Adaptive guaranteed estimation of a constant signal under uncertainty of measurement errors

Adaptive guaranteed estimation of a constant signal under uncertainty of measurement errors

Автор: Khadanovich D.V., Shiryaev V.I.

Журнал: Вестник Южно-Уральского государственного университета. Серия: Компьютерные технологии, управление, радиоэлектроника @vestnik-susu-ctcr

Рубрика: Управление в технических системах

Статья в выпуске: 4 т.20, 2020 года.

Бесплатный доступ

In the guaranteed estimation problems under uncertainty relative to disturbances and measurement errors, the admissible sets of their possible values are determined. The solution is chosen due to conditions of guaranteed bounded estimates optimization corresponding to the worst realization of disturbances and measurement errors. The result of the guaranteed estimation is an unimprovable bounded estimate (information set), which turns to be overly pessimistic (reinsurance) if a prior admissible set of measurement errors is too large compared to their realized values. The admissible sets of disturbances and measurement errors can turn to be only rough upper estimates on a short observation interval. The goal of research is the accuracy enhancement problem of guaranteed estimation when measurement errors are not realized in the worst way, i.e. the environment in which the object operates does not behave as aggressively as it is built in a priori data on the permissible set of error values. Research design. The problem of adaptive guaranteed estimation of a constant signal from noisy measurements is considered. The adaptive filtering problem is, according to the results of measurement processing, from the whole set of possible realizations of errors, to choose the one that would generate the measurement sequence. Results. An adaptive guaranteed estimation algorithm is presented. The adaptive algorithm construction is based on a multi-alternative method based on the Kalman filter bank. The method uses a set of filters, each of which is tuned to a specific hypothesis about the measurement error model. Filter residuals are used to compute estimates of realized measurement errors. The choice of the realization of possible errors is performed using a function that has the meaning of the residual variance over a short time interval. Conclusion. The computational scheme of the adaptive algorithm, the numerical example, and comparative analysis of obtained estimates are presented.

Еще

Constant signal estimation, guaranteed estimation, adaptive algorithm, bounded estimate, measurement residual

Короткий адрес: https://sciup.org/147233782

IDR: 147233782   |   DOI: 10.14529/ctcr200403

Список литературы Adaptive guaranteed estimation of a constant signal under uncertainty of measurement errors

  • Fomin V.N. Rekurrentnoye otsenivaniye i adaptivnaya fil'tratsiya [Recurrent Estimation and Adaptive filtering]. Moscow, Nauka Publ., 1984, 288 p.
  • Sorenson H.W. Least-squares estimation: from Gauss to Kalman. IEEE Spectrum, 1970, vol. 7, iss. 7, pp. 63-68.
  • Kalman R.E. A New Approach to Linear Filtering and Prediction Problems. Transactions of the ASME - Journal of Basic Engineering, 1960, vol. 82, pp. 35-45.
  • Stepanov O.A. Kalman Filtering: Past and Present. An Outlook from Russia. Gyroscopy and Navigation, 2011, vol. 2, iss. 2, pp. 99-110.
  • Kalman R.E. Identification of noisy systems. Russian Mathematical Surveys, 1985, vol. 40, iss. 4, pp. 25-42.
  • Jazwinski A.H. Adaptive filtering. Automatica, 1969, no. 4, pp. 475-485.
  • Mehra R.K. Approaches to adaptive filtering. IEEE Transactions on Automatic Control, 1972, vol. 17, iss. 5, pp. 693-698.
  • Malyshev V.V., Kibzun A.I. Analiz i sintez vysokotochnogo upravleniya letatel'nymi apparatami [Analysis and Synthesis of High-Precision Control of Aircrafts]. Moscow, Mashinostroenie Publ., 1987, 302 p.
  • Kantorovich L.V. [On Some New Approaches to Computational Methods and Observation Processing]. Siberian Mathematical Journal, 1962, vol. 3, no. 5, pp. 701-709. (in Russ.)
  • Schweppe F. Recursive state estimation: Unknown but bounded errors and system input. IEEE Transactions on Automatic Control, 1968, vol. 13, iss.1, pp. 22-28.
  • Bertsekas D., Rhodes I. Recursive state estimation for a set-membership description of uncertainty. IEEE Transactions on Automatic Control, 1971, vol. 16, iss. 2, pp. 117-128.
  • Kats I.Ya., Kurzhanski A.B. [Minimax Multi-Step Filtering in Statistically Uncertain Situations]. Automation and Remote Control, 1979, vol. 39, iss. 11, pp. 1643-1650. (in Russ.)
  • Bakan G.M. [Non-Statistical Statement and Solution of One Filtering Problem]. Automation and Remote Control, 1983, vol. 44, iss. 9, pp. 1125-1136. (in Russ.)
  • Kane V.M. Optimizatsiya sistem upravleniyapo minimaksnomu kriteriyu [Optimization of Control Systems According to the Minimax Criterion]. Moscow, Nauka Publ., 1985, 258 p.
  • Chernousko F.L. [Guaranteed Uncertainty Estimates Using Ellipsoids]. Soviet Mathematics. Doklady, 1980, vol. 251, no. 1, pp. 51-54. (in Russ.)
  • Kurzhansky A.B. [The Identification Problem - Theory of Guaranteed Estimates]. Automation and Remote Control, 1991, vol. 52, iss. 4, pp. 447-465. (in Russ.)
  • Shiryaev V.I. [Synthesis of Control of Linear Systems in Incomplete Information]. Journal of Computer and Systems Sciences International, 1994, no. 3, pp. 229-237. (in Russ.)
  • Shiryaev V.I. [Control Algorithms for Dynamical Systems under Uncertainty]. Mekhatronica, 2001, no. 8, pp. 2-5. (in Russ.)
  • Kuntsevich V.M. Upravleniye v usloviyakh neopredelennosti: garantirovannyye rezul'taty v zadache upravleniya i identifikatsii [Control under Uncertainty: Guaranteed Results in Control and Identification Problems]. Kiev, Naukova Dumka Publ., 2006, 264 p.
  • Polyak B.T., Topunov M.V. Filtering under Nonrandom Disturbances: the Method of Invariant Ellipsoids. Doklady Mathematics, 2008, vol. 77, no.1, pp. 158-162. (in Russ.)
  • Matasov A.I. Metod garantiruyushchego otsenivaniya [Guaranteed Estimation Method]. Moscow, Moscow State University Publ., 2009, 100 p.
  • Nazin S.A., Polyak B.T. Ellipsoid-based parametric estimation in the linear multidimensional systems with uncertain model description. Automation and Remote Control, 2007, vol. 68, iss. 6, pp. 993-1005. (in Russ.)
  • Salnikov N.N. Estimation of State and Parameters of Dynamic System with the Use of Ellipsoids at the Lack of a Priori Information on Estimated Quantities. Journal of Automation and Information Sciences, 2014, no. 2, pp. 144-156. (in Russ.)
  • Shalygin A.S., Lysenko L.N., Tolpegin O.A. Modeling Techniques of Situational Control of the Movement of Unmanned Aerial Vehicles. Eds. A.V. Nozdrachev and L.N. Lysenko. Moscow, Mashinostroenie Publ., 2012, 584 p.
  • Le V.T.H., Stoica C., Alamo T., Camacho E.C., Dumur D. Zonotopes: from Guaranteed State-estimation to Control. Wiley-ISTE, 2013, 335 p.
  • Blanchini F., Miani S. Set-Theoretic Methods in Control. Birkhauser, 2015, 630 p.
  • Elyasberg P.E. Measurement information: how much is it needed? How to process it? Moscow, Nauka Publ., 1983, 209 p.
  • Koscheev A.S., Kurzhansky A.B. [Adaptive Estimation of Multistep Systems Evolution under Uncertainty]. Engineering Cybernetics, 1983, no. 2, pp. 72-93. (in Russ.)
  • Barabanov A.E. Linear filtering with adaptive adjustment of the disturbance covariation matrices in the plant and measurement noise. Automation and Remote Control, 2016, vol. 77, pp. 21-36.
  • Gritsenko N.S., Gusarov A.I., Loginov V.P., Sevastyanov K.K. [Adaptive Estimation. Part 1]. Zarubezhnaja Radioelektronika, 1983, no. 7, pp. 3-27. (in Russ.)
  • Pervachev S.V., Perov A.I. Adaptivnaya fl'tratsiya soobshcheniy [Adaptive Message Filtering]. Moscow, Radio i svyaz Publ., 1991, 160 p.
  • Kogan M.M. Optimal estimation and filtration under unknown covariances of random factors. Automation and Remote Control, 2014, vol. 75, iss. 11, pp. 1964-1981.
  • Magill D.T. Optimal Adaptive Estimation of Sampled Stochastic Processes. IEEE Transactions on Automatic Control, 1965, vol. 10, iss. 4, pp. 434-439.
  • Lainiotis D.G. Partitioning: A unifying framework for adaptive systems, I: Estimation. Proceedings of the IEEE, 1976, vol. 64, iss. 8, pp. 1126-1143.
  • Koshaev D.A. Kalman filter-based multialternative method for fault detection and estimation. Automation and Remote Control, 2010, vol. 71, pp. 790-802.
  • Dmitriev S.P., Stepanov O.A. [Multialternative filtering in navigation information processing problem]. Radioengineering, 2004, no. 7, pp. 11-17. (in Russ.)
  • Fisher K.A., Maybeck P.S. Multiple model adaptive estimation with filter spawning. IEEE Transactions on Aerospace and Electronic Systems, 2002, vol. 38, iss. 3, pp. 755-768.
  • Rong Li X., Jilkov V.P. Survey of maneuvering target tracking. Part V. Multiple-model methods. IEEE Transactions on Aerospace and Electronic Systems, 2005, vol. 41, iss. 4, pp. 1255-1321.
  • Khadanovich D.V., Shiryaev V.I. On the estimation of measurement errors in linear dynamical systems. Proceedings of 2016 3rd Russian Conference "Mathematical Modeling and Information Technologies" (MMIT 2016), 2016, vol. 1825, pp. 35-43.
  • Khadanovich D.V., Shiryaev V.I. To the Problem of Measurement Errors Estimation in Control Systems with Incomplete Information. Bulletin of South Ural State University. Ser. Computer technologies, automatic control, radioelectronics, 2018, vol. 18, no. 4, pp. 25-40. (in Russ.)
  • Sheludko A.S., Shiryaev V.I. Minimax Filtering Algorithm for One-Dimensional Chaotic Process. Mekhatronika, Avtomatizatsiya, Upravlenie, 2014, no. 5, pp. 8-12. (in Russ.)
Еще
Статья научная
QR-код для установки приложения SciUp Наведите камеру и скачайте бесплатное приложение SciUp