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实现ARMA过程AR参数估计的一种有效手段是解由修正Yule-Walker等式组成的超定方程组。本文导出了超定Yule-Walker方程组的一种递归快速求解法,它具有以下优点:1)把直接求广义逆法所需的P~2N+O(P~3)量级的计算量减小到PN量级,避免了矩阵求逆问题,这里P和N分别是模型阶数和采样数据点数;2)通过对递归过程中拟合残差的观察,用合适的中间参数估计结果作为最终所求结果,从而提高参数估计的精度。文中用数值结果说明了所给方法的实际运用。
An effective means of AR parameter estimation for ARMA process is to solve overdetermined system of equations consisting of a modified Yule-Walker equation. In this paper, we derive a recursive fast solution method for overdetermined Yule-Walker equations, which has the following advantages: 1) Calculate the P ~ 2N + O (P ~ 3) As small as the order of PN, to avoid the matrix inversion problem, where P and N are the model order and the number of sampled data points respectively. 2) By observing the residual of fitting in the recursion process, using the appropriate intermediate parameter estimation results as the final The result that is sought, so as to improve the precision of parameter estimation. The numerical results illustrate the practical application of the proposed method.