Abstract:  In actual industrial applications, many measurement problems are essentially the corresponding sine signal amplitude and phase characteristics' measurement. For the sine signal with DC offset, measurement noise and frequency change, an amplitude and phase's measurement method based on iterative learning is proposed. Firstly, the parameters which need to be measured should be estimated one step. The iterative learning law should be set as the derivatives of the difference's square of measurement output value and estimation output value, and the parameters. The estimation algorithm is established when the derivatives are weighted properly. Simulation results show that when the measurement error's variance is at the level of the tenth of the maximum measured value, each measured parameter's estimated error can be up to one percent or smaller. Moreover, with a decrease of noise level, each parameter's estimated accuracy increase rapidly. This method can achieve high-precision measurement of sine signal's amplitude, phase, frequency and DC offset, and it also has great prospect for interferometer's electronic subdivision and motor's displacement measurement based on magnetic field information.

Key words: Sine signal, iterative learning, amplitude and phase property

摘要： 在实际工业应用中，许多测量问题实质上是对相应正弦信号幅相特性的测量。文章针对存在直流偏移及测量噪声，且频率存在变化的正弦信号，提出一种基于迭代学习思想的幅相特性测量方法。对各待测参数进行一步估计之后，以测量输出值与估计输出值之差平方对各参数导数作为其迭代学习律，通过对其进行适当加权，建立起参数估计算法。仿真结果表明，在测量误差方差为最大测量值十分之一水平下，各待测参数测量误差可达百分之一甚至更小，且随着噪声水平的下降，各参数估计精度迅速提高。该方法可实现正弦信号幅值、相位、频率以及直流偏移的高精度测量，在激光干涉仪电子细分、基于磁场信息的电机位移测量等方面有巨大应用前景。

关键词: 正弦信号, 迭代学习, 幅相特性