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中文摘要：
针对多元非线性时间序列，结合回声状态网络和Kalman滤波提出一种新的在线自适应预报方法．该方法将Kalman滤波应用于回声状态网络储备池高维状态空间中，直接对网络的输出权值进行在线更新，省去了传统递归网络扩展Kalman滤波中Jacobian矩阵的计算，在提高预测精度的同时令算法的适用范围得到扩展．在回声状态网络稳定时给出所提算法的收敛性证明．仿真实例验证了所提方法的有效性．
英文摘要：
A novel online adaptive prediction method is pro- posed for multivariable nonlinear time series, which is based on echo state network （ESN） and Kalman filtering （KF） algorithm. The KF is adopted in the high-dimension ＂reservoir＂ state space to directly update the output weights of the ESN online. It is implemented without the computation of Jacobian matrices which is in the expanded KF （EKF） algorithm of traditional recurrent neural network （RNN）, so as to improve the prediction accuracy and extend the applications. The convergence of the proposed method is proved when the ESN is steady. Simulation examples demonstrate the validity of the proposed method.
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