Abstract
The relation between the time-varying optimal algorithms of Kalman filtering and the time-invariant algorithms obtained within the framework of the frequency approach using the approximate method of local approximation of spectral densities was revealed. Introduced was the notion of time-and-frequency approach lying in combined use of the Kalman and frequency approaches, including the method of local approximation. Consideration was given to the examples of processing the navigation information, and the practical importance of the results obtained was discussed.
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References
Kalman, R.E., New Results in Linear Filtering and Prediction Theory, Eng. Trans. ASME, Ser. D, 1961, vol. 83, pp. 95–107.
Gelb, A., Applied Optimal Estimation, Cambridge: MIT Press, 1974.
Rivkin, S.S., Ivanovskii, R.I., and Kostrov, A.V., Statisticheskaya optimizatsiya navigatsionnykh sistem (Statistical Optimization of Navigation Systems) Leningrad: Sudostroenie, 1976.
Dmitriev, S.P., Vysokotochnaya morskaya navigatsiya (High-precision Marine Navigation), Leningrad: Sudostroenie, 1991.
Anderson, B.D.O. and Morre, J.B., Kalman Filtering: Whence, What and Whither?, in Mathematical System Theory. The Influence of R.E. Kalman, Berlin: Springer, 1991, pp. 41–54.
Brown, R.G. and Hwang, P.Y.C., Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises and Solutions, New York: Wiley, 1997.
Dmitriev, S.P. and Stepanov, O.A., Noninvariant Algorithms to Process Information of Inertial Navigation Systems, Giroskop. Navigats., 2000, no. 1, pp. 24–38.
Grewall, M., Weill, L.R., and Andrews, A.P., Global Positioning Systems, Inertial Navigation, and Integration, New York: Wiley, 2007.
Sovremennye informatsionnye tekhnologii v problemakh navigatsii i navedeniya bespilotnykh manevrennykh letatel’nykh apparatov (Modern Information Technologies in Navigation and Guidance of Unmanned Maneuvrable Flight Vehicles), Krasil’shchikov, M.N. and Sebryakov, G.G., Eds., Moscow: Nauka, 2009.
Raspopov, V.Ya., Osnovy postroeniya besplatformennykh inertsial’nykh navigatsionnykh sistem (Fundamentals of Designing Strapdown Inertial Navigation Systems), St. Petersburg: GNTs RF TsNII “Elektropribor,” 2009.
Koshaev, D.A., Kalman Filter-based Multialternative Method for Fault Detection and Estimation, Autom. Remote Control, 2010, vol. 71, no. 5, pp. 790–802.
Golovan, A.A. and Parusnikov, N.A., Matematicheskie osnovy navigatsionnykh sistem, tom 1: Matematicheskie modeli inertsial’noi navigatsii (Mathematical Fundamentals of Inertial Navigation Systems, vol. 1: Mathematical Models of Inertial Navigation), Moscow: Maks Press, 2011.
Stepanov, O.A., Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii, tom 2: Vvedenie v teoriyu fil’tratsii (Fundamentals of Estimation Theory with Applications to Problems of Navigation Information Processing. vol. 2: Introduction to Filtering Theory), St. Petersburg: GNTs RF TsNII “Elektropribor,” 2012.
Kharin, E.G. and Kopylov, I.A., Tekhnologii letnykh ispytanii bortovogo oborudovaniya letatel’nykh apparatov s primeneniem kompleksa bortovykh traektornykh izmerenii (Technologies of Flight Tests of Flight Vehicle On-board Equipment Using System of On-board Trajectory Measurements), Moscow: MAI-Print, 2012.
Wiener, N., Extrapolation, Interpolation and Smoothing of Stationary Time Series, with Engineering Applications, New York: Wiley, 1949.
Chelpanov, I.B., Optimal’naya obrabotka signalov v navigatsionnykh sistemakh (Optimal Processing of Signals in Navigation Systems), Moscow: Nauka, 1967.
Van Trees, H.L., Detection, Estimation, and Modulation Theory, vol 1: Detection, Estimation and Linear Modulation Theory, New York: Wiley, 1968. Translated under the title Teoriya obnaruzheniya, otsenok i modulyatsii, Moscow: Sovetskoe Radio, 1972.
Chelpanov, I.B., Nesenyuk, L.P., and Braginskii, M.V., Raschet kharakteristik navigatsionnykh priborov (Calculation of Characteristics of Navigation Devices), Leningrad: Sudostroenie, 1978.
Nesenyuk, L.P., Engineering Approach to Design of Kalman-Wiener Filters, Aviakosm. Priborostr., 2003, no. 11, pp. 37–42.
Pamyati professora Nesenyuka L.P. Izbrannye trudy i vospominaniya (In Memory of Prof. Nesenyuk L.P.), Peshekhonov, V.G., et al., Eds., St. Petersburg: GNTs RF TsNII “Elektropribor,” 2010.
Loparev, A.V., Stepanov, O.A., and Chelpanov, I.B., Using Frequency Approach to Time-Variant Filtering for Processing of Navigation Information, Giroskop. Navigats., 2012, vol. 3, no. 1, pp. 9–19.
Zinenko, V.M., Application of Suboptimal Time-and-Invariant Filters, Giroskop. Navigats., 2012, vol. 3, no. 4, pp. 286–297.
Stepanov, O.A., Chelpanov, I.B., and Loparev, A.V., Using Time-Frequency Approach to Solve Non-stationary Navigation Problems, in Materials of Plenary Session of Fifth Russian Multiconf. on Control Problems, St. Petersburg, 2012, pp. 64–80.
Ivanovski, R.I., Some Aspects of Development and Application of Stationary Filters to Navigation Systems, Giroskop. Navigats., 2012, vol. 3, no. 1, pp. 1–8.
Kurdyukov, A.P. and Poznyak, A.S., Sensitivity of H ∞-functionals to Internal Disturbances in Linear Control Systems, Autom. Remote Control, 1993, vol. 54, no. 4, part 2, pp. 644–652.
Tupysev, V.A., Stepanov, O.A., Loparev, A.V., et al., Guaranteed Estimation in the Problems of Navigation Information Processing, in 3rd IEEE Multi-Conf. Systems and Control, St. Petersburg, 2009, pp. 1672–1677.
Tupysev, V.A., Using Wiener Models for Describing Gyro Drifts and Measurement Errors in INS State Estimation, in 9th St. Petersburg Int. Conf. Integrated Navigation Systems, St. Petersburg, 2002, pp. 250–253.
Nebylov, A.V., Ensuring Control Accuracy, Lecture Notes in Control and Information Sciences, vol. 305, Heidelberg: Springer, 2004.
Kulakova, V.I. and Nebylov, A.V., Guaranteed Estimation of Signals with Bounded Variances of Derivatives, Autom. Remote Control, 2008, vol. 69, no. 1, pp. 76–88.
Loparev, A.V., Stepanov, O.A., and Chelpanov, I.B., Relationship between Time-Invariant and Time-Variant Filtering Algorithms for a Class of Problems of Navigation Data Processing, in 51st IEEE Conf. Decision Control, Maui, 2012, pp. 2016–2021.
Blazhnov, B.A., Koshaev, D.A., and Stepanov, O.A., Study of Efficiency of Using Satellite Measurements at Measuring Gravitational Acceleration on Flight Vehicle, Giroskop. Navigats., 2002, no. 3, pp. 33–47.
Jordan, S.K., Self-Consistent Statistical Models for Gravity Anomaly and Undulation of the Geoid, J. Geophys. Res., 1972, vol. 77, no. 20, pp. 3660–3670.
Loparev, A.V., Stepanov, O.A., and Yashnikova, O.M., On Using Method of Rectifiable Logarithmic Characteristics in Smoothing Problems, Nauch.-Tekh. Vestn. Inform. Tekhnol., Mekh., Opt., 2012, no. 5, pp. 151–152.
Loparev, A.V. and Yashnikova, O.M., Method of Rectifiable Logarithmic Characteristics in Smoothing Problems, in Proc. XIV Conf. “Navigation and Motion Control,” St. Petersburg, 2012, pp. 257–263.
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Original Russian Text © O.A. Stepanov, A.V. Loparev, I.B. Chelpanov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 6, pp. 132–153.
In memory of L.P. Nesenyuk
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Stepanov, O.A., Loparev, A.V. & Chelpanov, I.B. Time-and-frequency approach to navigation information processing. Autom Remote Control 75, 1090–1108 (2014). https://doi.org/10.1134/S0005117914060095
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DOI: https://doi.org/10.1134/S0005117914060095