由随机过程的一次实现估计输入数据的方差

Estimating the Variance of the Initial Input Data of Inverse Problem in One Realization of a Stochastic Process

目的 为了满足正则化方法求解反问题之需要 ,提出了一种由随机过程的一次物理实现估计原始数据方差的新方法 .方法 通过假设一个随机误差的分布 ,然后通过数值仿真得到了方差估算的公式 .结果与结论 用不同的随机测量过程对估算方法进行了验证 .结果表明 ,由该方法及公式估算得到的方差具有较高的精度 。

Aim\ A method to estimate the variance of the initial input data of the inverse problem in one realization of a stochastic process is proposed. Methods\ A formula is obtained on the basis of an assumption to the random error distribution and numerical simulation. Results and Conclusion\ Some examples for different stochastic process models are used to verify the effectiveness of the estimating method. It is demonstrated that the accuracy of the estimated variance of the initial data is satisfactory and the formula represents the inherent statistical characteristics of the random error with high accuracy.