A.A. Skripkin1, V.A. Shcherbachev2

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

The method for joint estimation of the frequency and rate of its change by differential-phasic measurements when processing coherent packets is proposed. A computationally efficient method for estimating the frequency and rate of its change for successive coherent packets of complex sinusoidal signals based on the optimal weighting of differential-phasic statistics is synthesized. The proposed estimates are calculated as a linear function of differential-phasic measurements and, within the framework of the accepted assumptions, the estimate is a linear unbiased estimate with minimum variance.

An explicit expression for the lower limit of the variance of the estimate considered is obtained, and a comparative study of the accuracy characteristics of the proposed estimation method with other similar methods is performed. A significant increase in the accuracy of joint estimation by taking into account the coherence of the processed signal packets is shown. The efficiency of the method at a moderately high signal-to-noise ratio is confirmed; at its values from 11.5 dB, an almost complete coincidence of the estimation RMS with its permissible lower limit is demonstrated.

Skripkin A.A., Shcherbachev V.A. Joint estimation of frequency and rate of its change by differenced phase measurements when processing coherent packets of sinusoidal signals. Radioengineering. 2022. V. 86. № 11. P. 34−41. DOI: https://doi.org/10.18127/j00338486-202211-06 (in Russian)

1. Handbook on Satellite Communications. Edition 3rd. ITU. 2002.
2. Heine G. GSM Networks: Protocols, Terminology, and Implementation, Artech House, Boston, London. 1999.
3. Tretter S.A. Estimating the frequency of a noisy sinusoid by linear regressio. EEE Trans. on Information theory. 1985. V. IT‑31.Nov. P. 832−835.
4. Skripkin A.A., Shcherbachev V.A. Utochnenie otsenki chastoty pri obrabotke kogerentnykh paketov sinusoidalnykh signalov. Radiotekhnika. 2021. T. 85. № 11. S. 27−33. (in Russian)
5. Steven M.Kay. A Fast and Accurate Single Frequency Estimator. EEE Transactions on Acoustics, Speech and Signal Processing. 1989. V. 37. № 12. P. 1987−1990.
6. Pat. na izobretenie RF № 2183839. Sposob izmereniya chastoty sinusoidalnykh signalov i ustroistvo dlya ego realizatsii. Podchinenko N.E., Skripkin A.A., Shcherbachev V.A. M.:FIPS. 2002. (in Russian)
7. Abatzoglou T.J. Fast maximum likelihood joint estimation of frequency and frequency rate. IEEE Trans. on AES. 1986. V. 22. № 6. P. 708−715.
8. Djuric P.M., Kay S.M. Parameter estimation of chirp signals. IEEE Transactions on Acoustics, Speech and Signal Processing. 1990. V. 38. № 12. P. 2118−2126.
9. Tribolet I.M. A new phase unwrapping algorithm. IEEE Transactions on Acoustics Speech and Signal Processing. 1977. V. ASSP‑25. № 2. P. 170−177.
10. Skripkin A.A., Shcherbachev V.A. Sovmestnoe otsenivanie chastoty i skorosti ee izmeneniya po raznostno-fazovym izmereniyam. Radiotekhnika. 2021. T. 85. № 11. S. 34−40. (in Russian)
11. Albert A. Regressiya, psevdoinversiya i rekurrentnoe otsenivanie. M.: Nauka. 1977. (in Russian)
12. Podchinenko N.E., Skripkin A.A., Shcherbachev V.A. Rekurrentnyi metod otsenivaniya chastoty sinusoidalnogo signala. Dokl. 8‑i Mezhdunar. konf. «Tsifrovaya obrabotka signalov i ee primenenie». 2006. T. 1. S. 322−326. (in Russian)