基于AP的Volterra级数自适应多重回归及其多步预测应用

Multi-step predicting model based on multi-recursive AP algorithm of Volterra series

为解决时间序列多步预测的高效率、高精度问题,提出一种基于Volterra级数的多重回归仿射投影自适应算法。应用虚假最临近点法算法选择最优嵌入维数,优化模型初始参数。以系统Volterra核向量增量的模与某约束总和为损失函数,按照最陡下降原理导出各阶Volterra核更新公式,再利用矩阵求逆引理递推求取各阶Volterra子系统自相关逆矩阵导出算法,从而实现了对多输入多输出数据样本的建模,采用该模型对Henon映射产生的时间序列进行多步预测实验,结果表明可以对该时间序列进行准确建模和预测,证明了所提模型的有效性。

To improve the efficiency and accuracy of multi-step predicting of the time series,a Volterra series model based on the multi-recursive affine projection （AP）algorithm is proposed.The optimal embedding dimension is identified by false nearest neighbors to optimize the initial parameters of the model.Taking the minimum norm of the Volterra kernel vector increments and certain constraints as the overall cost function,by the steepest descent principle,the adaptive updating formula of the Volterra kernel vector of each order is derived.And the matrix inverse lemma is applied to recursively estimate the inverse of the autocorrelation matrix of Volterra subsystems of each order,thus the algorithm is derived.To illustrate the performance of the method,simulations on Henon time series prediction are performed.The results show that the Henon time series are accurately predicted,which demonstrates the effectiveness of the proposed method.