been shown that discovered estimate is near optimal with moderate SNRs.

Kay’s suggested frequency estimation method [1] may be characterized as batch sample frequency estimation method. Point frequency estimate is obtained as scalar product of N-dimensional phase-difference statistic vector with optimal weighing function, that depends from vector dimension.

It’s not efficient to accumulate and keep some volume of signal’s samples before obtaining first initial point frequency estimate, especially, for embedded estimator. There is necessity to create recurrent frequency estimation algorithm or method for such case, when point frequency estimate may be obtained with small time independent (or accordingly from data volume) state parameters.

The paper is devoted to recurrent frequency estimation algorithm creation for known, Kay’s suggested cisoid frequency estimation method (with keeping optimality but without phase-difference data accumulation and holding).

Cisoid frequency estimate may be received and improved (with created recurrent cisoid frequency estimation method) on real time as new phase-difference data sample becomes available. Accumulation and holding means may be excluded from the estimator.

The recurrent cisoid frequency estimation method has been tested by statistical simulation. The simulation test results have been in close agreement with theoretical curve.

Most industrial frequency counters are used rectangular window weighing function for frequency estimation.

Frequency estimation accuracy of such industrial frequency counters is several times less than estimation accuracy of frequency counters based on suggested frequency estimation method with paraboloidal weighing [1].

Skripkin A.A., Shcherbachev V.A. Recurrent frequency estimation of sinusoidal signals. Radioengineering. 2023. V. 87. № 11. P. 25−29. DOI: https://doi.org/10.18127/j00338486-202311-05 (in Russian)

1. Kay S.M. A Fast and Accurate Single Frequency Estimator. IEEE Transactions on Acoustics. Speech and Signal Processing. December 1989. V. 37. № 12. P. 1987−1990.
2. Rife D.C. and Boorstin R.R. Single tone parameter estimation from discrete-time observations. IEEE Transactions on Information theory. September 1974. V. IT-20. P. 591−598.
3. Tretter S.A. Estimating the frequency of a noisy sinusoid by linear regression. IEEE Transactions on Information theory. November 1985. V. IT-31. P. 832−835.
4. Patent na izobretenie RU 2183839. Opubl. 20.06.2002. Byul. 17. Sposob izmereniya chastoty sinusoidalnykh signalov i ustroistvo dlya ego realizatsii. Podchinenko N.E., Skripkin A.A., Shcherbachev V.A. (in Russian)