状态空间模型辨识方法研究
|
摘要
利用系统辨识方法建立对象数学模型是进行系统分析、设计和优化的前提,系统辨识在理论和工程方面都存在诸多有待解决的问题。本文开展了状态空间模型的辨识方法研究,论文的主要工作和创新点如下：
(1)提出了线性状态空间系统的基于梯度优化的参数估计方法。首先,基于状态空间系统相似变换分析,给出了在观测等价类的相切平面正交子空间确定参数搜索方向的正交梯度方法,不仅能防止参数陷入局部极小值,还可以降低算法复杂度。然后,提出了能控能观的动态系统参数的递阶辨识方法。同时探讨了算法复杂度与系统的能控性、能观测性的内在联系。最后进行了状态空间系统的蒙特一卡罗数值仿真试验,结果表明提出的方法用于线性系统的参数估计是有效的。
(2)提出了状态空间双线性系统基于投影梯度搜索的预报误差辨识方法。通过极小化输出预报误差而获得系统的参数估计。为解决全参数化引起的状态空间模型描述非唯一性问题,提出了在观测等价类相切面投影子空间更新系统参数的方法。给出了融合预报误差局部线性逼近性能的正则化因子自适应调整方法。探讨了算法复杂度与双线性模型子系统的能控性、能观测性的内在联系,给出了算法收敛速度的解析表达式。最后进行了稀土萃取过程的建模与输出预报试验,结果说明了所提出方法的有效性。
(3)利用分段线性化的思想,提出了加权状态空间模型参数的正交梯度辨识方法,适用于非线性动态系统的建模。通过极小化系统输出预报误差而得到系统参数估计。采用径向基函数作为分状态的加权系数,给出了融合观测等价类信息的系统参数的正交梯度计算方法,同时获得了径向基函数参数梯度的递推计算方法,在此基础上,给出了系统参数的迭代辨识算法。揭示了加权状态空间模型各个子系统的能控性和能观测性对算法复杂度的影响机制。最后用提出的方法分别进行了非线性动态系统的建模以及预测的仿真试验,结果说明了提出的方法用于非线性动态系统的建模是有效的。
(4)针对参考输入已知、控制器信息未知的闭环状态空间系统,提出了一种基于辅助变量的子空间辨识方法。针对辨识问题特点构造了辅助变量,通过将输入—输出数据块进行投影运算,而估计出系统扩展观测矩阵的正交补空间,结合SVD分解方法获得了系统扩展观测矩阵与下三角Toeplitz矩阵的估计。给出了系统参数的估计方法。闭环动态系统的仿真试验结果说明提出的子空间辨识方法是有效性。
(5)基于期望极大原理提出了观测输出数据含有状态缺失的动态系统参数辨识方法。在期望极大算法框架下,给出了融合状态缺失信息的联合条件期望解析式,得到了极大化联合条件期望的系统参数计算方法,基于QR分解提高了算法的数值鲁棒性。数值仿真结果验证了所提辨识方法的性能。(6)基于自适应非参数核密度估计方法,提出了未知噪声分布的动态系统的极大似然辨识方法。设计了高斯型核密度估计器,进而给出了系统参数的极大似然估计算法,同时分析了算法的收敛性。仿真结果表明该算法的有效性。
The aim of system identification is building dynamic models. It is an important step before system analysis, control and optimization. And there are many problems to be resolved in the field of system identification. The problems of parameter estimation of state-space models are considered in this thesis. The main work and the innovations of this thesis are as follows:
(1) A parameter estimation method, based on gradient optimization search, is proposed for the linear time-invariant (LTI) state-space models. By the analysis of the similar transformation of LTI systems, the system parameters are updated to the orthogonal space to the manifold of observationally equivalent state-space systems, whose advantage is that local minimization can be advoided and the computational load can be decreased. Moreover, the relation between computational load and system properties such as the observability and controllability is also discussed in detail. Finally, simulation studies show the enhanced performance of the proposed method.
(2) An output error identification method by projected gradient search is proposed for the parameter estimation of multivariable bilinear state-space systems. The system parameters are estimated by iteratively optimizing an output-error cost function. The nonuniqueness of the fully parameterized state-space model is taken into account by solving the optimization problem using a local gradient search that restricts the update of the parameters to directions that change the input-output behavior. In addition, the regulation parameter is adaptively determined by considering the local linear approximation of the output error. Moreover, the relation between the computational load and system properties such as the observability and controllability is discussed in detail. At the same time, the analytic expression of the convergence rate of the identification algorithm is also presented. Finally, the effectiveness of the proposed method is illustrated by practical study with data collected from a rare earth extraction process.
(3) According to the local-linearization, a orthogonal gradient identification method is proposed for weighted state-space models, which is suited for nonlinear dynamical system modelling. The system parameters are determined by minimizing the output-error cost function. normalized radial basis functions are taken as weights of local state. And the orthogonal gradient computation method is given by considering the information of input-output equivalent class. At the same time, the iterative computation for parameters of system and radial basis function is given, and the iterative identification algorithm is also proposed. In addition, the influence of the subsystem's controbility and observability to the computational load is discussed in detail. Finally, a numerical study is given to illustrate the performance of the proposede method for non-linear dynamic systems.
(4) A subspace identification method based on instrumental variable is proposed for parameter estimation of closed-loop state-space systems with known setpoint input and unknown controller information. The instrumental variable is designed according to the characteristics of identification problem. In addition, the orthogonal complement to the extended observability matrix can be estimated. And the extended observability matrix and lower triangular block-Toeplitz matrix are computed by the SVD decomposition. Finally, a simulation study of closed-loop dynamic system is implemented and the result illustructed the performance of the proposed method.
(5) An identification method, based on the expectation maximization (EM) algorithm, is proposed for dynamic systems with missing state information. In the framework of EM algorithm, the expression of joint conditional expectation is obtained and the parameter computation for the maximization of the joint conditional expectation is also derived. In addition, the algorithmic robustness can be enhanced by the QR decomposition. The result of the numerical simulation shows the performance of the proposed method.
(6) Based on adaptive nonparametric density estimation method, a maximum likelihood (ML) identification method is proposed for dynamic systems with unknown noise density distribution. The Gaussian kernel density estimator is designed and the ML estimation algorithm is presented. At the same time, the algorithmic convergence is also analysized in detail. The performance of the proposed method is illustracted by the simulation result.
(1)提出了线性状态空间系统的基于梯度优化的参数估计方法。首先,基于状态空间系统相似变换分析,给出了在观测等价类的相切平面正交子空间确定参数搜索方向的正交梯度方法,不仅能防止参数陷入局部极小值,还可以降低算法复杂度。然后,提出了能控能观的动态系统参数的递阶辨识方法。同时探讨了算法复杂度与系统的能控性、能观测性的内在联系。最后进行了状态空间系统的蒙特一卡罗数值仿真试验,结果表明提出的方法用于线性系统的参数估计是有效的。
(2)提出了状态空间双线性系统基于投影梯度搜索的预报误差辨识方法。通过极小化输出预报误差而获得系统的参数估计。为解决全参数化引起的状态空间模型描述非唯一性问题,提出了在观测等价类相切面投影子空间更新系统参数的方法。给出了融合预报误差局部线性逼近性能的正则化因子自适应调整方法。探讨了算法复杂度与双线性模型子系统的能控性、能观测性的内在联系,给出了算法收敛速度的解析表达式。最后进行了稀土萃取过程的建模与输出预报试验,结果说明了所提出方法的有效性。
(3)利用分段线性化的思想,提出了加权状态空间模型参数的正交梯度辨识方法,适用于非线性动态系统的建模。通过极小化系统输出预报误差而得到系统参数估计。采用径向基函数作为分状态的加权系数,给出了融合观测等价类信息的系统参数的正交梯度计算方法,同时获得了径向基函数参数梯度的递推计算方法,在此基础上,给出了系统参数的迭代辨识算法。揭示了加权状态空间模型各个子系统的能控性和能观测性对算法复杂度的影响机制。最后用提出的方法分别进行了非线性动态系统的建模以及预测的仿真试验,结果说明了提出的方法用于非线性动态系统的建模是有效的。
(4)针对参考输入已知、控制器信息未知的闭环状态空间系统,提出了一种基于辅助变量的子空间辨识方法。针对辨识问题特点构造了辅助变量,通过将输入—输出数据块进行投影运算,而估计出系统扩展观测矩阵的正交补空间,结合SVD分解方法获得了系统扩展观测矩阵与下三角Toeplitz矩阵的估计。给出了系统参数的估计方法。闭环动态系统的仿真试验结果说明提出的子空间辨识方法是有效性。
(5)基于期望极大原理提出了观测输出数据含有状态缺失的动态系统参数辨识方法。在期望极大算法框架下,给出了融合状态缺失信息的联合条件期望解析式,得到了极大化联合条件期望的系统参数计算方法,基于QR分解提高了算法的数值鲁棒性。数值仿真结果验证了所提辨识方法的性能。(6)基于自适应非参数核密度估计方法,提出了未知噪声分布的动态系统的极大似然辨识方法。设计了高斯型核密度估计器,进而给出了系统参数的极大似然估计算法,同时分析了算法的收敛性。仿真结果表明该算法的有效性。
The aim of system identification is building dynamic models. It is an important step before system analysis, control and optimization. And there are many problems to be resolved in the field of system identification. The problems of parameter estimation of state-space models are considered in this thesis. The main work and the innovations of this thesis are as follows:
(1) A parameter estimation method, based on gradient optimization search, is proposed for the linear time-invariant (LTI) state-space models. By the analysis of the similar transformation of LTI systems, the system parameters are updated to the orthogonal space to the manifold of observationally equivalent state-space systems, whose advantage is that local minimization can be advoided and the computational load can be decreased. Moreover, the relation between computational load and system properties such as the observability and controllability is also discussed in detail. Finally, simulation studies show the enhanced performance of the proposed method.
(2) An output error identification method by projected gradient search is proposed for the parameter estimation of multivariable bilinear state-space systems. The system parameters are estimated by iteratively optimizing an output-error cost function. The nonuniqueness of the fully parameterized state-space model is taken into account by solving the optimization problem using a local gradient search that restricts the update of the parameters to directions that change the input-output behavior. In addition, the regulation parameter is adaptively determined by considering the local linear approximation of the output error. Moreover, the relation between the computational load and system properties such as the observability and controllability is discussed in detail. At the same time, the analytic expression of the convergence rate of the identification algorithm is also presented. Finally, the effectiveness of the proposed method is illustrated by practical study with data collected from a rare earth extraction process.
(3) According to the local-linearization, a orthogonal gradient identification method is proposed for weighted state-space models, which is suited for nonlinear dynamical system modelling. The system parameters are determined by minimizing the output-error cost function. normalized radial basis functions are taken as weights of local state. And the orthogonal gradient computation method is given by considering the information of input-output equivalent class. At the same time, the iterative computation for parameters of system and radial basis function is given, and the iterative identification algorithm is also proposed. In addition, the influence of the subsystem's controbility and observability to the computational load is discussed in detail. Finally, a numerical study is given to illustrate the performance of the proposede method for non-linear dynamic systems.
(4) A subspace identification method based on instrumental variable is proposed for parameter estimation of closed-loop state-space systems with known setpoint input and unknown controller information. The instrumental variable is designed according to the characteristics of identification problem. In addition, the orthogonal complement to the extended observability matrix can be estimated. And the extended observability matrix and lower triangular block-Toeplitz matrix are computed by the SVD decomposition. Finally, a simulation study of closed-loop dynamic system is implemented and the result illustructed the performance of the proposed method.
(5) An identification method, based on the expectation maximization (EM) algorithm, is proposed for dynamic systems with missing state information. In the framework of EM algorithm, the expression of joint conditional expectation is obtained and the parameter computation for the maximization of the joint conditional expectation is also derived. In addition, the algorithmic robustness can be enhanced by the QR decomposition. The result of the numerical simulation shows the performance of the proposed method.
(6) Based on adaptive nonparametric density estimation method, a maximum likelihood (ML) identification method is proposed for dynamic systems with unknown noise density distribution. The Gaussian kernel density estimator is designed and the ML estimation algorithm is presented. At the same time, the algorithmic convergence is also analysized in detail. The performance of the proposed method is illustracted by the simulation result.
引文
[1]方崇智,萧德云.过程辨识[M].北京：清华大学出版社,1987.
[2]徐小平.模块化非线性系统辨识算法研究[D].西安理工大学博士论文,2009.
[3]吴亚锋.子空间辨识方法及其在复杂结构中的应用[D].西北工业大学博士学位论文,2000.
[4]Van Overschee, P and De Moor. B. Subspace identification for linear systems: Throry-Implementation-Application[D]. Leuven Univeisity,1996.
[5]冯培悌.系统辨识[M]。杭州：浙江大学出版社,1999.
[6]吕立华.复杂工业系统基于小波网络与鲁棒估计建模方法研究[D].浙江大学博士学位论文,2001.
[7]Ljung. L. Convergence analysis of parametric identification methods. IEEE Trans. Automat.Contr,1987, vol. AC-23, pp.770-783.
[8]Ljung. L.System Identification:Theory for the User, Second Edition. Englewood Cliffs[M], NJ:Prentice-Hall,1999.
[9]Van Overschee, P and De Moor. B. N4SID:Subspace algorithms for the identification of identification of combined deterministic-stochastic systems. Automatica,1994, vol.30, no.l, pp.75-93.
[10]Qin, S. J., Lin, W. and Ljung, L. A novel subspace identification approach with enforced causal models. Automatica,2005,41(2), pp.2043-2053.
[11]Wang, J. and Qin. S. J. Closed-loop subspace identification using the parity space. Automatica,2006, vol.42, no.2, pp.315-320
[12]Favoreel. W, Moor. B. D and Overschee. P. V. Subspace Identification of Bilinear Systems Subject to White Inputs. IEEE Transactions on Automatic Control,1999, vol.44, no.9, pp. 1157-1165
[13]Van Overschee, P and De Moor. B. A unifying theorem for three subspace system identification algorithms, Automatica.1995, vol.31,no.12, pp.1853-1864
[14]Wang, J. and Qin, S. J. A new subspace identification approach based on principal component analysis. Journal of Process Control,2002,12, pp.841-855
[15]Verdult,V., Bergboer, N. and Verghaegen, M. Maximum likelihood identification of multivariable bilinear state-space systems by projected gradient search. In Proceeding of the 41st IEEE Conference on Decision and Control Las Vegas, Nevada USA, December, 2002.
[16]Ribarits, T., Deistler, M., and Mckelvey, T. An analysis of the parametrization by data driven local coordinates for multivariable linear systems. Automatica,2004, vol.40, no.5, pp.789-803
[17]Ribarits, T., Deistler, M., and Hanzon, B. On new parametrization methods for the estimation of linear state-space models. International Journal of adaptive control and signal processing,2004, vol.18, no.9-10, pp.718-743
[18]Ribarits, T., Deistler, M., and Hanzon, B. An analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems. Automatica,2005, vol.41, no.3, pp.531-544
[19]SoderStrom. T, Wigren. T and Abd-Elrady. E. Periodic signal analysis by maximum likelihood modeling of orbits of nonlinear ODEs. Automatica,2005,41,pp.793-805
[20]Calafior. G and Ghaoui. L. E. Robust maximum likelihood estimation in the linear model. Automatica,2001,37, pp.573-580
[21]Van Overschee, P and De Moor. B. Closed-loop Subspace System Identification. Proceedings of the 36th Conference on Decision & Control San Diego, California,1997
[22]Van Overschee, P and De Moor. B. Closed-loop Subspace System Identification. Technique report ESAT-SISTA/TR 1996-52I, Katholieke Universiteit Leuven,1996.
[23]Van Overschee, P and De Moor. B. Continuous-time frequency domain subspace system identification. Signal Processing,1996,52, pp.179-194
[24]李幼凤,苏宏业,褚健.子空间模型辨识方法综述.化工学报,2006,57(3)：473-479·
[25]贺尚.连续动力学系统参数模型辨识及工业试验[D].中南大学博士学位论文,2002.
[26]王树青.海洋平台结构的系统辨识与振动控制技术研究[D].中国海洋大学博士论文,2003.
[27]Ho, B.L. and Kalman. R.E. Effective construction of linear state-variable models from input-output functions. Regelungstechnik,1965,12, pp.545-548
[28]Astrom. K.J. and Bohlin. T. Numerical identification of linear dynamic systems from normal operating records. In Proceedings of IFAC Symposium on Self-Adaptive Systems, Teddington, UK,1965.
[29]Gevers. M. A personal view of the development of system identification; A 30-year journey through an exciting field. IEEE Control Systems magazine,2006, vol.26, no.6, pp.93-105
[30]Box G.E.P. and Jenkins G.M.. Time Series Analysis, Forecasting and Control. Oakland, CA:Holden-Day,1970.
[31]Ljung. L. Asymptotic variance expressions for identified black-box transfer function models. IEEE Trans. Automat. Contr.,1985, vol. AC-30, pp.834-844.
[32]Ljung. L. System Identification:Theory for the User. Englewood Cliffs[M], NJ: Prentice-Hall,1987.
[33]Ljung. L. Development of system identification[A]. Pr oc.13th World Congress of IFAC[C].SanFrancisco, California, Vol. G:141-146,1996.
[34]Smith, R. S. and Dahleh, M. The Modeling of Uncertainty in Control Systems (Lecture Notes in Control and Information Sciences, vol.192). London,U.K.:Springer-Verlag,1994.
[35]Ljung, L. and Glover, K. Frequency domain versus time domain methods in system identification. Automatica,1981, vol.17, no.1, pp.71-86.
[36]McKelvey, T, Akcay, H, Ljung, L. Subspace based multivariable system identification from frequency response data. IEEE Trans. On Automatic Control,1996,41(7):960-979.
[37]Pintelon, R. Frequency domain subspace system identification using non-parametric noise models. Automatica,2002,38, pp.1295-1311.
[38]Yang, Z. J.,& Sanada, S. Frequency domain subspace identification with the aid of the w-operator. Electrical Engineering in Japan,2000,132(1),46-56.
[39]Forssell, U. and Ljung, L. Closed-loop identification revisited. Automatica,1999, vol.35, pp.1215-1241.
[40]Van den Hol. P. M. J and Schrama. R. J. P. Identificaton and Control-closed loop issures. Automatica,1995, vol.31, no.12, pp.1751-1770
[41]Chiuso, A. and Picci, G. Consistency analysis of some closed-loop subspace identification methods. Automatica,2005,41, pp.377-391.
[42]Ljung. L and McKelvey, T. Subspace identification from closed loop data. Signal processing, 1996,52,pp.209-215.
[43]莫建林,张卫东,许晓鸣.鲁棒辨识研究的现状.控制与决策,2002,17(3)：257-263.
[44]Ninness, B., Hjalmarsson, H., and Gustafsson, F. On the fundamental role of orthonor-mal bases in system identification. IEEE Trans.Automat. Contr.,1999, vol.44, no.7, pp. 1384-1407.
[45]Chou, C.T. and Verhaegen, M. Subspace algorithms for the identification of multivariable dynamic errors-in-variable mosels. Automatica,1997, vol.33, no.10, pp.1857-1869
[46]王行愚.系统辨识的若干新动向.控制理论与应用,1992,9(3)：319-321.
[47]吴旭光.不确定性系统的鲁捧辨识及其发展.控制与决策(增刊)1996,：113-118.
[48]冯旭,孙优贤.鲁棒辨识问题评述.控制理论与应用,1993,10(6)：609-616.
[49]Berger,J. Q., and Wolpert. R. The likelihood principle. Hayward, CA:Institute of Mathematical Statistcs,1988.
[50]Wang.X and Poor, H.V. Robust Multiuser Detector in Non-Gaussian Channels. IEEE Transactions on Signal Processing,1999,47(2):289-305
[51]Calafiore. G, and Ghaoui. L. Robust maximum likelihood estimation in the linear model. Automatica,2001,37, pp.573-580.
[52]Richard J K, Sadler B M. Maximum-likelihood array processing in non-gaussian noise with gaussian mixtures. IEEE Trans. Signal Processsing.2000, vol.48, no.12, pp.3520-3535.
[53]Gustafsson F and Hjalmarsson H. Twenty-one estimators for model selection. Automatica, 1995, vol.33, no.10, pp.1377-1392.
[54]王海清.工业过程监测：基于小波和统计学的方法[D].浙江大学博士学位论文,2000.
[55]Zoubin, A.M. and Brcich, R. F. Multiuser Detection in Heavy Tailed Noise. Digital Signal Processing,2002,12(2):262-273
[56]Tsai C, Chen J J. Kernel estimation for adjusted p-values in multiple testing. Comp Stat & Data Ana,2007,51,pp.3885-3897
[57]张炤,张素,章琛曦,陈亚珠.基于支持向量机的概率密度估计方法.系统仿真学报,2005,17(10),pp.2355-2357.
[58]杨宜东,孙志挥,张净.基于核密度估计的分布数据流离群点检测.计算机研究与进展,2005,42(9),pp.1498-1504.
[59]Bhatia V, Mulgrew B. Non-parametric likelihood based channel estimator for Gaussian mixture noise. Signal Processing,2007,4(6), pp.1-18.
[60]Wu X, Perloff J M. GMM estimation of a maximum entropy distribution with interval data. Journal of Econometrics,2007,138, pp.532-546.
[61]Mckelvey, T. and Helmersson, A. System identification using an over-parametrized model class-Improving the optimization algorithm. Proceedings of the 36th Conference on Decision & Control San Diego, California USA,1997.
[62]Mckelvey, T., Helmersson, A., and Ribarits, T. Data driven local coordinates for multivariable linear systems and their application to system identification. Automatica,2004, vol.40, no.9, pp.1629-1635.
[63]Gibson. S and Wills. A and Ninness. B. Maximum-likelihood parameter estimation of bilinear systems. IEEE Transactions on Automatic control,2005, vol.50, no.10, pp.1581-1595
[64]Verdult. V, Ljung. L and Verhaegen. M. Identification of composite local linear state-space models using a projected gradient search. International Journal of Control,2002, vol.75, no.16/17,pp.1385-1398
[65]Verdult. V, Lovera. M and Verhaegen. M. Identification of linear parameter-varying state-space models with application to helicopter rotor dynamics. International Journal of Control,2004, vol.77, no.13, pp.1149-1159
[66]Bergboer, N. H., Verdult, V. and Verhaegen. M. H. G.. An efficient implemention of maximum likelihood identification of LTI state-space models by local gradient search, In Proceeding of the 41st IEEE Conference on Decision and Control Las Vegas, Nevada USA, December,2002.
[67]Verdult. V, Verhaegen. M, Chou. C.T. and Lovera. M. Efficient and systematic Identification of MIMO bilinear state space models. Proceedings of the 37th IEEE Conference on Decision & Control Tampa, Florida USA,1998, pp.1260-1265
[68]Broersen P M, Waele S et al. Autoregressive spectral analysis when observations are missing. Automatica,2004,40, pp.1495-1504.
[69]Sinopoli B, Schenato L et al. Kalman filtering with intermittent observations. IEEE Trans On Autom Contr,2004,49(9), pp.1453-1463.
[70]Chen J M and Chen B S(2000). System parameter estimation with input/output noisy data and missing measurements. IEEE Trans on Signal Processing,2000,48(6), pp.1548-1558.
[71]Isaksson, A. Identification of ARX-models subject to missing data, IEEE Trans. Aut.Contr, 1993, vol.38 no.5, pages 813-819.
[72]Petit J R et al. Climate and atmospheric history of the past 420.000 years form the Vostok ice core, Antarctica. Nature,1999,399,429-436.
[73]谢磊.间歇过程统计性能研究[D].浙江大学博十学位论文,2005.
[74]Broersen P M and Bos R.(2006a). Time-Series Analysis if Data Are Randomly Missing. IEEE Trans On Instru & Measu,2006,55(1), pp.79-84.
[75]Broersen P M. Automatic spectral analysis with missing data. Digital Signal Processing, 2006,16, pp.754-766.
[76]Rosen Y, Porat B. Optimal ARMA parameter estimation based on the sample convarinces for data with missing observations. IEEE Trans. Infor. Theory.1989, Vol.35, no.2, pp.342-348.
[77]Gordon N and Salmond D et al. A novel approach to nonlinear nongaussian Bayesian stae estimation. In proc. IEEE Conf. Radar and Signal Processing,,1993, vol140, pp.107-113.
[78]周东华,席裕庚,张钟俊.一种带多重次优渐消因子的扩展卡尔曼滤波器闭.自动化学报.1991,17(6)：689-695.
[79]Zhou D H, Frank P M. Strong tracking filtering of nonlinear time-varying stochastic systems with coloured noise:application to parameter estimation and empirical robustness analysis. Int. J Control,1996,65(2):295-307.
[80]Hadidi M. and S. Schwartz. Linear recursive state estimators under uncertain observations. IEEE Trans. Autom. Control,1979, vol.24, no.6, pp.944-948.
[81]Nahi N. Optimal recursive estimation with uncertain observation. IEEE Trans. Inf. Theory, 1969, vol. IT-15, no.4, pp.457-462.
[82]Wang Z D, W. D. Daniel et al. Variance-Constrained Filtering for Uncertain Stochastic Systems With Missing Measurements. IEEE Trans. On Autom Contr,2003, vol.48, no.7, pp.1254-1258
[83]Mariton M. Jump linear systems in automatic control. New York:Marcel Dekker[M],1990.
[84]Costa O. Stationary filter for linear minimum mean square error estimator of discrete-time markovian jump systems. IEEE Trans. Automat. Contr.,2002, vol.48, pp.1351-1356.
[85]Smith S. and P. Seiler(2003).Estimation with lossy measurements:Jump estimatorsfor jump systems. IEEE Trans. Autom. Control,2003, vol.48, no.12, pp.2163-2171.
[86]Anderson, B. D. O and Moore, J. B. Optimal Filtering. Englewood Cliffs, NJ, Prentice-Hall[M],1979,.
[87]Savkin A.V.,I. R. Petersen, and S. O. R. Moheimani. Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data," Comput. Elect. Eng.,1999, vol.25, no.1, pp.29-43.
[88]Gao H, Lam J et, al. New approach to mixedH2/H∞ filtering for polytopic discrete-time system. IEEE Trans on Signal Processing,2005, vol.53, no.8 pp.3183-3192.
[89]Gao H, Lam J et, al. Robust energy-to-peak filter design for stochastic time-delay systems. System & Control Letters.2006, Vol.55, no.2, pp.101-111.
[90]Pila A W, Shaked U. et al. H∞ filtering for continuous-time linear systems with delay. IEEE Trans. A-C,1999, vol.44, no.7, pp.1412-1417.
[91]Zhang H, Zhang D et al. An innovation to H∞ prediction with application to systems with delayed measurements. Automatica,2004, vol.40, no.7, pp.1253-1261.
[92]Mcgiffin P B and Murthy D N P. Parameter estimation for auto-regressive systems with missing observations. Int. J. Sys Sci.1980, vol.11, no.9, pp.1021-1034.
[93]Mcgiffin P B and Murthy D N P. Parameter estimation for auto-regressive systems with missing observations-Part2. Int. J. Sys Sci.1981, vol.12, no.6, pp.657-663.
[94]Wallin R Isaksson A et al. An iterative method for identification of ARX models from incomplete data. Proceedings of the 39th IEEE conf on Decision and Contr. Sydney, Australia,2000.
[95]Dempster A P, Laird N M et al. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser,1977,39, pp.1-38.
[96]Wu C F J. On the convergent properties of the EM algorithm. The Annal of Statistics,1983, Vol.11, no.1, pp.95-103.
[97]Meng X L and Rubin D B. On the global and componentwise rates of convergence of the EM algorithm. Linear algebra and its applications,1994,199, pp.413-425.
[98]Gibson. S and Ninness. B. Robust maximum-likelihood estimation of multivariable dynamic systems. Automatica,2005,41(10), pp.1667-1682.
[99]Shumway. R. H., and D. S. Stoffer. Time series analysis and its applications. New York: Springer-Verlag[M],2000.
[100]Charalambous, C.D, Logothetist, A. and Elliott, R.J. Bank Filters for ML parameter Estimation via the Expectation-Maximization Algorithm:The continuous-Time Case,Proceedings of the 37th IEEE Conference on Decision & Control, Tampa, Florida, USA, 1998.
[101]Charalambous and, C.D. and Logothetis, A. Maximum Likelihood Parameter Estimation from Incomplete Data via the Sensitivity Equations:The continuous-Time Case,IEEE Trans. Aut. Contr.,2000, vol.45 no.5, pp.928-934.
[102]Elliott, R.J. and Krishnamurthy, V. Exact finite-dimensional filters for maximum likelihood parameter estimation of continuous-time linear Gaussian systems. SIAM J. Control. Optim,1997, vol.35, No.6, pp.1908-1923.
[103]Elliott, R.J. and Krishnamurthy, V. New Finite-Dimensional Filters for Parameter Estimation of Discrete-Time Linear Gaussian Models, IEEE Trans. Aut. Contr.,1999, vol. 44no.5, pages 938-951.
[104]Langari, R., Wang, L., and Yen, J., "Radial basis function networks, regression weights, and the expectation-maximization algorithm," IEEE Transaction on systems, man, and cybernetics-part A:systems and humans,1997, vol.27, no.5, pp.613-623.
[105]Ravishanker, N., and Qiou, Z. Monte Carlo EM estimation for multivariate stable distributions. Statistics and Probability Letters,1999, vol.45, pp.335-340
[106]Lee, J. H, Han, J. C and Kim, S. C. Joint carrier frequency synchronization and channel estimation for OFDM systems via the EM algorithm. IEEE Transaction on vehicular technique,2006, vol.55, no.1, pp.167-172,
[107]Favoreel. W, Moor. B. D and Overschee. P. V. Subspace state space system identification for industrial processes. Journal of Process Control,2000,10, pp.149-155.
[108]Mckelvey, T., Helmersson, A., and Ribarits, T. Data driven local coordinates for multivariable linear systems and their application to system identification. Automatica,2004, vol.40, no.9, pp.1629-1635.
[109]Qin, S. An overview of subspace identification. Computer and Chemical Engineering,2006, 30, pp.1502-1513.
[110]Qin, S. J., and Ljung, L. Closed-loop subspace identification with innovation estimation. In Proceedings of the 13th IFAC symposium on system identification(pp.887-892). Rotterdam, Netherlands,2003.
[111]Qin, S. J., and Ljung, L. Parallel QR implementation of subspace identification with parsimonious models. estimation. In Proceedings of the 13th IFAC symposium on system identification(pp.1631-1636). Rotterdam, Netherlands,2003.
[112]Larimore. W. E. System identification, reduced-order filtering and modeling via canonical variate analysis. Proc.1983 American Control Conference, San Francisco, pp.445-451,1983.
[113]Larimore. W. E. Canonical variate analysis in identification, filtering, and adaptive control. Proc.29th IEEE Conference on Decision and Control. Honolulu, pp.596-604,1990.
[114]Larimore. W. E. The ADAPTx software for automated and real-time multivariable system identification. Proc.13th IFAC Symp. System Identification, Rotterdam,2003 pp.1496-1501.
[115]Verhaegen, M. Subspace model identification, Part1:The output-error state-space model identification class of algorithms. Int. J. Control,1992, vol.56, no.5, pp.1187-1210.
[116]Verhaegen, M. Subspace model identification, Part2:Analysis of the elementary output-error state-space model identification algorithm. Int. J. Control,1992, vol.56, no.5, pp.1211-1241.
[117]Verhaegen, M. Subspace model identification, Part3:Analysis of the ordinary output-error state-space model identification algorithm. Int. J. Control,1993, vol.58, no.3, pp.555-586.
[118]Verhaegen, M. Application of a subspace model identification technique to identify LTI systems operating in closed-loop. Automatica,1993, vol.29, no.4, pp.1027-1040.
[119]Verhaegen, M. Identification of the deterministic part of MIMO state space models given in innovations form from input-output data. Automatica,1995, vol.30, no.1, pp.61-74.
[120]Verhaegen, M. Identifying MIMO Wiener systems using subspace model identification methods. Signal Processing,1996,52(2):235-258
[121]Viberg, M. Subspace-based methods for the identification of linear time invariant systems. Automatica,1995,31(12):1835-1851
[122]Akaike. H. A new look at the statistical model identification. IEEE Trans. Auto. Cont., 1974,19,716-723.
[123]Gustafsson,T. Subspace identification using instrumental variable techniques. Automatica. 2001,37,pp.2005-2010.
[124]Verdult Vincent, Michel Verhaegen. Kernel methods for subspace identification of multivariable LPV and bilinear systems. Automatica,2005,41(9):1557-1565
[125]Verdult. V, Verhaegen. M. Subspace identification of multivariable linear parameter-varying systems, Automatica,2002, vol.38, no.5, pp.805-814.
[126]McKelvey, T. Frequency domain system identification with instrumental variable based subspace algorithm//Proceedings of the 1997 ASME Design Engineering Technical Conferences. Sacramento, CA, September 14-17 (pp.1-8),1997.
[127]Ohsumi, A., Kameyama, K. and Yamaguchi K-I. Subspace identification for continuous-time stochastic systems via distribution based approach. Automatica,2002,38, pp.63-79.
[128]刘浩.基于子空间方法的热工系统闭环辨识的研究[M].华北电力大学(河北),2008.
[129]石春(2008)DVD聚焦伺服系统研究[D].中国科学技术大学博十论文,2008.
[130]Chiuso, A. and Picci, G. Asymptotic variance of subspace methods by data orthogonalization and model decoupling:a comparative analysis. Automatica,2004, no.40, pp.1705-1717.
[131]Chiuso, A. and Picci, G.. Numerical conditioning and asymptotic variance of subspace estimates. Automatica,2004, no.40, pp.677-683.
[132]Chiuso, A. and Picci, G..Asymptotic variance of closed-loop subspace identification mthods. IEEE Trans on Auto Contr,2006, vol.51, no.8, pp.1299-1314.
[133]Dahlen,A., Lindquist, A., and Mari, J. Experiment evidence showing that stochastic subspace identification methods may fail Systems & Control Letters,1998, vol.34, no.5, pp.303-312.
[134]Maciejowski, J. M.. Guaranteed stability with subspace methods. Syst.& Control Letters, 1995, vol.26, pp.153-156.
[135]Van Gestel, T., Suykens, A. K. and Van Dooren, P. and De Moor, B. Identification of stable model in subspace identification by using regulation. IEEE Trans on Auto. Contr,2001, vol.46, no.9, pp.1416-1420.
[136]Chui, N. L. C and Maciejowski, J. M. Realization of stable models with subspace methods. Automatica,1996,32(11):1587-1595.
[137]Goethals, I., Van Gestel, T., Suykens, J, Van Dooren, P and De Moor, B. Identification of positive real models in subspace identification by using regulation. IEEE Trans on Autom Contr,2003, vol.48, no.10, pp.1843-1847.
[138]Goethals I, Pekckmans K et al. Subspace identification of Hammerstein systems using least squares support vector. IEEE Trans on Autom Contr,2005,50(10):1509-1519.
[139]Lacy, S. L and Bernstein, D. S.Subspace identification with guaranteed stability using constrained optimization. IEEE TFans. On Automatic Control,2003,48(7):1259-1263.
[140]Deistler, M., Peternell, K. and Scherrer, W. Consistency and relative efficiency of subspace method. Automatica,1995,31(12):1865-1875.
[141]Jansson, M. and Wahlberg, B. On consistency of subspace methods for system identification. Automatica,1998,34(12):1507-1519
[142]Jansson, M.. Subspace identification and ARX modeling. In Proceedings of the 13th IFAC symposium on system identification(pp.1625-1630) Rotterdam, Netherlands,2003.
[143]Huang, B, Ding, S. X and Qin, S. J. Closed-loop subspace identification:an orthogonal projection approach. Journal of process control,2005,15, pp.53-66.
[144]Bauer, D. and Jansson, M. Analysis of the asymptotic properties of the MOESP type of subspace algorithms. Automatica,2000,36:497-509
[145]Bauer, D. and Ljung, L. Some facts about the choice of the weighting matrices in Larimore type of subspacealgorithms. Automatica,2002,38:763-773.
[146]Lester, S. H. and Sjoberg, J. Efficient training of neural nets for nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithm. IEEE Trans. On Neural Network,2000, vol.48, no.7,pp.1915-1927.
[147]Gorinevsky,D. An approach to parametric nonlinear least square optimization and application to task-level learning control. IEEE Trans. On Automatic Control,1997, vol.42, no.7, pp.912-927.
[148]Vanbleu, K., Ysebaert, G., Cuypers, G. and Moonen, M. Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems. IEEE Trans. On Signal Processing, 2006, vol.54, no.2, pp.483-498.
[149]邓乃扬.无约束最优化计算方法[M].北京：科学出版社,1982.
[150]Dennis, J. E. and Schnabel, R. B. Numerical methods for unconstrained optimization and nonlinear equations[M]. Englewood Cliffs, NJ:Prentice-Hall,1983.
[151]Kailath. T., Sayed.A., and Hassabi. B. Linear Estimation[M]. Upper Saddle River, NJ: Prentice-Hall,2000.
[152]McKelvey, T.. identification State-space models from time and frequency data. Ph. D. thesis, Department of Electrical Engineering, Link"oping University, Link"oping, Sweden,1995. ISBN 91-7871-531-8. Available from Internet:http://www.control.isy.liu.se/(Retrieved June 27,2001).
[153]Ding, F. and Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Transactions on Automatic Control,2005, vol.50, no.3, pp397-402
[154]Wills A and Brett Ninness. On Gradient-Based Search for Multivariable System Estimates. IEEE Transactions on Automatic Control,2008,53(1):298-306
[155]A. Wills, B. Ninness, S. Gibson. Maximum Likelihood Estimation of State Space Models from Frequency Domain Data. IEEE Transactions on Automatic Control,2009,54(1): 19-33.
[156]粟塔山.最优化计算原理与算法程序设计[M].长沙：国防科技大学出版社,2001.
[157]郑大钟.线性系统理论[M].北京：清华大学出版社,1990.
[158]Lu Guoping, Feng Gang, and Jiang Zhong-Ping. Saturated Feedback Stabilization of Discrete-Time Descriptor Bilinear Systems. IEEE Transactions on Automatic Control,2007, 52(9):1700-1704
[159]朱怀念,张成科,武赛,宾宁.离散双线性系统鞍点均衡的迭代算法.广东工业大学学报,2010,27(1)：8-15
[160]余勇,万德钧.一类双线性时间序列模型基于累积量的辨识.东南大学学报,1999,29(3)：139-143
[161]Vasilis Tsoulkas, Panos Koukoulas, and Nicholas Kalouptsidis. Identification of Input-Output Bilinear Systems Using Cumulants. IEEE Transactions on Signal Processing, 2001,49(11):2753-2761
[162]黄正良,万百五,韩崇昭.双线性系统稳态模型估计及其强一致性分析.自动化学报,1995,21(5)：562-569
[163]Nicholas Kalouptsidis,Panos Koukoulas,and V. John Mathews. Blind Identification of Bilinear Systems. IEEE Transactions on Signal Processing,2003,51(2):484-499
[164]Wingerden Jan-Willem van, Michel Verhaegen(2009)ace. Identification of Bilinear and LPV systems for open- and closed-loop data. Automatica,2009,45(2):372-381
[165]Zou Qiyue, Zhiping Lin,and Raimund J. Ober. The Cramer-Rao Lower Bound for Bilinear Systems. IEEE Transactions on Signal Processing,2006,54(5):1666-1680
[166]ZHONG Lusheng, FAN Xiaoping, YANG Hui. System Identification of Bilinear State-space Models by Modified Gradient Search Method.Proceedings of the 29th Chinese Control Conference July 29-31, Beijing, China,1282-1286,2010.
[167]衷路生,宋执环.基于正交梯度搜索的动态系统递阶优化辨识.自动化学报,2008,34(6)：711-715.
[168]徐光宪.稀土(第二版.上册)[M].北京：冶金工业出版社,1995.
[169]柯晶.强跟踪状态估计与集群辨识[M].浙江大学博士学位论文,2003.
[170]Palanthandalam-Madapusi, H. J., Lacy, S, Loagg, J. B and Bernstein, D. S. Subspace-based identification for linear and nonlinear systems. In Proceedings of the 2005 American Control Conference, ACC,2005, pp.2320-2334.
[171]Sjoberg J. et.al. Nonlinear black-box modelling in system identification:a unified overview. Automatica,1995,31(2):991-994.
[172]Peng. J. X, Li. K, and Huang. D. S. A Hybrid Forward Algorithm for RBF Neural Network Construction.2006, Vol.17, no.6, pp.1439-1451.
[173]Takagi. T and Sugeno. M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans on Systems, Man & Cybernetics,1985,15,117-132.
[174]Gawthrop. P. J. Continuous-time local state local model networks. Proceedings of IEEE Conference on System, Man & Cybernetics, Vancouver, Canada,1995, pp.852-857.
[175]Leith. D. J and Leithead. W. E. Analytic framework for blended multiple model systems using linear local models. Int. J. Cont, vol.72,1999, no.7, pp.605-619.
[176]Rivals. I and Personnaz. L. Black-box modeling with state-space neural networks. Neural and Adaptive Control Technology (Singapore:World Science),1996, pp.237-264.
[177]Boukhris, A., Mourot. G. and Ragot. J. Non-linear dynamic system identification:A multi-model approach. International Journal of Control,1999,72, pp.591-604.
[178]Favoreel Wouter, Bart De Moor and Peter Van OverscheeSubspace. Identification of Bilinear Systems Subject to White Inputs. IEEE Transactions on Automatic Control,1999, 44(6):1157-1165
[179]Arun,K.S. and Ykung, S. Balanced Approximation of stochastic System, SIAM J. Matrix Analysis and Application,1990, voll1, pp.42-68.
[180]Moonen. M, De Moor. B. and Vandenberghe. V and Vandewalle. J. On and off line identification of linear state-space models. International journal of control,1989, vol.49. no.1, pp.219-232
[181]Devroye, L. A course in Density Estimation [M], Birkhauser, Basel,1987.
[182]Johansen. T. A., Shorten. R. and Murray. R. On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models. IEEE Trans on Fuzzy Systems,2000,8,297-313
[183]Laird, N. M., Dempster, A. P., and Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. Ann. Roy. Stat. Soc,1977, pp.1-38
[184]Li, W., Han, Z. and S. L. Shah. Subspace identification for FDI in systems with non-uniformly sampled multirate data. Automatica,2006, vol.42, no.4, pp.619-627
[185]Silverman, B. Density estimation for statistics and data analysis[M]. chapman and Hall, London,1986.
[186]Stark. J, Broomhead. D. S, Davies. M. E and Huke. J. Takens embedding theorems for forced and stochastic systems. Nonlinear Analysis, Theory, Methods and Applications,1997, 30, pp.5303-5314
[187]Yohai, V. J and Maronna, R. A. Asymptotic behavior of M-estimators for the linear model. Annals of Statistics,1979,7(2):258-268.
[188]丁锋.大系统的递阶辨识.自动化学报,1999,vol.25,no.5,pp：647-654
[189]Zabin,S. M. and Wright, G. A. Nonparametric Density Estimation and Detection in Impulsive Interference Channels-Part Ⅰ:Estimation. IEEE Transactions on Communication,1994,42(234):1684-1697.
[190]邱晓华,陈偕雄.随机自治状态空间模型的正交梯度辨识.浙江大学学报(理学版),2009,36(2)：170-174.
[191]薛定宇.控制系统仿真与计算机辅助设计[M].北京：机械工业出版社,2005.
[192]Huber, P. J. Robust estimation of local parameter. Annals of Mathematical Statistics,1964, 35(1):73-101.
[193]Huber, P. J Robust regression:Asymptotics,Conjectures and Monte Carlo. Annals of Statistics,1973,1(5):799-821.
[194]Huber, P. J. Robust Statistics [M]. New York:Wiley,1981.
[2]徐小平.模块化非线性系统辨识算法研究[D].西安理工大学博士论文,2009.
[3]吴亚锋.子空间辨识方法及其在复杂结构中的应用[D].西北工业大学博士学位论文,2000.
[4]Van Overschee, P and De Moor. B. Subspace identification for linear systems: Throry-Implementation-Application[D]. Leuven Univeisity,1996.
[5]冯培悌.系统辨识[M]。杭州：浙江大学出版社,1999.
[6]吕立华.复杂工业系统基于小波网络与鲁棒估计建模方法研究[D].浙江大学博士学位论文,2001.
[7]Ljung. L. Convergence analysis of parametric identification methods. IEEE Trans. Automat.Contr,1987, vol. AC-23, pp.770-783.
[8]Ljung. L.System Identification:Theory for the User, Second Edition. Englewood Cliffs[M], NJ:Prentice-Hall,1999.
[9]Van Overschee, P and De Moor. B. N4SID:Subspace algorithms for the identification of identification of combined deterministic-stochastic systems. Automatica,1994, vol.30, no.l, pp.75-93.
[10]Qin, S. J., Lin, W. and Ljung, L. A novel subspace identification approach with enforced causal models. Automatica,2005,41(2), pp.2043-2053.
[11]Wang, J. and Qin. S. J. Closed-loop subspace identification using the parity space. Automatica,2006, vol.42, no.2, pp.315-320
[12]Favoreel. W, Moor. B. D and Overschee. P. V. Subspace Identification of Bilinear Systems Subject to White Inputs. IEEE Transactions on Automatic Control,1999, vol.44, no.9, pp. 1157-1165
[13]Van Overschee, P and De Moor. B. A unifying theorem for three subspace system identification algorithms, Automatica.1995, vol.31,no.12, pp.1853-1864
[14]Wang, J. and Qin, S. J. A new subspace identification approach based on principal component analysis. Journal of Process Control,2002,12, pp.841-855
[15]Verdult,V., Bergboer, N. and Verghaegen, M. Maximum likelihood identification of multivariable bilinear state-space systems by projected gradient search. In Proceeding of the 41st IEEE Conference on Decision and Control Las Vegas, Nevada USA, December, 2002.
[16]Ribarits, T., Deistler, M., and Mckelvey, T. An analysis of the parametrization by data driven local coordinates for multivariable linear systems. Automatica,2004, vol.40, no.5, pp.789-803
[17]Ribarits, T., Deistler, M., and Hanzon, B. On new parametrization methods for the estimation of linear state-space models. International Journal of adaptive control and signal processing,2004, vol.18, no.9-10, pp.718-743
[18]Ribarits, T., Deistler, M., and Hanzon, B. An analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems. Automatica,2005, vol.41, no.3, pp.531-544
[19]SoderStrom. T, Wigren. T and Abd-Elrady. E. Periodic signal analysis by maximum likelihood modeling of orbits of nonlinear ODEs. Automatica,2005,41,pp.793-805
[20]Calafior. G and Ghaoui. L. E. Robust maximum likelihood estimation in the linear model. Automatica,2001,37, pp.573-580
[21]Van Overschee, P and De Moor. B. Closed-loop Subspace System Identification. Proceedings of the 36th Conference on Decision & Control San Diego, California,1997
[22]Van Overschee, P and De Moor. B. Closed-loop Subspace System Identification. Technique report ESAT-SISTA/TR 1996-52I, Katholieke Universiteit Leuven,1996.
[23]Van Overschee, P and De Moor. B. Continuous-time frequency domain subspace system identification. Signal Processing,1996,52, pp.179-194
[24]李幼凤,苏宏业,褚健.子空间模型辨识方法综述.化工学报,2006,57(3)：473-479·
[25]贺尚.连续动力学系统参数模型辨识及工业试验[D].中南大学博士学位论文,2002.
[26]王树青.海洋平台结构的系统辨识与振动控制技术研究[D].中国海洋大学博士论文,2003.
[27]Ho, B.L. and Kalman. R.E. Effective construction of linear state-variable models from input-output functions. Regelungstechnik,1965,12, pp.545-548
[28]Astrom. K.J. and Bohlin. T. Numerical identification of linear dynamic systems from normal operating records. In Proceedings of IFAC Symposium on Self-Adaptive Systems, Teddington, UK,1965.
[29]Gevers. M. A personal view of the development of system identification; A 30-year journey through an exciting field. IEEE Control Systems magazine,2006, vol.26, no.6, pp.93-105
[30]Box G.E.P. and Jenkins G.M.. Time Series Analysis, Forecasting and Control. Oakland, CA:Holden-Day,1970.
[31]Ljung. L. Asymptotic variance expressions for identified black-box transfer function models. IEEE Trans. Automat. Contr.,1985, vol. AC-30, pp.834-844.
[32]Ljung. L. System Identification:Theory for the User. Englewood Cliffs[M], NJ: Prentice-Hall,1987.
[33]Ljung. L. Development of system identification[A]. Pr oc.13th World Congress of IFAC[C].SanFrancisco, California, Vol. G:141-146,1996.
[34]Smith, R. S. and Dahleh, M. The Modeling of Uncertainty in Control Systems (Lecture Notes in Control and Information Sciences, vol.192). London,U.K.:Springer-Verlag,1994.
[35]Ljung, L. and Glover, K. Frequency domain versus time domain methods in system identification. Automatica,1981, vol.17, no.1, pp.71-86.
[36]McKelvey, T, Akcay, H, Ljung, L. Subspace based multivariable system identification from frequency response data. IEEE Trans. On Automatic Control,1996,41(7):960-979.
[37]Pintelon, R. Frequency domain subspace system identification using non-parametric noise models. Automatica,2002,38, pp.1295-1311.
[38]Yang, Z. J.,& Sanada, S. Frequency domain subspace identification with the aid of the w-operator. Electrical Engineering in Japan,2000,132(1),46-56.
[39]Forssell, U. and Ljung, L. Closed-loop identification revisited. Automatica,1999, vol.35, pp.1215-1241.
[40]Van den Hol. P. M. J and Schrama. R. J. P. Identificaton and Control-closed loop issures. Automatica,1995, vol.31, no.12, pp.1751-1770
[41]Chiuso, A. and Picci, G. Consistency analysis of some closed-loop subspace identification methods. Automatica,2005,41, pp.377-391.
[42]Ljung. L and McKelvey, T. Subspace identification from closed loop data. Signal processing, 1996,52,pp.209-215.
[43]莫建林,张卫东,许晓鸣.鲁棒辨识研究的现状.控制与决策,2002,17(3)：257-263.
[44]Ninness, B., Hjalmarsson, H., and Gustafsson, F. On the fundamental role of orthonor-mal bases in system identification. IEEE Trans.Automat. Contr.,1999, vol.44, no.7, pp. 1384-1407.
[45]Chou, C.T. and Verhaegen, M. Subspace algorithms for the identification of multivariable dynamic errors-in-variable mosels. Automatica,1997, vol.33, no.10, pp.1857-1869
[46]王行愚.系统辨识的若干新动向.控制理论与应用,1992,9(3)：319-321.
[47]吴旭光.不确定性系统的鲁捧辨识及其发展.控制与决策(增刊)1996,：113-118.
[48]冯旭,孙优贤.鲁棒辨识问题评述.控制理论与应用,1993,10(6)：609-616.
[49]Berger,J. Q., and Wolpert. R. The likelihood principle. Hayward, CA:Institute of Mathematical Statistcs,1988.
[50]Wang.X and Poor, H.V. Robust Multiuser Detector in Non-Gaussian Channels. IEEE Transactions on Signal Processing,1999,47(2):289-305
[51]Calafiore. G, and Ghaoui. L. Robust maximum likelihood estimation in the linear model. Automatica,2001,37, pp.573-580.
[52]Richard J K, Sadler B M. Maximum-likelihood array processing in non-gaussian noise with gaussian mixtures. IEEE Trans. Signal Processsing.2000, vol.48, no.12, pp.3520-3535.
[53]Gustafsson F and Hjalmarsson H. Twenty-one estimators for model selection. Automatica, 1995, vol.33, no.10, pp.1377-1392.
[54]王海清.工业过程监测：基于小波和统计学的方法[D].浙江大学博士学位论文,2000.
[55]Zoubin, A.M. and Brcich, R. F. Multiuser Detection in Heavy Tailed Noise. Digital Signal Processing,2002,12(2):262-273
[56]Tsai C, Chen J J. Kernel estimation for adjusted p-values in multiple testing. Comp Stat & Data Ana,2007,51,pp.3885-3897
[57]张炤,张素,章琛曦,陈亚珠.基于支持向量机的概率密度估计方法.系统仿真学报,2005,17(10),pp.2355-2357.
[58]杨宜东,孙志挥,张净.基于核密度估计的分布数据流离群点检测.计算机研究与进展,2005,42(9),pp.1498-1504.
[59]Bhatia V, Mulgrew B. Non-parametric likelihood based channel estimator for Gaussian mixture noise. Signal Processing,2007,4(6), pp.1-18.
[60]Wu X, Perloff J M. GMM estimation of a maximum entropy distribution with interval data. Journal of Econometrics,2007,138, pp.532-546.
[61]Mckelvey, T. and Helmersson, A. System identification using an over-parametrized model class-Improving the optimization algorithm. Proceedings of the 36th Conference on Decision & Control San Diego, California USA,1997.
[62]Mckelvey, T., Helmersson, A., and Ribarits, T. Data driven local coordinates for multivariable linear systems and their application to system identification. Automatica,2004, vol.40, no.9, pp.1629-1635.
[63]Gibson. S and Wills. A and Ninness. B. Maximum-likelihood parameter estimation of bilinear systems. IEEE Transactions on Automatic control,2005, vol.50, no.10, pp.1581-1595
[64]Verdult. V, Ljung. L and Verhaegen. M. Identification of composite local linear state-space models using a projected gradient search. International Journal of Control,2002, vol.75, no.16/17,pp.1385-1398
[65]Verdult. V, Lovera. M and Verhaegen. M. Identification of linear parameter-varying state-space models with application to helicopter rotor dynamics. International Journal of Control,2004, vol.77, no.13, pp.1149-1159
[66]Bergboer, N. H., Verdult, V. and Verhaegen. M. H. G.. An efficient implemention of maximum likelihood identification of LTI state-space models by local gradient search, In Proceeding of the 41st IEEE Conference on Decision and Control Las Vegas, Nevada USA, December,2002.
[67]Verdult. V, Verhaegen. M, Chou. C.T. and Lovera. M. Efficient and systematic Identification of MIMO bilinear state space models. Proceedings of the 37th IEEE Conference on Decision & Control Tampa, Florida USA,1998, pp.1260-1265
[68]Broersen P M, Waele S et al. Autoregressive spectral analysis when observations are missing. Automatica,2004,40, pp.1495-1504.
[69]Sinopoli B, Schenato L et al. Kalman filtering with intermittent observations. IEEE Trans On Autom Contr,2004,49(9), pp.1453-1463.
[70]Chen J M and Chen B S(2000). System parameter estimation with input/output noisy data and missing measurements. IEEE Trans on Signal Processing,2000,48(6), pp.1548-1558.
[71]Isaksson, A. Identification of ARX-models subject to missing data, IEEE Trans. Aut.Contr, 1993, vol.38 no.5, pages 813-819.
[72]Petit J R et al. Climate and atmospheric history of the past 420.000 years form the Vostok ice core, Antarctica. Nature,1999,399,429-436.
[73]谢磊.间歇过程统计性能研究[D].浙江大学博十学位论文,2005.
[74]Broersen P M and Bos R.(2006a). Time-Series Analysis if Data Are Randomly Missing. IEEE Trans On Instru & Measu,2006,55(1), pp.79-84.
[75]Broersen P M. Automatic spectral analysis with missing data. Digital Signal Processing, 2006,16, pp.754-766.
[76]Rosen Y, Porat B. Optimal ARMA parameter estimation based on the sample convarinces for data with missing observations. IEEE Trans. Infor. Theory.1989, Vol.35, no.2, pp.342-348.
[77]Gordon N and Salmond D et al. A novel approach to nonlinear nongaussian Bayesian stae estimation. In proc. IEEE Conf. Radar and Signal Processing,,1993, vol140, pp.107-113.
[78]周东华,席裕庚,张钟俊.一种带多重次优渐消因子的扩展卡尔曼滤波器闭.自动化学报.1991,17(6)：689-695.
[79]Zhou D H, Frank P M. Strong tracking filtering of nonlinear time-varying stochastic systems with coloured noise:application to parameter estimation and empirical robustness analysis. Int. J Control,1996,65(2):295-307.
[80]Hadidi M. and S. Schwartz. Linear recursive state estimators under uncertain observations. IEEE Trans. Autom. Control,1979, vol.24, no.6, pp.944-948.
[81]Nahi N. Optimal recursive estimation with uncertain observation. IEEE Trans. Inf. Theory, 1969, vol. IT-15, no.4, pp.457-462.
[82]Wang Z D, W. D. Daniel et al. Variance-Constrained Filtering for Uncertain Stochastic Systems With Missing Measurements. IEEE Trans. On Autom Contr,2003, vol.48, no.7, pp.1254-1258
[83]Mariton M. Jump linear systems in automatic control. New York:Marcel Dekker[M],1990.
[84]Costa O. Stationary filter for linear minimum mean square error estimator of discrete-time markovian jump systems. IEEE Trans. Automat. Contr.,2002, vol.48, pp.1351-1356.
[85]Smith S. and P. Seiler(2003).Estimation with lossy measurements:Jump estimatorsfor jump systems. IEEE Trans. Autom. Control,2003, vol.48, no.12, pp.2163-2171.
[86]Anderson, B. D. O and Moore, J. B. Optimal Filtering. Englewood Cliffs, NJ, Prentice-Hall[M],1979,.
[87]Savkin A.V.,I. R. Petersen, and S. O. R. Moheimani. Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data," Comput. Elect. Eng.,1999, vol.25, no.1, pp.29-43.
[88]Gao H, Lam J et, al. New approach to mixedH2/H∞ filtering for polytopic discrete-time system. IEEE Trans on Signal Processing,2005, vol.53, no.8 pp.3183-3192.
[89]Gao H, Lam J et, al. Robust energy-to-peak filter design for stochastic time-delay systems. System & Control Letters.2006, Vol.55, no.2, pp.101-111.
[90]Pila A W, Shaked U. et al. H∞ filtering for continuous-time linear systems with delay. IEEE Trans. A-C,1999, vol.44, no.7, pp.1412-1417.
[91]Zhang H, Zhang D et al. An innovation to H∞ prediction with application to systems with delayed measurements. Automatica,2004, vol.40, no.7, pp.1253-1261.
[92]Mcgiffin P B and Murthy D N P. Parameter estimation for auto-regressive systems with missing observations. Int. J. Sys Sci.1980, vol.11, no.9, pp.1021-1034.
[93]Mcgiffin P B and Murthy D N P. Parameter estimation for auto-regressive systems with missing observations-Part2. Int. J. Sys Sci.1981, vol.12, no.6, pp.657-663.
[94]Wallin R Isaksson A et al. An iterative method for identification of ARX models from incomplete data. Proceedings of the 39th IEEE conf on Decision and Contr. Sydney, Australia,2000.
[95]Dempster A P, Laird N M et al. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser,1977,39, pp.1-38.
[96]Wu C F J. On the convergent properties of the EM algorithm. The Annal of Statistics,1983, Vol.11, no.1, pp.95-103.
[97]Meng X L and Rubin D B. On the global and componentwise rates of convergence of the EM algorithm. Linear algebra and its applications,1994,199, pp.413-425.
[98]Gibson. S and Ninness. B. Robust maximum-likelihood estimation of multivariable dynamic systems. Automatica,2005,41(10), pp.1667-1682.
[99]Shumway. R. H., and D. S. Stoffer. Time series analysis and its applications. New York: Springer-Verlag[M],2000.
[100]Charalambous, C.D, Logothetist, A. and Elliott, R.J. Bank Filters for ML parameter Estimation via the Expectation-Maximization Algorithm:The continuous-Time Case,Proceedings of the 37th IEEE Conference on Decision & Control, Tampa, Florida, USA, 1998.
[101]Charalambous and, C.D. and Logothetis, A. Maximum Likelihood Parameter Estimation from Incomplete Data via the Sensitivity Equations:The continuous-Time Case,IEEE Trans. Aut. Contr.,2000, vol.45 no.5, pp.928-934.
[102]Elliott, R.J. and Krishnamurthy, V. Exact finite-dimensional filters for maximum likelihood parameter estimation of continuous-time linear Gaussian systems. SIAM J. Control. Optim,1997, vol.35, No.6, pp.1908-1923.
[103]Elliott, R.J. and Krishnamurthy, V. New Finite-Dimensional Filters for Parameter Estimation of Discrete-Time Linear Gaussian Models, IEEE Trans. Aut. Contr.,1999, vol. 44no.5, pages 938-951.
[104]Langari, R., Wang, L., and Yen, J., "Radial basis function networks, regression weights, and the expectation-maximization algorithm," IEEE Transaction on systems, man, and cybernetics-part A:systems and humans,1997, vol.27, no.5, pp.613-623.
[105]Ravishanker, N., and Qiou, Z. Monte Carlo EM estimation for multivariate stable distributions. Statistics and Probability Letters,1999, vol.45, pp.335-340
[106]Lee, J. H, Han, J. C and Kim, S. C. Joint carrier frequency synchronization and channel estimation for OFDM systems via the EM algorithm. IEEE Transaction on vehicular technique,2006, vol.55, no.1, pp.167-172,
[107]Favoreel. W, Moor. B. D and Overschee. P. V. Subspace state space system identification for industrial processes. Journal of Process Control,2000,10, pp.149-155.
[108]Mckelvey, T., Helmersson, A., and Ribarits, T. Data driven local coordinates for multivariable linear systems and their application to system identification. Automatica,2004, vol.40, no.9, pp.1629-1635.
[109]Qin, S. An overview of subspace identification. Computer and Chemical Engineering,2006, 30, pp.1502-1513.
[110]Qin, S. J., and Ljung, L. Closed-loop subspace identification with innovation estimation. In Proceedings of the 13th IFAC symposium on system identification(pp.887-892). Rotterdam, Netherlands,2003.
[111]Qin, S. J., and Ljung, L. Parallel QR implementation of subspace identification with parsimonious models. estimation. In Proceedings of the 13th IFAC symposium on system identification(pp.1631-1636). Rotterdam, Netherlands,2003.
[112]Larimore. W. E. System identification, reduced-order filtering and modeling via canonical variate analysis. Proc.1983 American Control Conference, San Francisco, pp.445-451,1983.
[113]Larimore. W. E. Canonical variate analysis in identification, filtering, and adaptive control. Proc.29th IEEE Conference on Decision and Control. Honolulu, pp.596-604,1990.
[114]Larimore. W. E. The ADAPTx software for automated and real-time multivariable system identification. Proc.13th IFAC Symp. System Identification, Rotterdam,2003 pp.1496-1501.
[115]Verhaegen, M. Subspace model identification, Part1:The output-error state-space model identification class of algorithms. Int. J. Control,1992, vol.56, no.5, pp.1187-1210.
[116]Verhaegen, M. Subspace model identification, Part2:Analysis of the elementary output-error state-space model identification algorithm. Int. J. Control,1992, vol.56, no.5, pp.1211-1241.
[117]Verhaegen, M. Subspace model identification, Part3:Analysis of the ordinary output-error state-space model identification algorithm. Int. J. Control,1993, vol.58, no.3, pp.555-586.
[118]Verhaegen, M. Application of a subspace model identification technique to identify LTI systems operating in closed-loop. Automatica,1993, vol.29, no.4, pp.1027-1040.
[119]Verhaegen, M. Identification of the deterministic part of MIMO state space models given in innovations form from input-output data. Automatica,1995, vol.30, no.1, pp.61-74.
[120]Verhaegen, M. Identifying MIMO Wiener systems using subspace model identification methods. Signal Processing,1996,52(2):235-258
[121]Viberg, M. Subspace-based methods for the identification of linear time invariant systems. Automatica,1995,31(12):1835-1851
[122]Akaike. H. A new look at the statistical model identification. IEEE Trans. Auto. Cont., 1974,19,716-723.
[123]Gustafsson,T. Subspace identification using instrumental variable techniques. Automatica. 2001,37,pp.2005-2010.
[124]Verdult Vincent, Michel Verhaegen. Kernel methods for subspace identification of multivariable LPV and bilinear systems. Automatica,2005,41(9):1557-1565
[125]Verdult. V, Verhaegen. M. Subspace identification of multivariable linear parameter-varying systems, Automatica,2002, vol.38, no.5, pp.805-814.
[126]McKelvey, T. Frequency domain system identification with instrumental variable based subspace algorithm//Proceedings of the 1997 ASME Design Engineering Technical Conferences. Sacramento, CA, September 14-17 (pp.1-8),1997.
[127]Ohsumi, A., Kameyama, K. and Yamaguchi K-I. Subspace identification for continuous-time stochastic systems via distribution based approach. Automatica,2002,38, pp.63-79.
[128]刘浩.基于子空间方法的热工系统闭环辨识的研究[M].华北电力大学(河北),2008.
[129]石春(2008)DVD聚焦伺服系统研究[D].中国科学技术大学博十论文,2008.
[130]Chiuso, A. and Picci, G. Asymptotic variance of subspace methods by data orthogonalization and model decoupling:a comparative analysis. Automatica,2004, no.40, pp.1705-1717.
[131]Chiuso, A. and Picci, G.. Numerical conditioning and asymptotic variance of subspace estimates. Automatica,2004, no.40, pp.677-683.
[132]Chiuso, A. and Picci, G..Asymptotic variance of closed-loop subspace identification mthods. IEEE Trans on Auto Contr,2006, vol.51, no.8, pp.1299-1314.
[133]Dahlen,A., Lindquist, A., and Mari, J. Experiment evidence showing that stochastic subspace identification methods may fail Systems & Control Letters,1998, vol.34, no.5, pp.303-312.
[134]Maciejowski, J. M.. Guaranteed stability with subspace methods. Syst.& Control Letters, 1995, vol.26, pp.153-156.
[135]Van Gestel, T., Suykens, A. K. and Van Dooren, P. and De Moor, B. Identification of stable model in subspace identification by using regulation. IEEE Trans on Auto. Contr,2001, vol.46, no.9, pp.1416-1420.
[136]Chui, N. L. C and Maciejowski, J. M. Realization of stable models with subspace methods. Automatica,1996,32(11):1587-1595.
[137]Goethals, I., Van Gestel, T., Suykens, J, Van Dooren, P and De Moor, B. Identification of positive real models in subspace identification by using regulation. IEEE Trans on Autom Contr,2003, vol.48, no.10, pp.1843-1847.
[138]Goethals I, Pekckmans K et al. Subspace identification of Hammerstein systems using least squares support vector. IEEE Trans on Autom Contr,2005,50(10):1509-1519.
[139]Lacy, S. L and Bernstein, D. S.Subspace identification with guaranteed stability using constrained optimization. IEEE TFans. On Automatic Control,2003,48(7):1259-1263.
[140]Deistler, M., Peternell, K. and Scherrer, W. Consistency and relative efficiency of subspace method. Automatica,1995,31(12):1865-1875.
[141]Jansson, M. and Wahlberg, B. On consistency of subspace methods for system identification. Automatica,1998,34(12):1507-1519
[142]Jansson, M.. Subspace identification and ARX modeling. In Proceedings of the 13th IFAC symposium on system identification(pp.1625-1630) Rotterdam, Netherlands,2003.
[143]Huang, B, Ding, S. X and Qin, S. J. Closed-loop subspace identification:an orthogonal projection approach. Journal of process control,2005,15, pp.53-66.
[144]Bauer, D. and Jansson, M. Analysis of the asymptotic properties of the MOESP type of subspace algorithms. Automatica,2000,36:497-509
[145]Bauer, D. and Ljung, L. Some facts about the choice of the weighting matrices in Larimore type of subspacealgorithms. Automatica,2002,38:763-773.
[146]Lester, S. H. and Sjoberg, J. Efficient training of neural nets for nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithm. IEEE Trans. On Neural Network,2000, vol.48, no.7,pp.1915-1927.
[147]Gorinevsky,D. An approach to parametric nonlinear least square optimization and application to task-level learning control. IEEE Trans. On Automatic Control,1997, vol.42, no.7, pp.912-927.
[148]Vanbleu, K., Ysebaert, G., Cuypers, G. and Moonen, M. Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems. IEEE Trans. On Signal Processing, 2006, vol.54, no.2, pp.483-498.
[149]邓乃扬.无约束最优化计算方法[M].北京：科学出版社,1982.
[150]Dennis, J. E. and Schnabel, R. B. Numerical methods for unconstrained optimization and nonlinear equations[M]. Englewood Cliffs, NJ:Prentice-Hall,1983.
[151]Kailath. T., Sayed.A., and Hassabi. B. Linear Estimation[M]. Upper Saddle River, NJ: Prentice-Hall,2000.
[152]McKelvey, T.. identification State-space models from time and frequency data. Ph. D. thesis, Department of Electrical Engineering, Link"oping University, Link"oping, Sweden,1995. ISBN 91-7871-531-8. Available from Internet:http://www.control.isy.liu.se/(Retrieved June 27,2001).
[153]Ding, F. and Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Transactions on Automatic Control,2005, vol.50, no.3, pp397-402
[154]Wills A and Brett Ninness. On Gradient-Based Search for Multivariable System Estimates. IEEE Transactions on Automatic Control,2008,53(1):298-306
[155]A. Wills, B. Ninness, S. Gibson. Maximum Likelihood Estimation of State Space Models from Frequency Domain Data. IEEE Transactions on Automatic Control,2009,54(1): 19-33.
[156]粟塔山.最优化计算原理与算法程序设计[M].长沙：国防科技大学出版社,2001.
[157]郑大钟.线性系统理论[M].北京：清华大学出版社,1990.
[158]Lu Guoping, Feng Gang, and Jiang Zhong-Ping. Saturated Feedback Stabilization of Discrete-Time Descriptor Bilinear Systems. IEEE Transactions on Automatic Control,2007, 52(9):1700-1704
[159]朱怀念,张成科,武赛,宾宁.离散双线性系统鞍点均衡的迭代算法.广东工业大学学报,2010,27(1)：8-15
[160]余勇,万德钧.一类双线性时间序列模型基于累积量的辨识.东南大学学报,1999,29(3)：139-143
[161]Vasilis Tsoulkas, Panos Koukoulas, and Nicholas Kalouptsidis. Identification of Input-Output Bilinear Systems Using Cumulants. IEEE Transactions on Signal Processing, 2001,49(11):2753-2761
[162]黄正良,万百五,韩崇昭.双线性系统稳态模型估计及其强一致性分析.自动化学报,1995,21(5)：562-569
[163]Nicholas Kalouptsidis,Panos Koukoulas,and V. John Mathews. Blind Identification of Bilinear Systems. IEEE Transactions on Signal Processing,2003,51(2):484-499
[164]Wingerden Jan-Willem van, Michel Verhaegen(2009)ace. Identification of Bilinear and LPV systems for open- and closed-loop data. Automatica,2009,45(2):372-381
[165]Zou Qiyue, Zhiping Lin,and Raimund J. Ober. The Cramer-Rao Lower Bound for Bilinear Systems. IEEE Transactions on Signal Processing,2006,54(5):1666-1680
[166]ZHONG Lusheng, FAN Xiaoping, YANG Hui. System Identification of Bilinear State-space Models by Modified Gradient Search Method.Proceedings of the 29th Chinese Control Conference July 29-31, Beijing, China,1282-1286,2010.
[167]衷路生,宋执环.基于正交梯度搜索的动态系统递阶优化辨识.自动化学报,2008,34(6)：711-715.
[168]徐光宪.稀土(第二版.上册)[M].北京：冶金工业出版社,1995.
[169]柯晶.强跟踪状态估计与集群辨识[M].浙江大学博士学位论文,2003.
[170]Palanthandalam-Madapusi, H. J., Lacy, S, Loagg, J. B and Bernstein, D. S. Subspace-based identification for linear and nonlinear systems. In Proceedings of the 2005 American Control Conference, ACC,2005, pp.2320-2334.
[171]Sjoberg J. et.al. Nonlinear black-box modelling in system identification:a unified overview. Automatica,1995,31(2):991-994.
[172]Peng. J. X, Li. K, and Huang. D. S. A Hybrid Forward Algorithm for RBF Neural Network Construction.2006, Vol.17, no.6, pp.1439-1451.
[173]Takagi. T and Sugeno. M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans on Systems, Man & Cybernetics,1985,15,117-132.
[174]Gawthrop. P. J. Continuous-time local state local model networks. Proceedings of IEEE Conference on System, Man & Cybernetics, Vancouver, Canada,1995, pp.852-857.
[175]Leith. D. J and Leithead. W. E. Analytic framework for blended multiple model systems using linear local models. Int. J. Cont, vol.72,1999, no.7, pp.605-619.
[176]Rivals. I and Personnaz. L. Black-box modeling with state-space neural networks. Neural and Adaptive Control Technology (Singapore:World Science),1996, pp.237-264.
[177]Boukhris, A., Mourot. G. and Ragot. J. Non-linear dynamic system identification:A multi-model approach. International Journal of Control,1999,72, pp.591-604.
[178]Favoreel Wouter, Bart De Moor and Peter Van OverscheeSubspace. Identification of Bilinear Systems Subject to White Inputs. IEEE Transactions on Automatic Control,1999, 44(6):1157-1165
[179]Arun,K.S. and Ykung, S. Balanced Approximation of stochastic System, SIAM J. Matrix Analysis and Application,1990, voll1, pp.42-68.
[180]Moonen. M, De Moor. B. and Vandenberghe. V and Vandewalle. J. On and off line identification of linear state-space models. International journal of control,1989, vol.49. no.1, pp.219-232
[181]Devroye, L. A course in Density Estimation [M], Birkhauser, Basel,1987.
[182]Johansen. T. A., Shorten. R. and Murray. R. On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models. IEEE Trans on Fuzzy Systems,2000,8,297-313
[183]Laird, N. M., Dempster, A. P., and Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. Ann. Roy. Stat. Soc,1977, pp.1-38
[184]Li, W., Han, Z. and S. L. Shah. Subspace identification for FDI in systems with non-uniformly sampled multirate data. Automatica,2006, vol.42, no.4, pp.619-627
[185]Silverman, B. Density estimation for statistics and data analysis[M]. chapman and Hall, London,1986.
[186]Stark. J, Broomhead. D. S, Davies. M. E and Huke. J. Takens embedding theorems for forced and stochastic systems. Nonlinear Analysis, Theory, Methods and Applications,1997, 30, pp.5303-5314
[187]Yohai, V. J and Maronna, R. A. Asymptotic behavior of M-estimators for the linear model. Annals of Statistics,1979,7(2):258-268.
[188]丁锋.大系统的递阶辨识.自动化学报,1999,vol.25,no.5,pp：647-654
[189]Zabin,S. M. and Wright, G. A. Nonparametric Density Estimation and Detection in Impulsive Interference Channels-Part Ⅰ:Estimation. IEEE Transactions on Communication,1994,42(234):1684-1697.
[190]邱晓华,陈偕雄.随机自治状态空间模型的正交梯度辨识.浙江大学学报(理学版),2009,36(2)：170-174.
[191]薛定宇.控制系统仿真与计算机辅助设计[M].北京：机械工业出版社,2005.
[192]Huber, P. J. Robust estimation of local parameter. Annals of Mathematical Statistics,1964, 35(1):73-101.
[193]Huber, P. J Robust regression:Asymptotics,Conjectures and Monte Carlo. Annals of Statistics,1973,1(5):799-821.
[194]Huber, P. J. Robust Statistics [M]. New York:Wiley,1981.