Estimation of the measurement accuracy of the scalar information parameter of signal along with the multiplicative noise

**
V. M. Artyushenko**^{1}, V. I. Volovach^{2}

^{
1}Technological
University, 42, Gagarin Street, Korolev, 141070, Russia

^{
2}Volga
Region State University of Service, 4, Gagarin Street, Togliatti,
445017, Russia

The paper is received on March 1, 2016

**Abstract.
**In the article the estimation of error
of measurement scalar information parameter of the useful signal along with the
non-Gaussian multiplicative noise is considered. To estimate the information
parameters of the signal we use the method of maximum a posteriori probability
density and lower bounds of Rao-Cramer inequality. It is shown that in general
case the impact of multiplicative noise on the useful signal leads to shift of
estimates of measured parameters. It is shown that with known distribution
parameters of the multiplicative noise we can determine the shift value and get
to an unbiased estimate. It is shown that the accuracy of the measurement of
motion parameters increases with the difference of the density of the
probability distribution of the estimated parameter and influence of
multiplicative noise of Gaussian noise.

**Key
words:** radar meter, multiplicative non-Gaussian
noise, displacement estimates, signal/interference
ratio, measurement error.

**
References**

1. Sosulin, Yu. G., (1992), *Theoretical Foundations of radar and
navigation: Textbook for High Schools*, Radio and Communications,
Moscow: 304 p. (in Russian).

2. Finkelstein, M. I., (1983), *Fundamentals of radar*, Radio and
Communications, Moscow: 536 p. (in Russian).

3. *Radar handbook* (1990), edited by M. I. Scolnik, 2nd ed.,
McGraw-Hill, New York: 1199 p. (in English).

4. Rodimov, A. P. and Popovsky, V. V., (1984), *Statistical theory of
polarization-time signal processing and noise*, Radio and
Communications, Moscow: 272 p. (in Russian).

5. Nebabin, V. G., (1994),* Methods and Techniques of Radar
Recognition*, Artech House, Boston – London: 273 p. (in English).

6. *Radar characteristics of the aircraft*, (1985), M. E. Margenov,
S. Y. Zinoviev, L. Y. Astanin and others, edited by L. T. Tuchkov, Radio
and Communications, Moscow: 236 p. (in Russian).

7. Falkovich, S. E. and Khomyakov, E. N., (1981), *Statistical theory
of measurement Radiosystems*,* *Radio and Communications,
Moscow: 288 p. (in Russian).

8. Komarov, I. V. and Smolskiy, S. M., (2003), *Fundamentals of
short-range FM radar*, Artech House, Norwood: 289 p. (in English).

9. Artóushenko,
V. M. and Volovach, V. I., (2015),* *Evaluation of error of
measurement of parameters of motion of extended objects under changing
range, *Izvestiya vuzov. Electronics*. **58**(1):26-37 (in
Russian).

10. Volovach, V. I., (2013), *Methods and algorithms for the analysis
of radio engineering devices of short-range*, Radio and
Communications, Moscow: 228 p. (in Russian).

11. Hammarstrand, L., Svensson, L., Sandblom, F. and Sorstedt, J.
(2012), Extended object tracking using a radar resolution model, *IEEE
Trans. Aerosp. Electron. Syst*. **
48**(3):
2371-2386 (in English).

12. Hughes, P. K.* *A high-resolution radar detection strategy
(1983), *
IEEE Trans. Aerosp. Electron. Syst.*
**19**(5): 663-667 (in English).

13. Artóushenko,
V. M. and Volovach, V. I., (2015),* *The estimation of measurement
accuracy of information parameters of the signal along with the
correlated additive noise under continuous processing, *The successes
of modern Radioelectronics*. (8):80-89 (in English).

14. Artóushenko,
V. M. and Volovach, V. I., (2015),* *
Analysis of influence of additive
non-Gaussian noise on accuracy of motion parameters measurement in
short-range radio systems, *Non-linear world.* **
13**(1): 16-30
(in English).

15. Artyushenko, V. M. and Volovach, V. I., (2015), Evaluation of
measurement uncertainty scalar information parameter of an extended
object moving on the background of additive non-Gaussian noise, *
Journal of Radio Electronics*: *e-zine.* (1):`
URL: `
http://jre.cplire.ru/jre/jan15/12/text.html
(in Russian).

16. Artyushenko, V. M. and Volovach, V. I., (2016), Evaluation of the
measurement error vector of the information parameter of a signal
against additive uncorrelated non-Gaussian noise, *Journal* *of
Radio Electronics*: *e-zine.* (1):
`
URL: `
http://jre.cplire.ru/jre/jan16/6/text.html
(in Russian).

17. Kassam, S. A., (1989), *Signal Detection in Non-Gaussian Noise*,
Springer Verlag, New York: 242 p. (in English).

18. Lu, N. H., and* *Eisenstein, Bruce A., (1981), Detection of
weak signals in non-Gaussian noise, *IEEE Trans. Microwave Theory Tech*.
**27**(6): 755-771 (in English).

19. *Theory of detection of signals*, (1984), P. S. Akimov, P.
À.
Bakut, V.
À.
Bogdanovich and others, edited by P.
À.
Bakut, Radio and Communications, Moscow: 440 p. (in Russian).

20. Tikhonov, V. I., and Kul'man, N. K., (1975), *Non-linear
filtration and quasi-coherent reception of signals*, Sovestkoe radio,
Moscow: 704 p. (in Russian).

21. Levin, B. R., (1989), *Theoretical foundations of radio
engineering static*, 3rd ed., Sovestkoe radio, Moscow: 656 p. (in
Russian).

22. Tikhonov, V. I., and Kharisov, V. N., (1991), *Statistical
analysis both synthesis of radio engineering devices and systems:
Textbook for High Schools*, Radio and Communications, Moscow: 608 p.
(in Russian).

23. Kramer, G., (1975), *Mathematical methods of statistics*,
edited by A. N. Kolmogorov, World, Moscow: 648 p. (in Russian).

24. *Modulating (multiplicative) interferences and reception of radio
signals*, (1972), I. Ya. Kremer, V. I. Vladimirov, V. I. Karpukhin,
edited by I. Ya. Kremer, Sovestkoe radio, Moscow: 480 p. (in Russian).

25. Vasylyev, K. K., (1983), *The Reception of signals in
multiplicative noise*, Publishing house of Saratov University,
Saratov: 128 p. (in Russian).

26. Artyushenko, V. M., (2014), *Processing information signal
parameters under additive-multiplicative non-Gaussian noise*, Finance
and Technology Academy, publishing Kantsler, Moscow: 298 p. (in
Russian).

27. Bakut, P. A., Loginov, V. P., and Shumilov, Yu., (1978), Methods of
determining the limits of accuracy in the estimation problems of unknown
parameters, *Foreign Radioelectronics*, (5):3-36 (in Russian).

28. Tzay, Y. Yong,* *and Westerberg, R. A., (1971), Error bounds
for stochastic estimation of signal parameters, *IEEE Trans. on
Information Theory*, 17(5):549-557 (in English).

29. Nakagami, M., (1960), The *m*-distribution-A-general
formula of intensity of rapid fading, *Statistical Methods in Radio
Wave Propagation: Proceedings of a Symposium Held at the University of
California*, *Los Angeles*, Pergamon Press, New York: 3-36
(in English).

30. Biletov, M. V., Wasserstein, I. S., and Ryl'sky, V. V., (1976),
Detection of radar signals in the fluctuations of their intensity under
the law Nakagami, *Radioelectronics*,
**
31**(1):16-19
(in Russian).

31. Doluhanov, M. P., (1971), *Fluctuation processes in the
propagation of radio*, Svyaz', Moscow: 360 p. (in Russian).

32. Tsypkin, Ya. Z., (1984), *Fundamentals of information theory of
identification*, Nauka, Moscow: 360 p. (in Russian).

33. Fomin, A. F., Khoroshavin, A. N., and Shelukhin, O. I., (1987), *
Analog and digital phase meters and demodulators*, Radio and
Communications, Moscow: 248 p. (in Russian).