The paper presents a method to estimate frequencies of a multi-sinusoidal signal in finite time. Expressing the signal via delayed measurements, we transform this nonlinear problem into a linear regression, where unknown parameters depend on signal frequencies. Dynamic Regressor Extension and Mixing method is used to replace $n$th order regression model with scalar regression. After, the parameters are estimated separately with the standard gradient descent method. On the last step, the finite time frequency estimate is found algebraically. In contrast to the standard gradient descent method, there is not a trade-off between estimation duration and sensitivity to measurement noise.

本文提出了一种在有限时间内估计多正弦信号频率的方法。通过延迟测量来表达信号，我们将此非线性问题转换为线性回归，其中未知参数取决于信号频率。使用动态回归扩展和混合方法来替换$ñ$标量回归的三阶回归模型。之后，使用标准梯度下降法分别估计参数。在最后一步，以代数方式找到有限的时间频率估计。与标准梯度下降方法相反，在估计持续时间和对测量噪声的敏感度之间没有权衡取舍。