Abstract
The application of the method of local approximations of power spectral densities to robust filtering problems with bounded variances of signal derivatives is considered. The algorithm design is based on the assumption that the signal is formed as n-times integrated white noise. It is important that the upper bound of the root-mean-square filtering error increases by no more than 1% as compared with the exact solution of the robust filtering problem. An example is given to illustrate the effectiveness of the algorithm proposed.
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References
Chelpanov, I.B., Nesenyuk, L.P., and Braginskii, M.V., Raschet kharakteristik navigatsionnykh priborov (Calculation of Characteristics of Navigation Instruments), Leningrad: Sudostroenie, 1978.
Chelpanov, I.B., Stepanov, O.A., and Loparev, A.V., Experience and Prospects for the Application of Time-Varying Filtering Algorithms in Navigation Problems, Giroskopiya i Navigatsiya, 2010, no. 4, pp. 88–89.
Loparev, A.V., Stepanov, O.A., and Chelpanov, I.B., Using Frequency Approach to Time-Variant Filtering for Processing of Navigation Information, Gyroscopy and Navigation, 2012, vol. 3, no. 1, pp. 9–19.
Stepanov, O.A., Chelpanov, I.B., and Loparev, A.V., Using Time-Frequency Approach to Solve Problems of Navigation Data Processing, Materialy plenarnogo zasedaniya pyatoi Rossiiskoi mul’tikonferentsii po problemam upravleniya, St. Petersburg, 2012, pp. 64–80.
Stepanov, O.A., Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii. Chast’ 2. Vvedenie v teoriyu fil’tratsii (The Fundamentals of Estimation Theory with Applications to Problems of Navigation Information Processing. Part 2. Introduction to the Theory of Filtering), St. Petersburg, 2010.
Kulakova, V.I. and Nebylov, A.V., Guaranteed Estimation of Signals with Bounded Variances of Derivatives, Automation and Remote Control, vol. 69, is. 1, Jan. 2008, pp. 76–88.
Besekerskii, V.A. and Nebylov, A.V., Robastnye sistemy avtomaticheskogo upravleniya (Robust Automatic Control Systems), Moscow: Nauka, 1983.
Nebylov, A.V., Ensuring Control Accuracy, Lecture Notes in Control and Information Sciences, Heidelberg: Springer-Verlag, 2004, vol. 305.
Kulakova, V.I., Nebylov, A.V., and Stepanov, O.A., Application of H 2/H ∞ Approach to the Problem of Aviation Gravimetery, Giroskopiya i Navigatsiya, 2008, no. 2, pp. 53–62.
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Published in Giroskopiya i Navigatsiya, 2013, No. 3, pp. 85–90.
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Loparev, A.V., Stepanov, O.A. & Kulakova, V.I. Robust filtering using the method of local approximations of power spectral densities. Gyroscopy Navig. 5, 40–43 (2014). https://doi.org/10.1134/S2075108714010088
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DOI: https://doi.org/10.1134/S2075108714010088