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Numerically Stable and Efficient Implementation of a Continuous-Discrete Multiple-Model Estimator

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This paper deals with the problem of implementing adaptive radar tracking filters based on continuous-time models of target motion and on discrete-time models of measurement process. The particular difficulties addressed include: nonlinear and non-stationary target movement models with uncertain parameters, and low data rate due to a rotating radar antenna. The proposed tracking filter relies basically on the continuous-discrete variant of the extended Kalman filter (EKF), the probabilistic data association (PDA) technique and the interacting multiplemodel (IMM) state estimation scheme. Numerical properties of the algorithm are discussed and a software implementation is developed using the open-source BLAS library. Several design concepts are combined to assure numerical stability, convergence and efficiency of the estimator.
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  • Intel Technology Poland Sp. z o.o., Słowackiego 173, 80-298 Gdańsk, Poland
Bibliografia
  • [1] R. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME, vol. 82D, pp. 35-45, Mar. 1960.
  • [2] R. Kalman and R. Bucy, “New results in linear filtering and prediction theory,” Trans. ASME, vol. 83D, pp. 95-108, Mar. 1961.
  • [3] Y. Bar-Shalom, X. Rong Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation. New York, NY: John Wiley& Sons, Inc., 2001.
  • [4] P. Costa, “Adaptive model architecture and extended Kalman-Bucy filters,” IEEE Trans. Aerosp. Electron. Syst., vol. 30, no. 2, pp. 525-533, Apr. 1994.
  • [5] H. Blom and Y. Bar-Shalom, “The interacting multiple model algorithm for systems with Markovian switching coefficients,” IEEE Trans. Autom. Control, vol. 33, no. 8, pp. 780-783, Aug. 1988.
  • [6] Y. Bar-Shalom and E. Tse, “Tracking in a cluttered environment with probabilistic data association,” Automatica, vol. 11, pp. 451-460, 1975.
  • [7] G. Bierman, Factorization Methods for Discrete Sequential Estimation. New York: Academic Press, 1977.
  • [8] R. Kenefic, “Active sonar application of a U-D square root PDAF,” IEEE Trans. Aerosp. Electron. Syst., vol. 26, no. 5, pp. 850-857, Sep. 1990.
  • [9] X. Rong Li and Y. Zhang, “Numerically robust implementation of multiple-model algorithms,” IEEE Trans. Aerosp. Electron. Syst., vol. 36, no. 1, pp. 266-278, Jan. 2000.
  • [10] J. Jørgensen, P. Thomsen, H. Madsen, and M. Kristensen, “A computationally efficient and robust implementation of the continuous-discrete extended Kalman filter,” in Proc. American Control Conf., New York, NY, Jul. 2007, pp. 3706-3712.
  • [11] T. Mazzoni, “Computational aspects of continuous-discrete extended Kalman-filtering,” Computational Statistics, vol. 23, pp. 519-539, Oct. 2008.
  • [12] M. Sankowski, “Continuous-discrete estimation for tracking ballistic missiles in air surveillance radar,” IET Radar, Sonar and Navig., vol. 5, no. 9, pp. 978-986, Dec. 2011.
  • [13] M. Sankowski and W. Buda, “Numerical implementation of continuousdiscrete IMM state estimators,” in Proc. Int. Radar Symp. IRS, Vilnius, Lithuania, Jun. 2010, pp. 474-477.
  • [14] G. Cardillo, A. Mrstik, and T. Plambeck, “A track filter for reentry objects with uncertain drag,” IEEE Trans. Aerosp. Electron. Syst., vol. 35, no. 2, pp. 394-408, Apr. 1999.
  • [15] F. Daum and R. Fitzgerald, “Decoupled Kalman filters for phased array radar tracking,” IEEE Trans. Autom. Control, vol. 28, no. 3, pp. 269-283, Mar. 1983.
  • [16] “BLAS – Basic Linear Algebra Subprograms,” 2010, http://www.netlib.org/blas/.
  • [17] “ATLAS – Automatically Tuned Linear Algebra Software,” 2011, http://math-atlas.sourceforge.net.
  • [18] X. Rong Li, “Tracking in clutter with strongest neighbor measurements - Part I: Theoretical analysis,” IEEE Trans. Autom. Control, vol. 43, no. 11, pp. 1560-1578, Nov. 1998.
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Bibliografia
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bwmeta1.element.baztech-73fd548a-6838-496a-8293-4ffd1126ab7c
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