ORIGINAL ARTICLE
Study of the Effectiveness of Different Kalman Filtering Methods and Smoothers in Object Tracking Based on Simulation Tests
1
University of Technology and Life Sciences Geomatics, Geodesy and Spatial Economy Department Bydgoszcz, Poland.
Online publication date: 2015-02-03
Reports on Geodesy and Geoinformatics 2014;97:1-22
KEYWORDS
Kalman filteringsmootherExtended Kalman Filterderivativefree filteringCentral Difference Kalman FilterUnscented Kalman Filterobject tracing
ABSTRACT
In navigation practice, there are various navigational architecture and integration strategies of measuring instruments that affect the choice of the Kalman filtering algorithm. The analysis of different methods of Kalman filtration and associated smoothers applied in object tracing was made on the grounds of simulation tests of algorithms designed and presented in this paper. EKF (Extended Kalman Filter) filter based on approximation with (jacobians) partial derivations and derivative-free filters like UKF (Unscented Kalman Filter) and CDKF (Central Difference Kalman Filter) were implemented in comparison. For each method of filtration, appropriate smoothers EKS (Extended Kalman Smoother), UKS (Unscented Kalman Smoother) and CDKS (Central Difference Kalman Smoother) were presented as well. Algorithms performance is discussed on the theoretical base and simulation results of two cases are presented.
REFERENCES (24)
1.
Andersen, B. D. O., Moore, J. B. (1979). „Filtracja optymalna.” WNT, Warszawa, 1984. (oryg. Andersen B.D.O., Moore J. B. „Optimal filtering” Prentice-Hall Inc., Englewood Cliffs, New Jersey, USA, 1979).
2.
Candy, J. V. (1987). „Signal Processing–The Model-Based Approch” McGraw-Hill, Singapore.
3.
Christian, K. (2000). „Improvements of GNSS Receiver Performance Using Deeply Coupled INS measurements.” ION GPS.
4.
Grejner-Brzezinska, D. A., Toth C. K., and Yi Y. (2005) „On Improving Navigation Accuracy of GPS/INS Systems.” Photogrammetric Engineering and Remote Sensing, Vol. 71, No. 4, 377–389.
5.
Ito, K., Xiong, K. (2000). „Gaussian Filters for Nonlinear Filtering Problems.” IEEE Transactions on Automatic Control, 45(5), 910–927.
6.
Kalman R. E., (1960) „A New Approach to Linear Filtering and Prediction Problems”, Trans. of the ASME - Journal of Basic Engineering, p. 35-45.
7.
Kaniewski, P., (2006) „Aircraft Positioning with INS/GNSS Integrated System” Molecular and Quantum Acoustics, Vol. 27, p. 149-168.
8.
Kim, H et al. (2003) „An Ultra Tightly coupled GPS/INS Integration using Federated Kalman Filter.” ION GPS.
9.
Knight, D. T. (1999). „Rapid Development of Tightly Coupled GPS/INS Systems.” Proceeding of ION International Meeting, Nashville, Tennessee.
10.
Kwiecień, J., Malinowski, M., Bujnowski, S., Bujarkiewicz, B. (2006) „ATR TRACK III: The real-time GPS for public security.” Reports on Geodesy, No. 2(77), 179-185.
11.
Konatowski, S.; Sipa, T. (2004) „Position estimation using Unscented Kalman Filter” Annual of Navigation, No. 8, p. 97-110.
12.
Nørgaard M., Poulsen N., Ravn O., (1998) „Advances in Derivative-Free State Estimation for Nonlinear Systems”, Technical Report IMM-REP-1998-15, Department of Mathematical Modelling, DTU, (revised Oct. 2004).
13.
Nørgaard M., Poulsen N., Ravn O., (2000) „New Developments in State Estimation for Nonlinear Systems”, Automatica, 36.
14.
Rauch, H. E., Tung, F., Striebel, C. T., (1965) „Maximum likelihood estimates of linear dynamic systems”. AIAA Journal, 3(8):1445–1450.
15.
Rogers, R.M. (2007). „Applied Mathematics in Integrated Navigation Systems.” 3rd ed. Blacksburg, VA, USA: American Institute of Aeronautics and Astronautics, Inc.
16.
Särkkä, S. (2006) „Recursive Bayesian Inference on Stochastic Differential Equations.” Doctoral dissertation, Helsinki University of Technology Laboratory of Computational Engineering Publications Raport B54, Espoo.
17.
Särkkä S., Vehtari A., and Lampinen J., (2007) „Prediction of ESTSP Competition Time Series by Unscented Kalman Filter and RTS Smoother”, In Proceedings of ESTSP 2007, Espoo.
18.
Särkkä, S., (2008) „Unscented Rauch-Tung-Striebel smoother”. IEEE Transactions on Automatic Control, 53(3):845–849.
19.
Shin E, El-Sheimy N., (2005) „Backward Smoothing for Pipeline Surveying Applications” in Proceedings of ION NTM, pp. 921-927, U. S. Institute of Navigation, Fairfax VA, 24-26 January, San Diego CA.
20.
Shin E., (2005) „Estimation Techniques for Low-Cost Inertial Navigation”, PhD Thesis, Department of Geomatics Engineering, University of Calgary, UCGE Report No. 20219, Canada.
21.
van der Merwe, R., Wan, E.A. (2001) „Efficient Derivative-Free Kalman Filters for Online Learning.” In Proc. of ESANN, Bruges.
22.
van der Merwe, R., Wan, E.A. (2001) „The square-root unscented kalman filter for state and parameter-estimation.” In Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Salt Lake City, Utah.
23.
van der Merwe. R., Wan. E.A., Julier. S.J. (2004). „Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion:Applications to Integrated Navigation.” In Proceedings of the AIAA Guidance, Navigation and Control Conference, Providence, RI.
24.
Vorbrich, K.K., (2011) „Analysis of some low- and high-dynamics errors of Low-Cost IMU”, Geodesy and Cartography, Vol. 60, No 1, 2011, pp. 35-59.
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