M. A. Volynsky, I. P. Gurov, P. A. Ermolaev, P. S. Skakov

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The paper deals with sequential Monte Carlo method applied to problem of interferometric signals parameters estimation. The method is based on the statistical approximation of the posterior probability density distribution of parameters. Detailed description of the algorithm is given. The possibility of using the residual minimum between prediction and observation as a criterion for the selection of multitude elements generated at each algorithm step is shown. Analysis of input parameters influence on performance of the algorithm has been conducted. It was found that the standard deviation of the amplitude estimation error for typical signals is about 10% of the maximum amplitude value. The phase estimation error was shown to have a normal distribution. Analysis of the algorithm characteristics depending on input parameters is done. In particular, the influence analysis for a number of selected vectors of parameters on evaluation results is carried out. On the basis of simulation results for the considered class of signals, it is recommended to select 30% of the generated vectors number. The increase of the generated vectors number over 150 does not give significant improvement of the obtained estimates quality. The sequential Monte Carlo method is recommended for usage in dynamic processing of interferometric signals for the cases when high immunity is required to non-linear changes of signal parameters and influence of random noise.

Keywords: interferometric signals, sequential Monte Carlo method

1.          Malacara D. Optical Shop Testing. NY, Wiley, 1978, 862 p.
2.          Gurov I., Volynsky M. Interference fringe analysis based on recurrence computational algorithms. Optics and Lasers in Engineering, 2012, vol. 50, no. 4, pp. 514–521. doi: 10.1016/j.optlaseng.2011.07.015
3.          Van Kampen N. Stochastic Processes in Physics and Chemistry.  North Holland, 1984, 464 p.
4.          Stepanov O.A. Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii. Ch. 1. Vvedenie v teoriyu otsenivaniya [Basics of estimation theory with applications to problems of navigational information processing. Part 1. Introduction to estimation theory]. St. Petersburg, Elektropribor Publ., 2009, 496 p.
5.          Kalman R.E. A new approach to linear filtering and prediction problems. Trans. ASME, J. Basic Eng., 1960, vol. 82, pp. 35–45.
6.          Simon D. Using nonlinear Kalman filtering to estimate signals. Embedded Systems Design, 2006, vol. 19, no. 7, pp. 38–53.
7.          Simon D. Optimal state estimation: Kalman, H∞, and Nonlinear Approaches. NY, John Wiley & Sons, Inc., 2006, 526 p. doi: 10.1002/0470045345
8.          Yarlykov M.S. Statisticheskaya teoriya radionavigatsii [Statistical theory of navigation]. Moscow, Radio i Svyaz', Publ. 1985, 345 p.
9.          Gurov I., Sheynihovich D. Interferometric data analysis based on Markov nonlinear filtering methodology.Journal of the Optical Society of America A: Optics and Image Science, and Vision, 2000, vol. 17, no.1, pp. 21–27.
10.       Gurov I., Ermolaeva E., Zakharov A. Analysis of low-coherence interference fringes by the Kalman filtering method. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 2004, vol. 21, no. 2, pp. 242–251. doi: 10.1364/JOSAA.21.000242
11.       Doucet A., de Freitas N., Gordon N. Sequential Monte Carlo methods in practice. NY, Springer-Verlag, 2001, 583 p.
12.       Iba Y. Population Monte Carlo algorithms. Transactions of the Japanese Society for Artificial Intelligence, 2001, vol. 16, no. 2, pp. 279–286. doi: 10.1527/tjsai.16.279
13.       Ristic B., Arulampalam S., Gordon N. Beyond the Kalman filter: Particle filters for tracking applications. Boston, Artech House, 2004, 318 p.
14.       Isard M., Blake A. Contour tracking by stochastic propagation of conditional density. European Conference on Computer Vision, 1996, pp. 343–356.
15.       MacCormick J., Blake A. Probabilistic exclusion principle for tracking multiple objects. Proc. of IEEE International Conference on Computer Vision, 1999, vol. 1, pp. 572–578.
16.       Del Moral P. Measure valued processes and interacting particle systems. Application to nonlinear filtering problems. Annals of Applied Probability, 1998, vol. 8, no. 2, pp. 438–495.
17.       Gurov I.P. Opticheskaya kogerentnaya tomografiya: printsipy, problemy i perspektivy [Optical coherence tomography: basics, problems and prospects]. In Problemy kogerentnoi i nelineinoi optiki [Problems of coherence and nonlinear optocs] / Eds I.P. Gurov, S.A. Kozlov. St. Petersburg, SPbSU ITMO Publ., 2004, pp. 6–30.
18.       Fercher A. Optical coherence tomography. Journal of Biomedical Optics, 1996, vol. 1, no. 2, pp. 157–173.
19.       Gurov I.P., Zhukova E.V., Margaryants N.B. Issledovanie vnutrennei mikrostruktury materialov metodom opticheskoi kogerentnoi mikroskopii s perestraivaemoi dlinoi [Investigation of materials internal microstructure by optical coherence microscopy with a tunable wavelength]. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 3 (79), pp. 40–45.
20.       Gurov I.P., Zhukova E.V., Levshina A.V. Primenenie metoda opticheskoi kogerentnoi tomografii dlya izucheniya predmetov iskusstva, vypolnennykh v tekhnike intarsii [Optical coherence tomography method application for art objects investigating performed in tarsia technique]. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 3 (79), pp. 55–59.
21.       Volynshy M.A., Vorob'yeva E.A., Gurov I.P., Margaryants N.B. Beskontaktnyi kontrol' mikroob"ektov metodami interferometrii maloi kogerentnosti i opticheskoi kogerentnoi tomografii [Remote testing of microlens with the use of low-coherence interferometry and optical coherence tomography]. Izv. vuzov. Priborostroenie,2011, vol. 54, no. 2, pp. 75–82.
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