Abstract
A new continuous-time particle filter algorithm is proposed for solving the problems of nonlinear estimation of signal when describing the mathematical models of an observed object and a measuring system by means of stochastic differential equations. This algorithm can be used in the estimation problems related to navigation data processing. The algorithm verification is presented by example of a navigation system error estimation using geophysical field map data.
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Stepanov, O.A., Primenenie teorii nelineinoi fil’tratsii v zadachakh obrabotki navigatsionnoi informatsii (Non-linear Filtering Theory Applied to Navigation Information Processing), St. Petersburg: Concern CSRI Elektropribor, 1998.
Bergman, N., Recursive Bayesian estimation navigation and tracking applications, Ph.D. Diss., Linköping University, 1999.
Doucet, A., De Freitas, N. and Gordon N. (Eds), Sequential Monte Carlo Methods in Practice, Springer, 2001.
Bain, A. and Crisan, D., Fundamentals of Stochastic Filtering, Springer, 2009.
Stepanov, O.A. and Toropov, A.B., Nonlinear filtering for map-aided navigation. Part 1. An overview of algorithms, Gyroscopy and Navigation, 2015, vol. 6, no. 4, pp. 324–337.
Stepanov, O.A. and Toropov, A.B., Nonlinear filtering for map-aided navigation. Part 2. Trends in the algorithm development, Gyroscopy and Navigation, 2016, vol. 7, no. 1, pp. 82–89.
Stepanov, O.A., Metody obrabotki navigatsionnoi izmeritel’noi informatsii (Methods of Navigation Measurement Data Processing), St. Petersburg: ITMO University, 2017.
Stepanov, O.A., Vasil’ev, V.A., Toropov, A.B., Loparev, A.V. and Basin, M.V., Analysis of filtering algorithms in navigation problems with polynomial measurements, Materialy XXXI konferentsii pamyati vydayushchegosya konstruktora giroskopicheskikh priborov N.N. Ostryakova (Proceedings of the 31st Conference in Memory of N.N. Ostryakov), St. Petersburg, Concern CSRI Elektropribor, 2018, pp. 146–154.
Sinitsyn, I.N., Fil’try Kalmana i Pugacheva (Kalman and Pugachev Filters), Moscow: Logos, 2007.
Rybakov, K.A., Statisticheskie metody analiza i fil’tratsii v nepreryvnykh stokhasticheskikh sistemakh (Statistical Methods of Analysis and Filtering in Continuous-Time Stochastic Systems), Moscow: Moscow Aviation Institute Publisher, 2017.
Stepanov, O.A. and Toropov, A.B., Application of sequential Monte Carlo methods using analytical integration procedures for navigation information processing, Proceedings of the 12th All-Russian Meeting on Control Issues (VSPU-2014), Moscow, June 16–19, 2014, Moscow: IPU RAN, 2014, pp. 3324–3337.
Bucy, R.S., Nonlinear filtering theory, IEEE Transactions on Automatic Control, 1965, vol. 10, no. 2, p. 198.
Liptser, R.Sh. and Shiryaev, A.N., Nonlinear filtering of Markovian diffusion processes, Trudy MIAN SSSR (Materials of Steklov Mathematical Institute, USSR Academy of Sciences), 1968, vol. 104, pp. 135–180.
Zaritskii, V.S., Svetnik, V.B. and Shimelevich, L.I., Monte Carlo technique in problems of optimal data processing, Avtomatika i telemekhanika, 1975, no. 12, pp. 95–103.
Gikhman, I.I. and Skorokhod, A.V., Vvedenie v teoriyu sluchainykh protsessov (Tutorial on the Theory of Random Processes), Moscow: Nauka, 1977.
Øksendal, B., Stochastic Differential Equations: An Introduction with Applications (Translation into Russian), Moscow: Mir, 2003.
Tikhonov, V.I. and Mironov, M.A., Markovskie protsessy (Markovian Processes), Moscow: Sovetskoe radio, 1977.
Mikhailov, G.A. and Voitishek, A.V., Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo (Numerical Statistical Modeling. Monte Carlo Methods), Moscow: Akademiya Publishing Center, 2006.
Silverman B.W. Density Estimation for Statistics and Data Analysis. Chapman & Hall, 1986.
Averina, T.A. and Rybakov, K.A., An approximate solution of the prediction problem for stochastic jump-diffusion systems, Numerical Analysis and Applications. 2017, vol. 10, no. 1, pp. 1–10.
Rudenko, E.A., Continuous finite-dimensional locally optimal filtering of jump diffusions, Journal of Computer and Systems Sciences International, 2018, vol. 57, no. 4, pp. 505–528.
Hazewinkel, M., Lectures on linear and nonlinear filtering, in Analysis and Estimation of Stochastic Mechanical Systems, eds. W.O. Schiehlen, W. Wedig, Springer-Verlag, 1988, pp. 103–136.
Luo, X., Yau, S.S.-T., Complete real time solution of the general nonlinear filtering problem without memory, IEEE Transactions on Automatic Control, 2013, vol. 58, no. 10, pp. 2563–2578.
Rybakov, K.A., Robust Duncan-Mortensen-Zakai equation for non-stationary stochastic systems, Proceedings of the 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), Novosibirsk Akademgorodok, Russia, September 18–22, 2017, IEEE, 2017, pp. 151–154.
Maruyama, G., Continuous Markov processes and stochastic equations, Rendiconti del Circolo Matematico di Palermo, Series 2, 1955, vol. 2, no. 4, pp. 48–90.
Burrage, K. and Tian, T., Predictor-corrector methods of Runge—Kutta type for stochastic differential equations, SIAM Journal on Numerical Analysis, 2002, vol. 40, no. 4, pp. 1516–1537.
Rybakov, K.A., On the particle filters software implementation for continuous-time observation and estimation systems, Materialy XXXI konferentsii pamyati vydayushchegosya konstruktora giroskopicheskikh priborov N.N. Ostryakova (Proceedings of the 31st Conference in Memory of N.N. Ostryakov), St. Petersburg, Concern CSRI Elektropribor, 2018, pp. 180–191.
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Rybakov, K.A. Solving the Nonlinear Problems of Estimation for Navigation Data Processing Using Continuous-Time Particle Filter. Gyroscopy Navig. 10, 27–34 (2019). https://doi.org/10.1134/S2075108719010061
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DOI: https://doi.org/10.1134/S2075108719010061