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access icon free Non-linear Kalman filters comparison for generalised autoregressive conditional heteroscedastic clutter parameter estimation

  • Author(s): Juan P. Pascual 1 ; Nicolás von-Ellenrieder 2 ; Javier Areta 3 ; Carlos H. Muravchik 4
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  • Source: Volume 13, Issue 6, August 2019, p. 606 – 613
    DOI:  10.1049/iet-spr.2018.5400 , Print ISSN 1751-9675, Online ISSN 1751-9683
© The Institution of Engineering and Technology
Received 24/08/2018, Accepted 25/04/2019, Revised 01/02/2019, Published 29/04/2019

In this work, the authors analyse the estimation of the generalised autoregressive conditional heteroscedastic (GARCH) process conditional variance based on three non-linear filtering approaches: extended Kalman filter (EKF), unscented Kalman filter and cubature Kalman filter. The authors present a state model for a GARCH process and derive an EKF including second-order non-linear terms for simultaneous estimation of state and parameters. Using synthetic data, the authors evaluate the consistency and the correlation of the innovations for the three filters, by means of numerical simulations. The authors also study the performance of smoothed versions of the non-linear Kalman filters using real clutter data in comparison with a conventional quasi-maximum likelihood estimation method for the GARCH process coefficients. The authors show that with all methods the process coefficients estimates are of the same order and the resulting conditional variances are commensurable. However, the non-linear Kalman filters greatly reduce the computational load. These kind of filters could be used for the radar detector based on a GARCH clutter model that uses an adaptive threshold that demands the conditional variance at each decision instant.

Inspec keywords: radar detection; autoregressive processes; radar clutter; Kalman filters; nonlinear filters; parameter estimation

Other keywords: extended Kalman filter; second-order nonlinear terms; GARCH process coefficients; cubature Kalman filter; parameter estimation; radar detector; unscented Kalman filter; GARCH process conditional variance; nonlinear Kalman filters; generalised autoregressive conditional heteroscedastic clutter; numerical simulations

Subjects: Other topics in statistics; Signal processing theory; Filtering methods in signal processing; Radar equipment, systems and applications; Radar theory; Other topics in statistics

References

    1. 1)
      • 5. Farina, A., Gini, F., Greco, M.V., et al: ‘High resolution sea clutter data: statistical analysis of recorded live data’, Proc. Inst. Electr. Eng.-Radar Sonar Navig., 1997, 144, (3), pp. 121–130.
    2. 2)
      • 6. Gini, F., Greco, M.V., Diani, M., et al: ‘Performance analysis of two adaptive radar detectors against non-Gaussian real sea clutter data’, IEEE Trans. Aerosp. Electron. Syst., 2000, 36, (4), pp. 1429–1439.
    3. 3)
      • 7. Xu, S., Shui, P., Yan, X.: ‘Non-coherent detection of radar target in heavy-tailed sea clutter using bi-window non-linear shrinkage map’, IET Signal Process., 2016, 10, (9), pp. 1031–1039.
    4. 4)
      • 1. Kelly, E.J.: ‘An adaptive detection algorithm’, IEEE Trans. Aerosp. Electron. Syst., 1986, AES-22, (1), pp. 115–127.
    5. 5)
      • 30. Bar-Shalom, Y., Li, X., Kirubarajan, T.: ‘Estimation with applications to tracking and navigation’ (John Wiley & Sons, New York, 2001).
    6. 6)
      • 37. Puskorius, G.V., Feldkamp, L.A.: ‘Parameter-based kalman filter training: theory and implementation’, in Haykin, S., (ed.): ‘Kalman filtering and neural networks’ (John Wiley & Sons, New York, 2001), pp. 23–67.
    7. 7)
      • 26. Julier, S., Uhlmann, J., Durrant-Whyte, H.: ‘A new method for the nonlinear transformation of means and covariances in filters and estimators’, IEEE Trans. Autom. Control, 2000, 45, (3), pp. 477–482.
    8. 8)
      • 25. Ljung, L., Söderström, T.: ‘Theory and practice of recursive identification’ (The MIT Press, Cambridge, MA, 1983).
    9. 9)
      • 15. Pascual, J.P., von Ellenrieder, N., Hurtado, M., et al: ‘Radar detection algorithm for GARCH clutter model’, Digit. Signal Process., 2013, 23, (4), pp. 1255–1264.
    10. 10)
      • 11. Shang, X., Song, H.: ‘Radar detection based on compound-Gaussian model with inverse gamma texture’, IET Radar Sonar Navig., 2011, 5, (3), pp. 315–321.
    11. 11)
      • 22. Mousazadeh, S., Cohen, I.: ‘AR-GARCH in presence of noise: parameter estimation and its application to voice activity detection’, IEEE Audio Speech Lang. Process., 2011, 19, (4), pp. 916–926.
    12. 12)
      • 28. Long, T., Zheng, L., Chen, X., et al: ‘Improved probabilistic multi-hypothesis tracker for multiple target tracking with switching attribute states’, IEEE Trans. Signal Process., 2011, 59, (12), pp. 5721–5733.
    13. 13)
      • 35. Bavdekar, V.A., Deshpande, A.P., Patwardhan, S.C.: ‘Identification of process and measurement noise covariance for state and parameter estimation using extended kalman filter’, J. Process. Control, 2011, 21, pp. 585–601.
    14. 14)
      • 24. Ferreira, G., Navarrete, J.P., Rodríguez Cortés, F.J., et al: ‘Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach’, J. Stat. Comput. Simul., 2017, 87, (12), pp. 2430–2449.
    15. 15)
      • 4. Haykin, S., Krasnor, C., Nohara, T., et al: ‘A coherent dual-polarized radar for studying the ocean environment’, IEEE Trans. Geosci. Remote Sens., 1991, 29, (1), pp. 189–191.
    16. 16)
      • 10. Sangston, K.J., Gini, F., Greco, M.S.: ‘Coherent radar target detection in heavy-tailed compound-Gaussian clutter’, IEEE Trans. Aerosp. Electron. Syst., 2012, 48, (1), pp. 64–77.
    17. 17)
      • 33. Kay, S.M.: ‘Fundamentals of statistical signal processing, estimation theory’ (Prentice Hall, Upper Saddle River, NJ, 1993).
    18. 18)
      • 3. Sheikhi, A., Nayebi, M.M., Aref, M.R.: ‘Adaptive detection algorithm for radar signals in autoregressive interference’, Proc. Inst. Electr. Eng.-Radar Sonar Navig., 1998, 145, (5), pp. 309–314.
    19. 19)
      • 23. Mousazadeh, S., Cohen, I.: ‘Simultaneous parameter estimation and state smoothing of complex GARCH process in the presence of additive noise’, Signal Process., 2010, 90, (11), pp. 2947–2953.
    20. 20)
      • 32. Dhaouadi, R., Mohan, N., Norum, L.: ‘Design and implementation of an extended Kalman filter for the state estimation of a permanent magnet synchronous motor’, IEEE Trans. Power Electron., 1991, 6, (3), pp. 491–497.
    21. 21)
      • 9. Sangston, K., Gerlach, K.: ‘Coherent detection of radar targets in a non-Gaussian background’, IEEE Trans. Aerosp. Electron. Syst., 1994, 30, (2), pp. 330–340.
    22. 22)
      • 12. Cui, G., Kong, L., Yang, X., et al: ‘Distributed target detection with polarimetric MIMO radar in compound-Gaussian clutter’, Digit. Signal Process., 2012, 22, (3), pp. 430–438.
    23. 23)
      • 20. Ossandón, S., Bahamonde, N.: ‘A new nonlinear formulation for GARCH models’, C.R. Math., 2013, 351, (5), pp. 235–239.
    24. 24)
      • 31. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman filters’, IEEE Trans. Autom. Control, 2009, 54, (6), pp. 1254–1269.
    25. 25)
      • 18. Kristensen, D., Linton, O.: ‘A closed-form estimator for the GARCH (1,1) model’, Econ. Theory, 2006, 22, (2), pp. 323–337.
    26. 26)
      • 14. Gini, F., Greco, M.V.: ‘Suboptimum approach to adaptive coherent radar detection in compound-Gaussian clutter’, IEEE Trans. Aerosp. Electron. Syst., 1999, 35, (3), pp. 1095–1104.
    27. 27)
      • 2. Bose, S., Steinhardt, A.: ‘A maximal invariant framework for adaptive detection with structured and unstructured covariance matrices’, IEEE Trans. Signal Process., 1995, 43, (9), pp. 2164–2175.
    28. 28)
      • 21. Pascual, J.P., von Ellenrieder, N., Muravchik, C.H.: ‘Conditional variance LMMSE estimator for a GARCH process clutter model’. Proc. 8th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2014), A Coruña, Spain, 2014, pp. 309–312.
    29. 29)
      • 17. Berkes, I., Horváth, L., Kokoszka, P.: ‘GARCH processes: structure and estimation’, Bernoulli, 2003, 9, (2), pp. 201–227.
    30. 30)
      • 13. Li, Y., Moran, W., Sira, S.P., et al: ‘Monte-Carlo based estimation methods for rapidly-varying sea clutter’. Proc. 13th IEEE Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, 2009. DSP/SPE 2009, Marco Island, FL, 2009, pp. 256–261.
    31. 31)
      • 36. Li, W., Sun, S., Jia, Y., et al: ‘Robust unscented Kalman filter with adaptation of process and measurement noise covariances’, Digit. Signal Process., 2016, 48, pp. 93–103.
    32. 32)
      • 34. Huang, G.P., Mourikis, A.I., Roumeliotis, S.I.: ‘Analysis and improvement of the consistency of extended kalman filter based SLAM’. Proc. IEEE Int. Conf. Robotics and Automation, Pasadena, CA, USA, 2008, pp. 473–479.
    33. 33)
      • 8. Shnidman, D.A.: ‘Generalized radar clutter model’, IEEE Trans. Aerosp. Electron. Syst., 1999, 35, (3), pp. 857–865.
    34. 34)
      • 29. Simon, D.: ‘Optimal state estimation - Kalman, H∞, and nonlinear approaches’ (John Wiley & Sons, New York, 2006).
    35. 35)
      • 19. Ossandón, S., Bahamonde, N.: ‘On the nonlinear estimation of GARCH models using an extended Kalman filter’. Proc. World Congress on Engineering, London, U.K., 2011, vol. 1.
    36. 36)
      • 16. Bollerslev, T.: ‘Generalized autoregressive conditional heteroscedasticity’, J. Econ., 1986, 31, (3), pp. 307–327.
    37. 37)
      • 27. Roy, A., Mitra, D.: ‘Multi-target trackers using cubature kalman filter for Doppler radar tracking in clutter’, IET Signal Process., 2016, 10, (8), pp. 888–901.
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