Flicker Noise Simulation by Superposition of Normal Stationary Processes
https://doi.org/10.17285/0869-7035.2018.26.2.059-076
Abstract
A well-known method of 1/f-noise representation as a sum of steady processes is considered. Two series of forming filters are used within the frequency band specified by the user. Ratios of filter parameters are determined. Spectrum approximation error is studied. An algorithm of fluctuations modeling is proposed as a system of stochastic differential equations of the first order. The algorithm can be applied to the simulated models used in studying the errors of navigation systems.
About the Authors
B. O. KachanovRussian Federation
S. A. Akhmedova
Russian Federation
N. A. Tuktarev
Russian Federation
V. A. Novikov
Russian Federation
References
1. Matveev, V.V. and Pogorelov, M.G., Analyzing the errors of micromechanical gyroscopes by Allan variance. Izvestiya TulGU, Tekhnicheskie nauki, 2015, vol. 3. Priborostroenie, metrologiya i informatsionno-izmeritel’nye pribory i sistemy, pp. 123–135.
2. Litvin, M.A., Malyugina, A.A, Miller A.B, Stepanov, A.N, and Chikrin D.E., Types of errors in inertial navigation systems and methods for their approximation, Informatsionnye protsessy. ISBN/ISSN 1819-5822. vol. 14, no. 4, 2014, pp. 326–339.
3. Buckingham, M.J., Noise in Electronic Devices and Systems, Chischester [West Sussex, England]: E. Horwood, 1983.
4. Yakimov, A.V., Fizika shumov i fluktuatsii parametrov: Elektronnoe uchebnoe posobie. (Physics of Noise and Parameter Fluctuations: Electronic textbook). Nizhnii Novgorod: Nizhegorodskii Gosuniversitet, 2013.
5. Borisov, B.D., Models of flicker noise spectral power density, Avtomatika i programmnaya inzheneriya, 2015, no. 2 (12), pp. 78–81.
6. Potemkin, V.V. and Stepanov, А.V., On the stationary nature of noise 1/f in low-frequency band, Radiotekhnika i elektronika, 1980, vol. 25, no. 6, p. 1269.
7. Edwards, S., Optimization of noise parameters of signal circuits. Part 1: Annoying noise in semiconductors – preventable or unavoidable? Elektronnye komponenty, 2013, no.10, pp. 9–15.
8. Barnes, J.A. and Allan, D.W., A statistical model of flicker noise, 1966, Proc. IEEE, 54, pp. 176–178.
9. Mandelbrot, B., Some noises with 1/f spectrum, a bridge between direct current and white noise, 1967, IEEE Trans. Inf. Theory, IT-13, pp. 289–298.
10. Mandelbrot, B. and Ness, J.W., Fractional Brownian motions, fractional noises and application, 1968, SIAM Rev., 10, pp. 422–437.
11. Radeka, V. 1/f noise in physical measurements, 1969, IEEE Trans. Nucl. Scl. NS-16, pp. 17–35.
12. Kasdin, N.J., Discrete simulation of colored noise and stochastic processes and 1/f power low noise generation, Proc. of the IEEE, vol. 83, no. 5, pp. 802, 1995.
13. Rakhviashvili, S.Sh., Modeling of flicker noise with the help of fractional integrodifferentiation, Zhurnal tekhnicheskoi fiziki, 2006, vol. 76, no. 6, pp. 123–126.
14. Feder, J., Fractals, New York: Plenum Press, 1988.
15. Shishkin, E.I., Modelirovanie i analiz prostranstvennykh i vremennykh fraktal’nykh ob’’ektov (Modeling and Analysis of Spatial and Temporal Fractal Objects), Ekaterinburg, Uralski Gos. Universitet, 2004.
16. Barabash, T.K., Maslovskaya, A.G., Computer modeling of fractal time series. Vestnik AmGU, 2010, no. 49, pp. 31–38.
17. Ostanin, S.А., A generator of fractal noise of arbitrary dimension, Zhurnal radioelektroniki. Elektronnyi zhurnal, ISSN 1684-1719, Institut radiotekhniki i elektroniki im. V.A. Kotel’nikova RAN, 2012, no. 8.
18. Savel’ev, V.M. and Antonov, D.A., Alignment of an inertial navigation system of an unmanned aerial vehicle on a moving base, Elektronnyi zhurnal (Electronic journal), “Trudy MAI”, no. 45, 2011.
19. Solov’ev, A.N., Sablin, A.V., and Lyalinskii, A.A., Development of simulation environment for inertial navigation systems. MES-2014. Vserossiiskaya nauchno-tekhnicheskaya konferentsiya “Problemy razrabotki perspektivnykh mikro- i nanoelektronnykh sistem” (All-Russian Scientific and Technical Conference “Problems of development of prospective micro- and nanoelectronic systems”), Russia, Moscow, October, 2014, IPPM RAN.
20. Zhidkova, N.V. and Volkov, V.L., Simulation of a strapdown orientation system. Modern problems of science and education. Elektronnyi zhurnal (Electronic journal). ISNN 2070-7428, 2015, no. 1, (Part 1). https://science-education.ru/ru/article/view?id=17099.
21. Stepanov, О.А., Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii (Fundamentals of the Estimation Theory with Applications to the Problems of Navigation Information Processing), Part 2, Vvedenie v teoriyu fil’tratsii (Introduction to the Filtering Theory), St. Petersburg: TsNII Elektropribor, 2012.
22. Ostrem, K.Yu., Introduction to stochastic control theory (Vvedenie v Stohasticheskuyu Teoriyu Upravleniya. M.: Mir, 1973.
23. IEEE Std 952-1997(R2008). IEEE Standard Specification Format Guide and Test Procedure for Single Axis Interferometric Fiber Optic Gyros.
24. Krobka, N.I., On the topology of the Allan variance graphs and typical misconceptions in the interpretation of the structure of the gyros noise, Panel discussion: Methods for Navigation Sensor Performance Determination. XXII Sankt-Peterburgskaya mezhd. konf. po integrirovannym navigatsionnym sistemam (22nd St. Petersburg Int. Conf. on Integrated Navigation Systems), 25–27 May, 2015, Saint Petersburg: Elektropribor, Russia.
Review
For citations:
Kachanov B.O., Akhmedova S.A., Tuktarev N.A., Novikov V.A. Flicker Noise Simulation by Superposition of Normal Stationary Processes. Giroskopiya i Navigatsiya. 2018;26(2):59-76. (In Russ.) https://doi.org/10.17285/0869-7035.2018.26.2.059-076



