While the estimation problem of the unknown frequencies for a continuous-time multi-tone sinusoidal signal was thoroughly solved in the early 2000s, the discrete-time version of this problem was studied only recently via a nonlinear control approach. In this paper, we present a simpler approach to the estimation problem of the unknown frequencies for a discrete-time multi-tone sinusoidal signal. Our approach only involves the design of two linear filters together with a linear adaptation law. As a result, the implementation of our two linear filters is easier than that of nonlinear ones. Moreover, the linear form of our filters lends itself to the establishment of the exponential convergence of the estimated frequencies to their actual values. In addition, we obtain an interesting exponential stability result for a class of discrete-time linear time-varying systems that can be viewed as a discrete-time counterpart of a well-known stability result arising from continuous-time adaptive identification.

虽然在2000年代初彻底解决了连续时间多音正弦信号未知频率的估计问题，但直到最近才通过非线性控制方法研究了该问题的离散时间版本。在本文中，我们为离散时间多音正弦信号的未知频率估计问题提出了一种更简单的方法。我们的方法仅涉及两个线性滤波器的设计以及线性适应定律。结果，我们的两个线性滤波器比非线性滤波器更容易实现。此外，滤波器的线性形式有助于建立估计频率与其实际值的指数收敛。此外，对于一类离散时间线性时变系统，我们获得了有趣的指数稳定性结果，可以将其视为由连续时间自适应识别引起的众所周知的稳定性结果的离散时间对应物。