Abstract: 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.

目标跟踪中一种新的基于H_∞滤波器的噪声统计特征估计方法

[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.

[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.

[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.

[4]Banavar, R.N., 1992. A Game Theoretic Approach to Linear Dynamic Estimation. PhD Thesis, Texas University, Austin, USA.

[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.

[6]Bélanger, P.R., 1974. Estimation of noise covariance matrices for a linear time-varying stochastic process. Automatica, 10(3):267-275.

[7]Bohlin, T., 1976. Four cases of identification of changing systems. Math. Sci. Eng., 126:441-518.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[19]Mehra, R., 1972. Approaches to adaptive filtering. IEEE Trans. Autom. Contr., 17(5):693-698.

[20]Myers, K., Tapley, B., 1976. Adaptive sequential estimation with unknown noise statistics. IEEE Trans. Autom. Contr., 21(4):520-523.

[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.

[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.

[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.

[24]Shen, X., Deng, L., 1997. Game theory approach to discrete H_∞ filter design. IEEE Trans. Signal Process., 45(4):1092-1095.

[25]Simon, D., 2006. Optimal State Estimation: Kalman, H_∞, and Nonlinear Approaches. Wiley, New York, USA.

[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.

[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.