Differentiating noisy, discrete measurements in order to fit an ordinary differential equation can be unreasonably effective. Assuming square-integrable noise and minimal flow regularity, we construct and analyze a finite-difference differentiation filter and a Tikhonov-regularized least squares estimator for the continuous-time parameter-linear system. Combining these contributions in series, we obtain a finite-sample bound on mean absolute error of estimation. As a by-product, we offer a novel analysis of stochastically perturbed Moore-Penrose pseudoinverses.

翻译：对含噪离散测量值进行微分以拟合常微分方程可能出奇有效。在假设噪声平方可积且流形具有极小正则性的前提下，我们构造并分析了一种有限差分微分滤波器以及用于连续时间参数线性系统的吉洪诺夫正则化最小二乘估计器。将这两项贡献串联结合后，我们得到了估计均值绝对误差的有限样本界。作为副产品，我们对随机扰动下的穆尔-彭罗斯伪逆提出了一种新分析。