Method for synthesizing efficient estimates of signal parameters using functions from complete sufficient statistics

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

A method for synthesizing efficient estimates of parameters of a random process whose distribution of samples has complete sufficient statistics is proposed. The method is based on the representation of the estimated parameters of the process in the form of a solution to the system of equations for mathematical expectations of functions derived from complete sufficient statistics, selected in such a way that the system of equations was solvable with respect to the estimated parameters. This solution is then replaced by the aforementioned functions in order to obtain the final estimate. The conditions under which the obtained estimates will be efficient are provided. Examples of parameter estimation for sample distributions from a uniform distribution and an additive mixture of Gaussian noise and a sequence of rectangular pulses with unknown amplitudes are presented, and their efficiency is demonstrated.

About the authors

А. G. Vostretsov

Novosibirsk State Technical University; Chinakal Institute of Mining of the Siberian Branch of the RAS

Author for correspondence.
Email: vostreczov@corp.nstu.ru
Russian Federation, 20 K. Marx Ave., Novosibirsk, 630073; 54, Krasny Ave., Novosibirsk, 630091

S. G. Filatova

Novosibirsk State Technical University; Federal Institute of Industrial Property

Email: vostreczov@corp.nstu.ru
Russian Federation, 20 K. Marx Ave., Novosibirsk, 630073; 30-1 Berezhkovskaya nab., Moscow, 125993

References

  1. Woodward P.M. Probability and Information Theory with Applications to Radar. N.Y.: McGraw-Hill, 1953.
  2. Гонсалес Р., Вудс Р. Цифровая обработка изображений. М.: Техносфера, 2006.
  3. den Dekker A. J., Sijbers J. // Physica Medica. 2014. V. 30. № 7. P. 725.
  4. Разников В.В., Разникова М.О. Информационно-аналитическая масс-спектрометрия. М.: Наука, 1991.
  5. Xinya Li, Zhiqun D.D., Rauchenstein L.T., Carlson T.J. // Rev. Sci. Instrum. 2016. V. 87. № 4. Article No. 041502. doi: 10.1063/1.5012687
  6. Губарев В.В. Алгоритмы статистических измерений. М.: Энергоатомиздат, 1985.
  7. Левин Б.Р. Теоретические основы статистической радиотехники. М.: Радио и связь, 1989.
  8. Миронов М.А. Марковская теория оптимального оценивания случайных процессов. М.: Изд-во ГосНИИАС, 2013.
  9. Emery A.F., Valenti E., Bardot D. // Measurement Sci. Technol. 2006. V. 18. № 1. P. 19. doi: 10.1088/0957-0233/18/1/003
  10. Morelli M., Moretti M. // IEEE Wireless Commun. Lett. 2013. V. 2. № 1. P. 42. doi: 10.1109/WCL.2012.100912.120508.
  11. Shieh W. // IEEE Photonics Technol. Lett. 2008. V. 20. № 8. P. 605. doi: 10.1109/LPT.2008.918873
  12. Сосулин Ю.Г. Теоретические основы радиолокации и радионавигации. М.: Радио и связь, 1992.
  13. Ivanov S.I., Liokumovich L.B., Medvedev A.V. // Proc. 2017 XX IEEE Int. Conf. on Soft Computing and Measurements (SCM). St. Petersburg. 24-26 May. N.Y.: IEEE, 2017. P. 11. doi: 10.1109/SCM.2017.7970480.
  14. Ivanov S.I., Liokumovich L.B., Medvedev A.V. Proc. 18 Int. Conf. NEW2AN. St. Petersburg. 26-27 Aug 2018/Eds by O.Galinina et al. Cham: Springer Switzerland AG, 2018. P. 666. doi: 10.1007/978-3-030-01168-0_61
  15. Zhuchkov K., Vasilchenko M., Zagrebneva A., Zavyalov A. // Sci. Rep. 2022 V. 12. P. 19932. doi: 10.1038/s41598-022-24457-2
  16. Vostretsov A.G., Filatova S.G. // J. Electronic Sci. Technol. 2023. V. 21. № 4. Article No. 100230. doi: 10.1016/j.jnlest.2023.100230
  17. Боровков А.А. Математическая статистика. М.: Наука, 1984.
  18. Закс Ш. Теория статистических выводов. М.: Мир, 1975.
  19. Акимов П.С., Бакут П.А., Богданович В.А. и др. Теория обнаружения сигналов. М.: Радио и связь, 1984.
  20. Леман Э. Проверка статистических гипотез. М.: Наука, 1979.
  21. Вострецов А.Г. // РЭ. 1999. Т. 44. № 5. С. 551.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences