Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal...Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal elements of upper triangular matrix, so thecolumn by column procedure can be used to develop a recursive algorithm for AR modeling andspectral estimation. In most cases, the present algorithm yields the same results as the covariancemethod or modified covariance method does. But in some special cases where the numerical ill-conditioned problems are so serious that the covariance method and modified covariance methodfail to estimate AR spectrum, the presented algorithm still tends to keep good performance. Thetypical computational results are presented finally.展开更多
Housecholder变换用于上三角化是基于线性预测误差方程的数据阵。可以证明,由上三角阵的主对角元素便可得到各阶AR模型的残差平方和。因此用逐列处理的方法可以构成 AR 模型化与谱估计的递推算法。在大多数情况下,本文的算法不仅给出与...Housecholder变换用于上三角化是基于线性预测误差方程的数据阵。可以证明,由上三角阵的主对角元素便可得到各阶AR模型的残差平方和。因此用逐列处理的方法可以构成 AR 模型化与谱估计的递推算法。在大多数情况下,本文的算法不仅给出与协方差算法或修正协方差算法相同的计算结果;而且当计算中存在严重的数值病态问题时,协方差法和修正协方差法无法获得好的AR谱估计,而本文的算法则仍然可以获得好的估计。文中给出了典型的计算例子。展开更多
文摘Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal elements of upper triangular matrix, so thecolumn by column procedure can be used to develop a recursive algorithm for AR modeling andspectral estimation. In most cases, the present algorithm yields the same results as the covariancemethod or modified covariance method does. But in some special cases where the numerical ill-conditioned problems are so serious that the covariance method and modified covariance methodfail to estimate AR spectrum, the presented algorithm still tends to keep good performance. Thetypical computational results are presented finally.
文摘Housecholder变换用于上三角化是基于线性预测误差方程的数据阵。可以证明,由上三角阵的主对角元素便可得到各阶AR模型的残差平方和。因此用逐列处理的方法可以构成 AR 模型化与谱估计的递推算法。在大多数情况下,本文的算法不仅给出与协方差算法或修正协方差算法相同的计算结果;而且当计算中存在严重的数值病态问题时,协方差法和修正协方差法无法获得好的AR谱估计,而本文的算法则仍然可以获得好的估计。文中给出了典型的计算例子。
