access icon free Generalised Kalman filter tracking with multiplicative measurement noise in a wireless sensor network

A new generalised Kalman filtering algorithm using a multiplicative measurement noise model is developed for tracking moving targets in a wireless sensor network. This multiplicative error model facilitates more accurate characterisation of the distance dependence measurement errors of range-estimating sensors. Two new formulations of extended Kalman filter (EKF) and unscented Kalman filter (UKF), called generalised EKF (GEKF) and generalised UKF (GUKF) are derived. Comparing with conventional EKF and UKF formulations, it is shown that GEKF and GUKF can achieve smaller tracking error than traditional EKF and UKF. Simulation results are also reported that demonstrated the superior performance of GEKF and GUKF over existing methods.

Inspec keywords: wireless sensor networks; Kalman filters; nonlinear filters

Other keywords: generalised UKF; extended Kalman filter; generalised EKF; range-estimating sensors; multiplicative measurement noise model; tracking error; multiplicative error model; unscented Kalman filter; wireless sensor network; generalised Kalman filter tracking; moving target tracking; distance dependence measurement errors

Subjects: Wireless sensor networks; Filtering methods in signal processing

References

    1. 1)
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
    7. 7)
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
    14. 14)
      • 10. Osborne, R.W.I., Bar-Shalom, Y., George, J., Kaplan, L.: ‘Statistical efficiency of simultaneous target and sensors localization with position dependent noise’, MA, USA, 2012, vol. 8392, pp. 0314.
    15. 15)
    16. 16)
      • 16. Spinello, D., Stilwell, D.: ‘Nonlinear estimation with state-dependent Gaussian observation noise’, IEEE Trans. Autom. Control, 2010, 55, (6), pp. 13581366 (doi: 10.1109/TAC.2010.2042006).
    17. 17)
      • 25. Sarkka, Y.: ‘Bayesian estimation of time-varying processes: discrete-time systems’ (Aalto University, Finland, 2011).
    18. 18)
      • 4. Kalman, R.E.: ‘A new approach to linear filtering and prediction problems’, J. Basic Eng., 1960, 82, (Series D), pp. 3545 (doi: 10.1115/1.3662552).
    19. 19)
      • 27. Horn, R., Johnson, C.: ‘Matrix analysis’ (Cambridge University Press, 1990). [Online]. Available at http://www.books.google.com/books?id=PlYQN0ypTwEC.
    20. 20)
      • 9. Hu, Y.H., Sheng, X.: ‘Dynamic sensor self-organization for distributed moving target tracking’, J. Signal Process. Syst. Signal Image Video Technol., 2008, 51, (2), pp. 161172 (doi: 10.1007/s11265-007-0104-3).
    21. 21)
      • 5. Julier, S., Uhlmann, J., Durrant-Whyte, H.: ‘A new approach for filtering nonlinear systems’. Proc. American Control Conf., 1995, vol. 3, pp. 16281632.
    22. 22)
      • 2. Estrin, D., Girod, L., Srivastava, G.P.M.: ‘Instrumenting the world with wireless sensor networks’. Proc. 2001 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Salt Lake City, UT, 2001, vol. 4, pp. 20332036.
    23. 23)
      • 21. Hu, Y., Sheng, X.: ‘Dynamic sensor self-organization for distributive moving target tracking’, J. Signal Process. Syst., 2008, 51, (2), pp. 161171 (doi: 10.1007/s11265-007-0104-3).
    24. 24)
      • 1. Conner, W.S., Krishnamurthy, L., Want, R.: ‘Making everyday life easier using dense sensor networks’. Proc. Third Int. Conf. Ubiquitous Computing, London, UK, 2001, pp. 4955.
    25. 25)
      • 22. Hu, X., Xu, B., Wen, S., Liu, Y.: ‘An energy balanced optimal distributed clustering scheme’, J. South China Univ. Technol. (Nat. Sci.), 2012, 40, (8), pp. 2734.
    26. 26)
      • 20. Hu, J., Wang, Z., Gao, H., Stergioulas, L.K.: ‘Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements’, Automatica, 2012, 48, (9), pp. 20072015. Available at http://www.sciencedirect.com/science/article/pii/S0005109812002555 (doi: 10.1016/j.automatica.2012.03.027).
    27. 27)
      • 17. Wang, X., Fu, M., Zhang, H.: ‘Target tracking in wireless sensor networks based on the combination of KF and MLE using distance measurements’, IEEE Trans. Mob. Comput., 2012, 11, (4), pp. 567576 (doi: 10.1109/TMC.2011.59).
    28. 28)
      • 12. Benet, G., Blanes, F., Sim, J., Prez, P.: ‘Using infrared sensors for distance measurement in mobile robots’, Robot. Auton. Syst., 2002, 40, (4), pp. 255266 (doi: 10.1016/S0921-8890(02)00271-3).
    29. 29)
      • 28. Julier, S., Uhlmann, J.: ‘Corrections to unscented filtering and nonlinear estimation’, Proc. IEEE, 2004, 92, (12), pp. 1958 (doi: 10.1109/JPROC.2004.837637).
    30. 30)
      • 14. Jimenez, J., Ozaki, T.: ‘Linear estimation of continuous-discrete linear state space models with multiplicative noise’, Syst. Control Lett., 2002, 47, (2), pp. 91101 (doi: 10.1016/S0167-6911(02)00150-0).
    31. 31)
      • 19. Patwari, N., Hero, A.O., Perkins, M., Correal, N., O'Dea, R.: ‘Relative location estimation in wireless sensor networks’, IEEE Trans. Signal Process., 2003, 51, (8), pp. 21372148 (doi: 10.1109/TSP.2003.814469).
    32. 32)
      • 13. Yang, F., Wang, Z., Hung, Y.: ‘Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises’, IEEE Trans. Autom. Control, 2002, 47, (7), pp. 11791183 (doi: 10.1109/TAC.2002.800668).
    33. 33)
      • 24. Hamill, T., Whitaker, J., Snyder, C.: ‘Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter’, Month. Weather Rev., 2001, 129, pp. 27762790 (doi: 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2).
    34. 34)
      • 7. Kotecha, J., Djuric, P.: ‘Gaussian particle filtering’, IEEE Trans. Signal Process., 2003, 51, (10), pp. 25922601 (doi: 10.1109/TSP.2003.816758).
    35. 35)
      • 3. He, T., Krishnamurthy, S., Luo, L., et al: ‘Vigilnet: an integrated sensor network system for energy-efficient surveillance’, ACM Trans. Sensor Netw., 2006, 2, (1), pp. 138. Available at http://www.dx.doi.org/10.1145/1138127.1138128 (doi: 10.1145/1138127.1138128).
    36. 36)
      • 8. Ho, K.: ‘Bias reduction for an explicit solution of source localization using TDOA’, IEEE Trans. Signal Process., 2012, 60, (5), pp. 21012114 (doi: 10.1109/TSP.2012.2187283).
    37. 37)
      • 10. Osborne, R.W.I., Bar-Shalom, Y., George, J., Kaplan, L.: ‘Statistical efficiency of simultaneous target and sensors localization with position dependent noise’, MA, USA, 2012, vol. 8392, pp. 0314.
    38. 38)
      • 15. Carravetta, F., Germani, A., Raimondi, M.: ‘Polynomial filtering of discrete-time stochastic linear systems with multiplicative state noise’, IEEE Trans. Autom. Control, 1997, 42, (8), pp. 11061126 (doi: 10.1109/9.618240).
    39. 39)
      • 6. Kirubarajan, T., Bar-Shalom, Y.: ‘Kalman filter versus IMM estimator: when do we need the latter?’, IEEE Trans. Aerosp. Electron. Syst., 2003, 39, (4), pp. 14521457 (doi: 10.1109/TAES.2003.1261143).
    40. 40)
      • 26. Eaton, M.L.: ‘Multivariate statistics: a vector space approach’ (John Wiley and Sons, 1983).
    41. 41)
    42. 42)
    43. 43)
      • 11. Logothetis, A., Isaksson, A., Evans, R.: ‘An information theoretic approach to observer path design for bearings-only tracking’. Proc. 36th IEEE Conf. Decision and Control, San Diego, CA, 1997, vol. 4, pp. 31323137.
    44. 44)
      • 18. Sheng, X., Hu, Y.: ‘Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks’, IEEE Trans. Signal Process., 2005, 53, (1), pp. 4453 (doi: 10.1109/TSP.2004.838930).
    45. 45)
      • 23. Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: ‘Estimation with applications to tracking and navigation’ (John Wiley, New York, 2001).
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