Abstract
The paper considers a procedure for linear time-variant filtering used in navigation data processing. The proposed procedure is based on studying and simplifying the valid signal and measurement error models in the frequency domain. The application of this procedure to synthesis of autonomous and corrected gyro verticals is illustrated by examples. Comparative analysis of the accuracy in transient state is performed for time-invariant and time-variant filtering.
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References
Chelpanov, I.B., Optimal’naya obrabotka signalov v navigatzionnykh sistemakh (Optimal Signal Processing in Navigation Systems), Moscow: Nauka, 1967.
Brown, R.G. and Hwang, P.Y.C., Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises and Solutions, 3rd edition, John Willey and Sons, 1997.
Rivkin, S.S., Ivanovskii, R.I., and Kostrov, A.V., Statisticheskaya optimizatsiya navigatsionnykh sistem (Statistical Optimization of Navigation Systems), Leningrad: Sudostroenie, 1976.
Chelpanov, I.B., Nesenyuk, L.P., and Braginskii, M.V., Raschet kharakteristik navigatsionnykh priborov (Calculation of Characteristics of Navigation Devices), Leningrad: Sudostroenie, 1978.
Dmitriev, S.P., Vysokotochnaya morskaya navigatsiya (High-accuracy Marine Navigation), Leningrad: Sudostroenie, 1991.
Anderson, B.D.O., Morre, J.B., Kalman Filtering: Whence, What and Whither? Mathematical System Theory, The Influence of R.E. Kalman, Autolas, A.C., Ed., Berlin: Springer-Verlag, 1991.
Stepanov, O.A., Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii (Fundamentals of Estimation Theory with Applications to Navigation Data Processing), Part 1: Vvedenie v Teoriyu Otsenivaniya (Introduction to Estimation Theory), St. Petersburg: Elektropribor, 2010.
Stepanov, O.A., Kalman Filtering: Past and Present. An Outlook from Russia. (On the occasion of the 80th birthday of Rudolf Emil Kalman, Gyroscopy Navigation, 2011, vol. 2, no. 2, pp. 99–110.
Wiener, N., Extrapolation, Interpolation and Smoothing of Stationary Time Series, with Engineering Applications, New York: John Wiley, 1949.
Kalman, R.E. and Bucy, R.S., New Results in Linear Filtering and Prediction Theory, Eng. Trans. ASME, Series D, 1961, vol. 83, pp. 95–107.
Nesenyuk, L.P. and Chelpanov, I.B., Synthesis of Optimal Dynamic Characteristics of Gyro Vertical with Account of the Vessel’s Roll, Pitch, and Yaw, Izv. Vuzov, Priborostroenie, 1971, vol. 14, no. 3, pp. 64–69.
Nesenyuk, L.P., Engineering Approach to Synthesis of Kalman and Wiener Filters Adapted for Gyroscopic and Navigation Systems, 2nd St.Petersburg Int. Conf. on Gyroscopic Technology and Navigation, St. Petersburg: Elektropribor, 1995, pp. 143–150.
Peshekhonov, V.G. et al., Pamyati professora Nesenyuka L.P, Izbrannye trudy i vospominaniya (In commemoration of Professor L.P. Nesenyuk, Selected papers and memoirs), St Petersburg: Elektropribor, 2010.
Zinenko, V.M., About an Approximate Method for Determining Frequency Characteristics of Optimal One-Dimensional Time-Invariant Filters, Sudostroitel’naya promyshlennost’, Ser. Navigatsiya i Giroskopiya, 1991, no. 1, pp. 15–25.
Oliveira, P. and Pascoal, A., Navigation Systems Design: An Application of Multi-Rate Filtering Theory, Proc. of OCEANS’98 Conference, Nice, France, 1998, vol. 3, pp. 1348–1353.
Ivanovski, R.I., Some Aspects of Development and Application of Stationary Filters to Navigation Systems, Gyroscopy Navigation, 2012, vol. 3, no. 1.
Chelpanov, I.B., Stepanov, O.A., and Loparev A.V., Experience and Prospects for Using Algorithms of Time-Invariant Filtering in Navigation Problems, Giroskopiya Navigatsiya, 2010, no. 4, pp. 88–89.
Kozelkova, N.A. and Loparev A.V., Efficiency Analysis of Time-Variant Filters for Processing of Information in the Problem of Construction of Inertial Vertical, XII Conf. Molodykh Uchenykh, Navigatsiya i Upravlenie Dvizheniem, St. Petersburg: Elektropribor, 2010, pp. 132–140.
Sbornik zadach po teorii avtomaticheskogo upravleniya i regulirovaniya (Collection of Problems on Theory of Automatic Control and Regulation), Besekerskii, V.A., Ed., 3rd ed, Moscow: Nauka-Fizmatlit, 1969.
Stepanov, O.A., An Efficient Unified Algorithm for Filtering and Smoothing Problems. Proc. IFAC Workshop on Adaptation and Learning in Control and Signal Processing. ALCOSP 04, 2004, Yokohama, Japan, pp. 759–763.
Stepanov, O.A. and Koshaev, D.A., Universal Matlab-Programs for Analysis of Potential Accuracy and Sensitivity of Algorithms for Linear Time-Variant Filtering, Giroskopiya Navigatsiya, 2004, no. 2, pp. 81–92.
Ivanovski, R.I., Sensitivity Problems in Data Processing and Control, Gyroscopy Navigation, 2011, vol. 2, no. 3, pp. 138–145.
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Published in Russian in Giroskopiya i Navigatsiya, 2011, No. 3, pp. 115–132.
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Loparev, A.V., Stepanov, O.A. & Chelpanov, I.B. Using frequency approach to time-variant filtering for processing of navigation information. Gyroscopy Navig. 3, 9–19 (2012). https://doi.org/10.1134/S2075108712010099
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DOI: https://doi.org/10.1134/S2075108712010099