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Optimal linear filtering design for discrete-time systems with cross-correlated stochastic parameter matrices and noises

Optimal linear filtering design for discrete-time systems with cross-correlated stochastic parameter matrices and noises

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This study investigates the design of an optimal linear estimator for a class of discrete-time linear systems with correlated stochastic parameter matrices and noises. The considered systems are endowed with the following two main features: (i) cross-correlated stochastic matrices involved in the state and observation equations are assumed and (ii) the process and observation noises have cross-correlation at the same time instant. A decorrelation framework is established to reconstruct such systems. With the equivalent transformation of original dynamic systems resulting from decorrelating operations, the optimal linear recursive filter in the minimum mean square error sense is developed by employing the results of Kalman filtering. The discrete-time linear systems with multiple packet dropouts are modelled as a particular case, and then the proposed filter is applied directly to estimate the system state, while a comparative analysis between the new method and the existing approaches is provided. Simulations demonstrate the effectiveness of the presented algorithm.

References

    1. 1)
      • 1. Feng, J., Wang, Z., Zeng, M.: ‘Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises’, Inf. Fusion, 2013, 14, (1), pp. 7886.
    2. 2)
      • 2. Hu, J., Wang, Z., Shen, B., et al.: ‘Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements’, Int. J. Control, 2013, 86, (4), pp. 650663.
    3. 3)
      • 3. Liu, Y., He, X., Wang, Z., et al.: ‘Optimal filtering for networked systems with stochastic sensor gain degradation’, Automatica, 2014, 50, (5), pp. 15211525.
    4. 4)
      • 4. Tian, T., Sun, S., Li, N.: ‘Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises’, Inf. Fusion, 2016, 27, pp. 126137.
    5. 5)
      • 5. Hu, J., Wang, Z., Liu, S., et al.: ‘A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements’, Automatica, 2016, 64, pp. 155162.
    6. 6)
      • 6. Koning, W.D.: ‘Optimal estimation of linear discrete-time systems with stochastic parameters’, Automatica, 1984, 20, (1), pp. 113115.
    7. 7)
      • 7. Luo, Y., Zhu, Y., Luo, D., et al.: ‘Globally optimal multisensor distributed random parameter matrices Kalman filtering fusion with applications’, Adam Hilger Ser. Sens., 2008, 8, (12), pp. 80868103.
    8. 8)
      • 8. Ding, D., Wang, Z., Dong, H., et al.: ‘Distributed H state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case’, Automatica, 2012, 48, (8), pp. 15751585.
    9. 9)
      • 9. Hu, J., Wang, Z., Gao, H.: ‘Recursive filtering with random parameter matrices, multiple fading measurements and correlated noises’, Automatica, 2013, 49, (11), pp. 34403448.
    10. 10)
      • 10. Caballero-Águilaa, R., García-Garridob, I., Linares-Pérezb, J.: ‘Quadratic estimation problem in discrete-time stochastic systems with random parameter matrices’, Appl. Math. Comput., 2016, 273, pp. 308320.
    11. 11)
      • 11. Wang, S., Fang, H., Tian, X.: ‘Recursive estimation for nonlinear stochastic systems with multi-step transmission delays, multiple packet dropouts and correlated noises’, Analog Integr. Circuits Signal Process., 2015, 115, pp. 164175.
    12. 12)
      • 12. Sun, S.: ‘Optimal linear filters for discrete-time systems with randomly delayed and lost measurements with/without time stamps’, IEEE Trans. Autom. Control, 2013, 58, (6), pp. 15511556.
    13. 13)
      • 13. Sun, S., Ma, J.: ‘Linear estimation for networked control systems with random transmission delays and packet dropouts’, Inf. Sci., 2014, 269, pp. 349365.
    14. 14)
      • 14. Sahebsara, M., Chen, T., Shah, S.L.: ‘Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations’, Int. J. Control, 2007, 80, (2), pp. 292301.
    15. 15)
      • 15. Sun, S., Xie, L., Xiao, W., et al.: ‘Optimal linear estimation for systems with multiple packet dropouts’, Automatica, 2008, 44, (5), pp. 13331342.
    16. 16)
      • 16. Yang, Y., Liang, Y., Pan, Q., et al.: ‘Linear minimum-mean-square error estimation of Markovian jump linear systems with stochastic coefficient matrices’, IET Control Theory Applic., 2014, 8, (12), pp. 11121126.
    17. 17)
      • 17. Caballero-Águila, R., Hermoso-Carazo, A., Linares-Pérez, J.: ‘Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements’, Int. J. Gen. Syst., 2015, 44, (2), pp. 142154.
    18. 18)
      • 18. Linares-Pérez, J., Caballero-Águila, R., García-Garrido, I.: ‘Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications’, Int. J. Syst. Sci., 2014, 45, (7), pp. 15481562.
    19. 19)
      • 19. Shen, X., Zhu, Y., Luo, Y.: ‘Optimal state estimation of linear discrete-time systems with correlated random parameter matrices’. Proc. 30th Chinese Control Conf., Yantai, China, 2011, pp. 14881493.
    20. 20)
      • 20. Sun, S., Tian, T., Lin, H.: ‘State estimators for systems with random parameter matrices, stochastic nonlinearities, fading measurements and correlated noises’, Inf. Sci., 2017, 397-398, pp. 118136.
    21. 21)
      • 21. Luo, Y., Zhu, Y., Shen, X., et al.: ‘Novel data association algorithm based on integrated random coefficient matrices Kalman filtering’, IEEE Trans. Aerosp. Electron. Syst., 2012, 48, (1), pp. 144158.
    22. 22)
      • 22. Han, F., Song, Y., Zhang, S., et al.: ‘Local condition-based finite-horizon distributed H-consensus filtering for random parameter system with event-triggering protocols’, Neurocomputing, 2017, 219, pp. 221231.
    23. 23)
      • 23. Caballero-Águila, R., Hermoso-Carazo, A., Linares-Pérez, J.: ‘Distributed fusion filters from uncertain measured outputs in sensor networks with random packet losses’, Inf. Fusion, 2017, 34, pp. 7079.
    24. 24)
      • 24. Song, E., Zhu, Y., Zhou, J., et al.: ‘Optimal Kalman filtering fusion with cross-correlated sensor noises’, Automatica, 2007, 43, (8), pp. 14501456.
    25. 25)
      • 25. Jiang, P., Zhou, J., Zhu, Y.: ‘Globally optimal Kalman filtering with finite-time correlated noises’. 49th IEEE Conf. on Decision and Control, Atlanta, GA, USA, 2010, pp. 1517.
    26. 26)
      • 26. Feng, J., Zeng, M.: ‘Optimal distributed Kalman filtering fusion for a linear dynamic system with cross-correlated noises’, Int. J. Syst. Sci., 2012, 43, (2), pp. 385398.
    27. 27)
      • 27. Liu, W., Wang, X., Deng, Z.: ‘Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises’, Inf. Fusion, 2017, 35, pp. 1125.
    28. 28)
      • 28. Ma, L., Wang, Z., Hu, J., et al.: ‘Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements’, Analog Integr. Circuits Signal Process., 2010, 90, (6), pp. 20602071.
    29. 29)
      • 29. Wang, X., Liang, Y., Pan, Q., et al.: ‘A Gaussian approximation recursive filter for nonlinear systems with correlated noises’, Automatica, 2012, 48, (9), pp. 22902297.
    30. 30)
      • 30. Yan, L., Li, X., Xia, Y., et al.: ‘Optimal sequential and distributed fusion for state estimation in cross-correlated noise’, Automatica, 2013, 49, (12), pp. 36073612.
    31. 31)
      • 31. Niu, Y., Dong, W., Ji, Y.: ‘State estimation for networked systems with a Markov plant in the presence of missing and quantised measurements’, IET Control Theory Applic., 2016, 10, (5), pp. 599606.
    32. 32)
      • 32. Bar-Shalom, Y., Li, X., Kirubarajan, T.: ‘Estimation with applications to tracking and navigation: theory algorithms and software’ (John Wiley & Sons, New York, NY, USA, 2001).
    33. 33)
      • 33. Chang, G.: ‘Comments on ‘A Gaussian approximation recursive filter for nonlinear systems with correlated noises’ [Automatica 48 (2012) 2290–2297]’, Automatica, 2014, 50, pp. 655656.
    34. 34)
      • 34. Wang, X., Liang, Y., Pan, Q., et al.: ‘General equivalence between two kinds of noise-correlation filters’, Automatica, 2014, 50, pp. 33163318.
    35. 35)
      • 35. Simon, D.: ‘Optimal state estimation: Kalman, H, and nonlinear approaches’ (John Wiley & Sons, Hoboken, NJ, USA, 2006).
    36. 36)
      • 36. Chen, B., Yu, L., Zhang, W.: ‘Robust Kalman filtering for uncertain state delay systems with random observation delays and missing measurements’, IET Control Theory Appl., 2011, 5, (17), pp. 19451954.
    37. 37)
      • 37. Wang, G., Chen, J., Sun, J.: ‘Stochastic stability of extended filtering for non-linear systems with measurement packet losses’, IET Control Theory Applic., 2013, 7, (17), pp. 20482055.
    38. 38)
      • 38. Wang, S., Fang, H., Liu, X.: ‘Distributed state estimation for stochastic non-linear systems with random delays and packet dropouts’, IET Control Theory Applic., 2015, 9, (18), pp. 26572665.
    39. 39)
      • 39. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, New York, NY, USA, 2013, 2nd edn.).
    40. 40)
      • 40. Bar-Shalom, Y., Li, X.R.: ‘Multitarget-multisensor tracking: principles and techniques’ (YBS Publishing, Storrs, CT, USA, 1995).
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