A novel approach of noise statistics estimate using H filter in target tracking

  • Xie Wang
  • Mei-qin LiuEmail author
  • Zhen Fan
  • Sen-lin Zhang


Noise statistics are essential for estimation performance. In practical situations, however, a priori information of noise statistics is often imperfect. Previous work on noise statistics identification in linear systems still requires initial prior knowledge of the noise. A novel approach is presented in this paper to solve this paradox. First, we apply the H filter to obtain the system state estimates without the common assumptions about the noise in conventional adaptive filters. Then by applying state estimates obtained from the H filter, better estimates of the noise mean and covariance can be achieved, which can improve the performance of estimation. The proposed approach makes the best use of the system knowledge without a priori information with modest computation cost, which makes it possible to be applied online. Finally, numerical examples are presented to show the efficiency of this approach.


Noise estimate H filter Target tracking 

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  1. Alouani, A.T., Blair, W.D., 1993. Use of a kinematic constraint in tracking constant speed, maneuvering targets. IEEE Trans. Autom. Contr., 38(7):1107–1111. Scholar
  2. Alspach, D.L., Scharf, L.L., Abiri, A., 1974. A Bayesian solution to the problem of state estimation in an unknown noise environment. Int. J. Contr., 19(2):265–287. Scholar
  3. Assa, A., Janabi-Sharifi, F., 2014. A robust vision-based sensor fusion approach for real-time pose estimation. IEEE Trans. Cybern., 44(2):217–227. Scholar
  4. Banavar, R.N., 1992. A Game Theoretic Approach to Linear Dynamic Estimation. PhD Thesis, Texas University, Austin, USA.Google Scholar
  5. Bavdekar, V.A., Deshpande, A.P., Patwardhan, S.C., 2011. Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter. J. Process Contr., 21(4):585–601. Scholar
  6. Bélanger, P.R., 1974. Estimation of noise covariance matrices for a linear time-varying stochastic process. Automatica, 10(3):267–275. Scholar
  7. Bohlin, T., 1976. Four cases of identification of changing systems. Math. Sci. Eng., 126:441–518. Scholar
  8. Carew, B., Belanger, P., 1973. Identification of optimum filter steady-state gain for systems with unknown noise covariances. IEEE Trans. Autom. Contr., 18(6):582–587. Scholar
  9. Duník, J., Straka, O., Šimandl, M., 2015. Estimation of noise covariance matrices for linear systems with nonlinear measurements. Proc. 17th Symp. on System Identification, p.1130–1135. Scholar
  10. Feng, B., Fu, M., Ma, H., et al., 2014. Kalman filter with recursive covariance estimation—sequentially estimating process noise covariance. IEEE Trans. Ind. Electron., 61(11):6253–6263. Scholar
  11. Fu, X., Jia, Y., Du, J., et al., 2013. H filtering with diagonal interacting multiple model algorithm for maneuvering target tracking. Proc. American Control Conf., p.6187–6192.Google Scholar
  12. Gales, M.J.F., 2009. Acoustic modelling for speech recognition: hidden Markov models and beyond? Proc. IEEE Workshop on Automatic Speech Recognition & Understanding, p.44. Scholar
  13. Jiang, T.Y., Liu, M.Q., Wang, X., et al., 2014. An efficient measurement-driven sequential Monte Carlo multi- Bernoulli filter for multi-target filtering. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 15(6):445–457. Scholar
  14. Jwo, D.J., Huang, C.M., 2007. An adaptive fuzzy strong tracking Kalman filter for GPS/INS navigation. Proc. 33rd Annual Conf. of the IEEE Industrial Electronics Society, p.2266–2271. Scholar
  15. Li, W., Jia, Y., 2010. Distributed interacting multiple model H filtering fusion for multiplatform maneuvering target tracking in clutter. Signal Process., 90(5):1655–1668. Scholar
  16. Li, X.R., Bar-Shalom, Y., 1994. A recursive multiple model approach to noise identification. IEEE Trans. Aerosp. Electron. Syst., 30(3):671–684. Scholar
  17. Li, X.R., Jilkov, V.P., 2005. Survey of maneuvering target tracking. Part V: multiple-model methods. IEEE Trans. Aerosp. Electron. Syst., 41(4):1255–1321. Scholar
  18. Mazor, E., Averbuch, A., Bar-Shalom, Y., et al., 1998. Interacting multiple model methods in target tracking: a survey. IEEE Trans. Aerosp. Electron. Syst., 34(1):103–123. Scholar
  19. Mehra, R., 1972. Approaches to adaptive filtering. IEEE Trans. Autom. Contr., 17(5):693–698. Scholar
  20. Myers, K., Tapley, B., 1976. Adaptive sequential estimation with unknown noise statistics. IEEE Trans. Autom. Contr., 21(4):520–523. Scholar
  21. Odelson, B.J., Rajamani, M.R., Rawlings, J.B., 2006. A new autocovariance least-squares method for estimating noise covariances. Automatica, 42(2):303–308. Scholar
  22. Rabiner, L.R., 1990. A tutorial on hidden Markov models and selected applications in speech recognition. In: Waibel, A., Lee, K.F. (Eds.), Readings in Speech Recognition. Morgan Kaufmann Publishers Inc., USA, p.267–296.CrossRefGoogle Scholar
  23. Rawicz, P.L., 2000. H /H2/Kalman Filtering of Linear Dynamical Systems via Variational Techniques with Applications to Target Tracking. PhD Thesis, Drexel University, Philadelphia, USA.Google Scholar
  24. Shen, X., Deng, L., 1997. Game theory approach to discrete H filter design. IEEE Trans. Signal Process., 45(4):1092–1095. Scholar
  25. Simon, D., 2006. Optimal State Estimation: Kalman, H , and Nonlinear Approaches. Wiley, New York, USA.CrossRefGoogle Scholar
  26. Yadav, A., Naik, N., Ananthasayanam, M.R., et al., 2012. A constant gain Kalman filter approach to target tracking in wireless sensor networks. Proc. 7th IEEE Int. Conf. on Industrial and Information Systems, p.1–7. Scholar
  27. Yaesh, I., Shaked, U., 1991. A transfer function approach to the problems of discrete-time systems: H -optimal linear control and filtering. IEEE Trans. Autom. Contr., 36(11):1264–1271. Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Xie Wang
    • 1
    • 2
  • Mei-qin Liu
    • 1
    • 2
    Email author
  • Zhen Fan
    • 2
  • Sen-lin Zhang
    • 2
  1. 1.State Key Laboratory of Industrial Control TechnologyZhejiang UniversityHangzhouChina
  2. 2.College of Electrical EngineeringZhejiang UniversityHangzhouChina

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