Input Recovery from Noisy Output Data, Using Regularized Inversion of the Laplace Transform
Input Recovery from Noisy Output Data, Using Regularized Inversion of the Laplace Transform
复制标题
使用拉普拉斯变换的正则化反转从噪声输出数据中恢复输入
DOI：
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发表时间：
1998
影响因子：
2.5
通讯作者：
F. Ruymgaart
中科院分区：
文献类型：
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作者：
A. K. Dey;C. Martin;F. Ruymgaart
在动态系统中，输入是从系统输出的有限多次测量中恢复的，这些测量因随机误差而变得模糊。像往常一样，在应用拉普拉斯变换后，描述系统的微分方程被简化为与多项式相乘。看来输出的拉普拉斯变换存在一个自然的、无偏的估计量，可以通过与多项式相乘并随后应用拉普拉斯变换的正则化逆来获得输入的估计量。此外，可以平衡这种逆效应的影响，使不适定性仍然局限于其实际来源：微分。积分均方误差的收敛速度是数据数量的正幂。微分方程的阶数会对速率产生不利影响，另一方面，速率会像往常一样随着输入的平滑度而增加。
In a dynamical system the input is to be recovered from finitely many measurements, blurred by random error, of the output of the system. As usual, the differential equation describing the system is reduced to multiplication with a polynomial after applying the Laplace transform. It appears that there exists a natural, unbiased, estimator for the Laplace transform of the output, from which an estimator of the input can be obtained by multiplication with the polynomial and subsequent application of a regularized inverse of the Laplace transform. It is possible, moreover, to balance the effect of this inverse so that ill-posedness remains restricted to its actual source: differentiation. The rate of convergence of the integrated mean-square error is a positive power of the number of data. The order of the differential equation has an adverse effect on the rate which, on the other hand, increases with the smoothness of the input as usual.