多尺度随机过程的线性预测方法

在反射系数未知的情况下，给出了基于已知观察数据的各向同性多尺度随机过程的线性预测公式，并据此提出了偏相关向量函数的概念，与反射系数相比，偏相关向量函数可由观察数据确定，它反映了前、后向预测误差分量之间的相关程度，为了进一步研究该函数的性质，分析了偏相关向量函数与反射系数的关系，该关系表明，偏相关向量函数可用于自回归过程的阶数确定，数值实验结果验证了所给方法的有效性及良好 的线性预测精度。

Linear Prediction for Multiscale Stochastic Processes

Without the reflection coefficients, the linear prediction formula based on the observed data for an isotropic process is given. By using the properties of linear prediction coefficients, the definition of partial correlation vector function is introduced. In contrast with the reflection coefficients, partial correlation vector functions correspond to the correlation of components of forward prediction error with those of backward prediction error, and are determined by the observed data. To study the properties of this function, the relation between it and the reflection coefficients is discussed. Our theoretical analysis indicates that this function can be used to determine the order p of autoregressive process. Finally, the efficiency of our method and the error of linear prediction are demonstrated with experimental results.