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Statistical filtering algorithms for systems with random structure

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New algorithms for solving the optimal filtering problem for continuous-time systems with a random structure are proposed. This problem is to estimate the current system state vector from observations. The mathematical model of the dynamic system includes nonlinear stochastic differential equations, the right side of which defines the system structure (regime mode). The right side of these stochastic differential equations may be changed at random time moments. The structure switching process is the Markov or conditional Markov random process with a finite set of states (structure numbers). The state vector of such system consists of two components: the real vector (continuous part) and the integer structure number (discrete part). The switch condition for the structure number may be different: the achievement of a given surface by the continuous part of the state vector or the distribution of a random time period between structure switchings. Each ordered pair of structure numbers can correspond to its own switch law. Algorithms for the estimation of the current state vector for systems with a random structure are particle filters, they are based on the statistical modeling method (Monte Carlo method). This work continues the authors’ research in the field of statistical methods and algorithms for the continuous-time stochastic systems analysis and filtering.

Keywords

estimation; filtering; maximum cross section method; stochastic differential equation; system with variable structure; system with random structure; statistical modeling; particle filter

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DOI

10.20310/2686-9667-2020-25-130-109-122

UDC

519.676

Pages

109-122

References

[1] T.A. Averina, K.A. Rybakov, Using the maximum cross section method in random processes estimation problems, Int. Conf. on Advanced Mathematics, Computations and Applications (AMCA-2019, Marchuk Scientific Readings), NSU Publ., Novosibirsk, 2019 (In Russian). [2] T. A. Averina, K. A. Rybakov, “Using maximum cross section method for filtering jumpdiffusion random processes”, Rus. J. Numer. Anal. Math. Modelling, 35:2 (2020), 55–67. [3] T.A. Averina, Statisticheskoe modelirovanie reshenii stokhasticheskikh differentsial’nykh uravnenii i sistem so sluchainoi strukturoi, Siberian Branch of the Russian Academy of Sciences Publ., Novosibirsk, 2019 (In Russian). [4] A. Bain, D. Crisan, Fundamentals of Stochastic Filtering, Springer, New York, 2009. [5] I.E. Kazakov, V.M. Artem’ev, Optimizatsiya dinamicheskikh system sluchainoi struktury, Nauka, Moscow, 1980 (In Russian). [6] X.R. Li, V.P. Jilkov, “Survey of maneuvering target tracking. Part V: Multiple-model methods”, IEEE Trans. Aerospace Electronic Syst., 41:4 (2005), 1255–1321. [7] M.S. Yarlykov, S.M. Yarlykova, “Optimal algorithms for complex nonlinear processing of vector discrete-continuous signals”, Radioengineering, 2004, №7, 18–29 (In Russian). [8] M.S. Yarlykov, S.M. Yarlykova, “The potential accuracy of synthesized suboptimal algorithms for complex nonlinear processing of vector discrete-continuous noises”, Radioengineering, 2007, №1, 46–61 (In Russian). [9] I.M. Kosachev, Yu.E. Kuleshov, “Methodology of high-precision optimal filtering of random processes observed in stochastic dynamical systems with random structure. Part 1”, Military Academy of the Republic of Belarus Proceedings, 2016, №3 (52), 57–66 (In Russian). [10] I.M. Kosachev, Yu.E. Kuleshov, “Methodology of high-precision optimal filtering of random processes observed in stochastic dynamical systems with random structure. Part 2”, Military Academy of the Republic of Belarus Proceedings, 2016, №4 (53), 64–73 (In Russian). [11] I.M. Kosachev, Yu.E. Kuleshov, “Methodology of high-precision optimal filtering of random processes observed in stochastic dynamical systems with random structure. Part 3”, Military Academy of the Republic of Belarus Proceedings, 2017, №1 (54), 56–65 (In Russian). [12] E.A. Rudenko, “Finite-dimensional recurrent algorithms for optimal nonlinear logical-dynamical filtering”, J. Comput. Sys. Sc. Int., 55:1 (2016), 36–58. [13] K.A. Rybakov, A.A. Yushchenko, “Continuous particle filters and its real-time implementation”, Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies, 2018, №3, 56–64 (In Russian). [14] F. Karamґe, “A new particle filtering approach to estimate stochastic volatility models with Markov-switching”, Econometrics and Statistics, 8:C (2018), 204–230. [15] T. Lux, “Inference for nonlinear state space models: A comparison of different methods applied to Markov-switching multifractal models”, Economics Working Paper, 2018-07 (2018), 1–43. [16] V.A. Bukhalev, Raspoznavanie, otsenivanie i upravlenie v sistemakh so sluchainoi skachkoobraznoi strukturoi, Fizmatlit, Moscow, 1996 (In Russian). [17] V.A. Bukhalev, A.A. Skrynnikov, V. A. Boldinov, Algoritmicheskaya pomekhozashchita bespilotnykh letatel’nykh apparatov, Fizmatlit, Moscow, 2018 (In Russian). [18] M. Ghosh, A. Arapostathis, S. Marcus, “Optimal control of switching diffusions with application to flexible manufacturing systems”, SIAM J. Control Optim., 31:5 (1993), 1183–1204. [19] A.P. Trifonov, Yu.S. Shinakov, Sovmestnoe razlichenie signalov i otsenka ikh parametrov na fone pomekh, Radio i svyaz’, Moscow, 1986 (In Russian). [20] K.A. Rybakov, “Calculation of weight coefficients in continuous particle filter”, Civil Aviation High Technologies, 21:2 (2018), 32–39 (In Russian). [21] N.V. Chernykh, P.V. Pakshin, “Numerical solution algorithms for stochastic differential systems with switching diffusion”, Autom. Remote Control, 74:12 (2013), 2037–2063. [22] T.A. Averina, K.A. Rybakov, “Modeling of multistructural systems on manifolds for statistical analysis and filtering problems”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018), 145–153 (In Russian). [23] T.A. Averina, “Construction and justification of statistical algorithms for simulation of switching diffusion, given by stochastic differential equations”, Tambov University Reports. Series: Natural and Technical Sciences, 20:5 (2015), 986–991 (In Russian). [24] T.A. Averina, “A randomized maximum cross-section method to simulate random structure systems with distributed transitions”, Numer. Anal. Appl., 9:3 (2016), 179–190.

Received

2020-03-25

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Scientific articles

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