Statistical simulation of the Gaussian random process parameter estimation

  • Oleg Chernoyarov ,
  • Larisa Korableva,
  • Yury Korchagin,
  • Alexander Makarov,
  • Michail Turbin
  • a,d  National Research Tomsk State University, Lenin Avenue 36, Tomsk, 634050, Russia
  • a,d National Research University “Moscow Power Engineering Institute”, Krasnokazarmennaya st. 14, Moscow, 111250, Russia
  • Maikop State Technological University, Pervomayskaya st. 191, Maikop, 385000, Russia
  • Moscow State University, Leninskiye Gory 1, Moscow, 119991, Russia
  • c,e  Voronezh State University, Universitetskaya sq. 1, Voronezh, 394018, Russia
Cite as
Chernoyarov O., Korableva L., Korchagin Y., Makarov A., Turbin M. (2021). Statistical simulation of the Gaussian random process parameter estimation. Proceedings of the 33rd European Modeling & Simulation Symposium (EMSS 2021), pp. 52-58. DOI:


One introduces the effective technique for the fast generation of the discrete samples of the logarithm of the functional of the likelihood ratio under a low-frequency Gaussian random process with the spectral density of an arbitrary shape being received against the background Gaussian white noise. The random processes that are part of the specified functional are presented by means of a finite set of discrete Fourier transform coefficients. The possible hardware and software implementation of the algorithms for estimating the frequency and energy parameters of a Gaussian process with the experimental determination of the characteristics of their performance are demonstrated. Based on the results obtained, the operation of various detectors and measurers is simulated for the case when the observable realization can be presented in the form of linear or nonlinear transformations of a Gaussian random process.


  1. Chernoyarov, O.V., Golpayegani, L.A., Zakharov, A.V., & Kalashnikov, K.S. (2020). Estimation of the stepwise random disturbance parameters with the unknown moment of appearance. Japan Journal of Industrial and Applied Mathematics, 37(1), 81-102. Retrieved from
  2. Chernoyarov, O.V., Sai Si Thu Min, Salnikova, A.V., Shakhtarin, B.I., & Artemenko, A.A. (2014). Application of the local Markov approximation method for the analysis of information processes processing algorithms with unknown discontinuous parameters. Applied Mathematical Sciences, 8(90), 4469-4496. Retrieved from
  3. Chernoyarov, O.V., Vaculik, M., Shirikyan, A., & Salnikova, A.V. (2015). Statistical analysis of fast fluctuating random signals with arbitrary-function envelope and unknown parameters. Communications - Scientific Letters of the University of Zilina, 17(1A), 35-43. Retrieved from
  4. Davis, P.J. & Rabinowitz, P. (2007). Methods of numerical integration. Mineola, NY: Dover Publications.
  5. Devroye, L. (1986). Non-uniform random variate generation. Berlin, Germany: Springer-Verlag.
  6. Middleton, D. (1996). An introduction to statistical communication theory. Hoboken, NJ: Wiley-IEEE Press.
  7. Tan, L. & Jiang, J. (2018). Digital signal processing. Cambridge, MA: Academic Press.
  8. Trifonov, A.P., Nechaev, E.P., & Parfenov, V.I. (1991). Detection of stochastic signals with unknown parameters [in Russian]. Voronezh, Russia: Voronezh State University.
  9. Van Trees, H.L., Bell, K.L., & Tian, Z. (2013). Detection, estimation, and modulation theory, Part I, Detection, estimation, and filtering theory. New York, NY: Wiley.