每年出版 12 期
ISSN 打印: 0040-2508
ISSN 在线: 1943-6009
Indexed in
ROBUST NONLINEAR FILTERING OF NAVIGATION SATELLITE MEASUREMENTS
摘要
A novel approach to processing satellite navigation measurements with high-precision positioning of mobile objects is considered. For its implementation, at the first stage, stochastic nonlinear differential equations of spatial coordinates of a mobile object were obtained from Doppler satellite measurements and their observer's equations were obtained from pseudo-range measurements. The form of the obtained equations allows one to use the methods of the theory of nonlinear and, in particular, robust filtering to estimate the coordinate vector of an object. As a rule, the nature of the type of interference distributions of Doppler and code measurements is uncertain. Therefore, a dynamic robust algorithm was developed to estimate the spatial coordinates of an object. This algorithm is optimal in terms of the minimum criterion of a nonlinear positive determined function from measurement inconsistency determined by the class of interference distributions of Doppler measurements and pseudo-range measurements. The comparative effectiveness of this algorithm with the conventional approach is illustrated by a numerical example.
-
Bhatti, J. and Humphreys, T., Hostile Control of Ships via False GPS Signals: Demonstration and Detection, Navigation, vol. 64, no. 1, pp. 51-66, 2017.
-
Bitar, E., Baeyens, E., Pasckard, A., and Poolla, K., Linear Minimax Estimation for Random Vectors with Parametric Uncertainty, Proc. of 2010 American Control Conf., Piscataway, NJ: IEEE, pp. 590-592, 2010.
-
Calafiore, G. and El Ghaoui, L., Minimum Variance Estimation with Uncertain Statistical Model, Proc. of 40th IEEE Conf. on Decision and Control, Piscataway, NJ: IEEE, pp. 3497-3499, 2001.
-
Dong, X., Battistelli, G., Chisci, L., and Cai, Y., An Adaptive Consensus Filter for Distributed State Estimation with Unknown Noise Statistics, IEEE Signal Process. Lett., vol. 28, pp. 1595-1599, 2021.
-
Emelyantsev, G.I. and Stepanov, A.P., Integrated Inertial Satellite Orientation and Navigation Systems, State Research Center of the Russian Federation JSC Concern TsNII Elektropribor, St. Petersburg, Russia, 2016.
-
Gao, H., Lam, J., and Wang, C., Induced l /sub 2/ and Generalized H /sub 2/ Filtering for Systems with Repeated Scalar Nonlinearities, IEEE Trans. Signal Process., vol. 53, no. 11, pp. 4215-4226, 2005a.
-
Gao, H., Lam, J., and Wang, C., Robust Ho> Filtering for Discrete Stochastic Time-Delay Systems with Nonlinear Disturbances, Nonlinear Dyn. Syst., vol. 4, no. 3, pp. 285-301, 2004.
-
Gao, H., Lam, J., Xie, L., and Wang, C., New Approach to Mixed H/sub 2//H/sub /spl infin// Filtering for Polytopic Discrete-Time Systems, IEEE Trans. Signal Process., vol. 53, no. 8, pp. 3183-3192, 2005b.
-
Hu, C., Chen, W., Chen, Y., and Liu, D., Adaptive Kalman Filtering for Vehicle Navigation, J. Glob. Position. Syst., vols. 2-1, pp. 42-47, 2003.
-
Hubert, P. J. and Ronchetti, E.M., Robust Statistics, Hoboken, NJ: Wiley, 2009.
-
Hubert P. J., Robustness in Statistics, Moscow: Mir, 1984.
-
Izanloo, R., Fakoorian, S.A., Yazdi, H.S., and Simon, D., Kalman Filtering Based on the Maximum Correntropy Criterion in the Presence of Non-Gaussian Noise, Proc. of Annual Conf. Information Science and Systems, Piscataway, NJ: IEEE, pp. 500-505, 2016.
-
Jin, T., Hu, B., Sun, Y., Huang, Z, Wang, Q., and Wu, Q., Optimal Solution to Multi-Frequency BDS Code Multipath Combination Measurement, J. Navig, vol. 72, no. 5, pp. 1297-1314, 2019.
-
Kazakov, I.E., Statistical Theory of Control Systems in State Space, Moscow: Nauka, 1975.
-
Kinculkin, I.E., Global Navigation Satellite Systems. Algorithms of Operation of Consumer Equipment, Moscow: Radiotekhnika, 2018.
-
Kogan, M.M., Robust Estimation and Filtering in Uncertain Linear Systems under Unknown Covariations, Autom. Remote Control, vol. 76, no. 10, pp. 1751-1764, 2015.
-
Kosarev, N.S., Padve, V.A., Sergeev, S.A., and Dudarev, V.I., The Use of a Synthesized Algorithm Variant of the Parametric Version of LSM-Optimization of the Results of GNSS Measurements for Their Comparative Analysis, Bull. Siber. State Univ. Geosyst Technol., vol. 23, no. 3, pp. 30-45, 2018.
-
Kotz, S., Kozubowski, T.J., and Podgorski, K., The Laplace Distribution and Generalizations, New York: Springer, 2001.
-
Krasovsky, A.A., Handbook on the Theory of Automatic Control, Moscow: Nauka, 1987.
-
Liu, X.H., Liu, X.X., Zhang, W., and Yang, Y., UAV Attitude Calculation Algorithm Based on Acceleration Correction Model, J. Northwestern Polytech. Univ., vol. 39, no. 1, pp. 175-181, 2021.
-
Lohner, R.L., Sustainable Statistical Data Assessment Methods, E.G. Volkova, Ed., Moscow: Mashinostroenie, 1984.
-
Maronna, R.A., Martin, D.R., and Yohai, V.J., Robust Statistics: Theory and Methods, London: Wiley, 2006.
-
Mikrin, E.A. and Mikhailov, V.A., Spacecraft Navigation Using Measurements from Global Navigation Satellite Systems, Moscow: Bauman MSTU Press, 2017.
-
Miller, B.M. and Kolosov, K.S., Robust Estimation Based on the Least Absolute Deviations Method and the Kalman Filter, Autom. Remote Control, vol. 81, no. 11, pp. 1994-2010, 2020.
-
Perov, A.I. and Kharisov, V.N., GLONASS: Principles of Construction and Operation, Moscow: Radiotekhnika, 2010.
-
Poor, H.V. and Looze, D.P., Minimax State Estimation for Linear Stochastic Systems with Noise Uncertainty, IEEE Trans. Autom. Control, vol. 26, no. 4, pp. 902-906, 1981.
-
Rosenberg, I.N., Sokolov, S.V., Umansky, V.I., and Pogorelov, V.A., Theoretical Foundations of Close Integration of Inertial Satellite Navigation Systems, Moscow: Fizmatlit, 2018.
-
Sage, E. and Mels, J., Theory of Evaluation and Its Application in Communication and Governance, Moscow: Svyaz', 1976.
-
Salychev, O.S., Verified Approaches to Inertial Navigation, Moscow: Bauman MSTU Press, 2017.
-
Sarkka, S. and Nummenmaa, A., Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations, IEEE Trans. Autom. Control, vol. 54, pp. 596-600, 2009.
-
Sayed, A.H., A Framework for State-Space Estimation with Uncertain Models, IEEE Trans. Autom. Control, vol. 46, no. 7, pp. 998-1013, 2001.
-
Sinitsyn, I.N., Kalman andPugachev Filters, Moscow: Logos, 2006.
-
Sokolov, S.V. and Pogorelov, V.A., Stochastic Assessment, Control and Identification in High-Precision Navigation Systems, Moscow: Fizmatlit, 2016.
-
Tikhonov, V.I. and Kharisov, V.N., Statistical Analysis and Synthesis of Radio Engineering Devices and Systems, Moscow: Radio i Svyaz', 2004.
-
Tsypkin, Y.Z. and Polyak, B.T., Coarse Method of Maximum Likelihood, Dynamics of Systems: Mathematical Methods of Oscillation Theory, Gor'kiy, no. 12, pp. 22-46, 1977.
-
Yu, C.Y. and Zhang, Z., Spherical Robot Attitude Calculation Based on Complementary Filtering and Particle Filter Fusion, Robot. J., vol. 524, no. 43, pp. 340-349, 2021.