Preview

Journal of the Russian Universities. Radioelectronics

Advanced search

Adaptive Prediction of a Random Process Using a Sequential Regression Algorithm

https://doi.org/10.32603/1993-8985-2019-22-6-6-13

Abstract

Introduction. Adaptive statistical prediction of a random process is relevant to a noise compensation in radar and optical location problems. The shape of the signal reflected from the target is often unknown due to the use of short probing pulses passing during their duration in a distance less than the size of the target. Subtracting the noise forecasted in the previous time point from its current value allows one to compensate for the noise.

Aim. Investigation of the problem of adaptive linear prediction of random processes by a non - recursive linear filter implementing a sequential regression algorithm for infinitely and finitely differentiable random processes.

Materials and methods. Models of random interferences in the form of infinitely and finitely differentiable random processes were considered. The sequential regression algorithm required to estimate the correlation selection matrix, the selection vector of correlation of the forecast and sample units. Due to random process and its derivative incorrelation, the sparse correlation selection matrix was formed. This factor reduced the number of mathematical operations.

Results. The results of numerical calculations and the implementation of random process, its optimal and adaptive prediction obtained during the simulation were presented. The adaptive predictive filter with random process derivative sampling provided at least a one third reduction of the number of mathematical operations in comparison with the transversal predictive filter.

Conclusion. An algorithm of sequential regression in predicting a random process and its a priori unknown parameters is the closest to the ideal algorithm of direct matrix inversion. It allows to adapt to the changing process parameters. The number of iterations in non-recursive filtering and the value of attenuation of the estimated linear regression coefficients during the adaptation can be used to adapt to the changes in the parameters of the predicted process.

About the Author

Vladimir A. Golovkov
Scientific Research Institute for Optoelectronic Instrument Engineering, JSC
Russian Federation

Vladimir A. Golovkov - Cand. Sci. (Eng.) (1982), Associate Professor (2009), Senior Researcher.

29 Leningradskaya Str., Sosnovy Bor 188541



References

1. Lebed'ko E. G. Sistemy impul'snoi opticheskoi lokatsii [Pulse Optical Location Systems]. SPb., Lan', 2014, 369 p. (In Russ.)

2. Yakushenkov Yu. G. Teoriya i raschet optiko-elektronnykh priborov [Theory and Calculation of Optoelectronic Devices]. Moscow, Logos, 2012, 568 p. (In Russ.)

3. Borzov A. B., Bystrov R. P., Zasovin E. A., Likhodeenko K. P., Muratov I. V., Pavlov G. L., Sokolov A. V., Suchkov V. B. Millimetrovaya radiolokatsiya: metody obnaruzheniya i navedeniya v usloviyakh estestvennykh i organizovannykh pomekh [Millimeter Radar: Detection and Guidance Methods under Natural and Organized Interference]. Moscow, Radiotekhnika, 2010, 376 p. (In Russ.)

4. Bystrov A. P., Potapov A. A., Sokolov A. V. Millimetrovaya radiolokatsiya s fraktal'noi obrabotkoi [Fractal Millimeter Radar]. Moscow, Radiotekhnika, 2005, 250 p. (In Russ.)

5. Golovkov V. A. Maximization of the Signal-To-Noise Ratio for Non-Steady-State Irradiation of a Target Using Optical Radar. J. of Optical Technology, 2018, vol. 85, no. 6, pp. 351-354. doi: 10.1364/JOT.85.000351

6. Adaptive Filters. Ed. by C. F. N. Cowan and P. M. Grant. Englewood Cliffs, NJ, Prentice-Hall, Inc., 1985, 308 p.

7. Lukashin Yu. P. Adaptivnye metody kratkosrochnogo prognozirovaniya vremennykh ryadov [Adaptive Methods of Short-Term Forecasting of Time Series]. Moscow, Finansy istatistika, 2003, 416 p. (In Russ.)

8. Box G. E. P., Jenkins G. M., Reinsel G. C. Time Series Analysis. Forecasting and Control. New York, J. Wiley & Sons, 2015, 709 p.

9. Golovkov V. A. Predictive Filter Characteristics. Journal of the Russian Universities. Radioelectronics. 2010, no. 2, pp. 3-8. (In Russ.)

10. Islam S. M. R., Kwak K. S. On Channel Estimation in MB-OFDM UWb Systems with Time Varing Dispersive Fading Channel. Intern. J. of Digital Content Technology and its Applications. 2010, vol. 4, no. 2, pp. 18-24.

11. Golovkov V. A. Interpolation of Random Processes Using Winner-Hopf Filtration. Radio Electronics and Communications Systems. 2009, vol. 52, no. 3, pp. 132-136. doi: 10.3103/S0735272709030030

12. Rozanov Yu. A. Statsionarnye sluchainye protsessy [Stationary Random Processes]. Moscow, Nauka, 1990, 272 p. (In Russ.)

13. Perov A. I. Statisticheskaya teoriya radiotekhnicheskikh sistem [Statistical Theory of Radio Engineering Systems]. Moscow, Radiotekhnika, 2003, 400 p. (In Russ.)

14. Khimenko V. I. Sluchainye dannye: struktura i analiz [Random Data: Structure and Analysis]. Moscow, Tekhnosfera, 2017, 424 p. (In Russ.)

15. Faulkenberry L. M. An Introduction to Operational Amplifiers with Linear IC Applications. New York, J. Wiley & Sons, 1982, 530 p.

16. Widrow B., Stearns S. D. Adaptive Signal Processing. Englewood Cliffs, NJ, Prentice-Hall, Inc., 1985, 492 p.

17. Monzingo R., Miller T. Introduction to Adaptive Arrays. New York, J. Wiley & Sons, 2004, 543 p.


Review

For citations:


Golovkov V.A. Adaptive Prediction of a Random Process Using a Sequential Regression Algorithm. Journal of the Russian Universities. Radioelectronics. 2019;22(6):6-13. (In Russ.) https://doi.org/10.32603/1993-8985-2019-22-6-6-13

Views: 853


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1993-8985 (Print)
ISSN 2658-4794 (Online)