Czasopismo
2006
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Vol. 52, z. 2
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229-243
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Position estimation using unscented Kalman filter
Języki publikacji
Abstrakty
Proces estymacji położenia w zintegrowanych systemach nawigacyjnych jest często realizowany na nieliniowych modelach systemów. Nieliniowość dynamiki obiektu, którego pozycję należy estymować, wymaga stosowania odpowiednich filtrów. Powszechnie przyjętym rozwiązaniem jest rozszerzony filtr Kalmana oparty na linearyzacji funkcji nieliniowych. W artykule przedstawiono ideę bezśladowego filtru Kalmana wykorzystującego przekształcenie bezśladowe. Zaprezentowano wyniki badań symulacyjnych, które wykazują lepszą dokładność estymacji położenia przy użyciu bezśladowego niż rozszerzonego filtru Kalmana.
In integrated navigation systems different kinds of Kalman Filter working as error estimators or navigation algorithms are widely used. These filters work in time-discrete mode. Kalman Filters utilize information about dynamics of the object (system). Knowledge about dynamics and its correct modelling is the main issue in implementation of the Kalman Filters. In systems with linear dynamics, it is adequately to use basic Kalman Filter. Systems with nonlinear dynamics require linearization of the system model and in such case Extended Kalman Filter (EKF) is generally accepted. Unscented Kalman Filter (UKF) is an alternative for EKF. UKF is a recursive-estimating filter, which properties meet well requirements of strongly nonlinear systems. UKF does not linearize the model but manipulate on statistical parameters of nonlinear transformed state and measurement vector. UKF bases on Unscented Transform (UT). UT converts the state vector into a set of weighted Sigma Points. These points are than used in algorithms of UKF. The UKF algorithm is a set of equations, which are necessary to do prediction, innovation and correction steps. Simulation results of position estimation using EKF and UKF show that UKF used as data processing algorithm gives better accuracy of estimation in system with nonlinear dynamics than EKF. Nonlinearity in system used in simulation causes by transformation of co-ordination systems. Such situation takes place very often in navigation. This shows that UKF is more suitable to systems with strong nonlinearities than EKF. Better accuracy of position estimation using UKF calls for large number of computations (especially evaluation of matrix square root), what makes it more demanding for computation units of integrated navigation systems. UKF may also be used to estimate errors in integrated navigation system based on the compensation mode.
Czasopismo
Rocznik
Tom
Strony
229-243
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Wojskowa Akademia Techniczna, Instytut Radioelektroniki Wydziału Elektroniki, ul. Kaliskiego 2, 00-908 Warszawa, skonatowski@wat.edu.pl
Bibliografia
- 1. R.G. Brown, P.Y.C. Hwang: Introduction to Random Signals and Applied Kalman Filtering with MATLAB Exercises and Solutions. John Wiley & Sons, Canada, 1997.
- 2. N.J. Gordon, B. Ristic, S. Arulampalam: Beyond the Kalman Filter - Particle Filters for Tracking Applications. Artech House, London, 2004.
- 3. M.S. Grewal, A.P. Andrews: Kalman filtering Theory and Practice Using MATLAB. John Wiley & Sons, Canada, 2001.
- 4. S.J. Julier, J.K. Uhlmann, H.F. Durrant-Whyte: A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators. IEEE Transactions on Automatic Control, vol. 45, no. 3, March 2000, pp. 477-482.
- 5. S.J. Julier, J.K. Uhlmann: A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of AeroSense: The 11-th International Symposium on Aerospace/Defense Sensing, Simulations and Controls, vol. II Multi Sensor Fusion, Tracking and Resource Management, Orlando, Florida, 1997, pp. 182-193.
- 6. L.A. Klein: Sensor Technologies and Data Reąuirements for ITS. Artech House, London, 2001.
- 7. R. van der Merwe, A. Doucet, N. de Freitas, E. A. Wan: The Unscented Particle Filter. Technical Report CUED/F-INFENG/TR 380, Cambridge University Engineering Department, Cambridge, 2000.
- 8. R. van der Merwe, E.A. Wan: The Square-root Unscented Kalman Filter for State and Parameter-estimation. Proceedings of International Conference on Acoustics, Speech, and Signal Processing, vol. 6, Salt Lake City, May 2001, pp. 3461-3464.
- 9. R. van der Merwe, E.A. Wan: The Unscented Kalman Filter. Department of Electrical and Computer Engineering, Oregon Graduate Institute of Science and Technology, Beaverton, Oregon, 2001.
- 10. E.A. Wan, R. van der Merwe: The Unscented Kalman Filter to appear in Kalman Filtering and Neural Networks. Chapter 7. Edited by Simon Haykin, John Wiley & Sons, USA, 2001.
- 11. E.A. Wan, R. van der Merwe: The Unscented Kalman Filter for Nonlinear Estimation. Proc. IEEE Symp. Adaptive Systems for Signal Proc., Communication and Control (AS-SPCC), Lake Louise, Alberta, Canada, October 2000, pp. 153-158.
Typ dokumentu
Bibliografia
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