正弦参数拟合误差量子化阶梯分布机理分析  

Analysis of the Quantized Step Distribution Mechanism of Sine Parameter Fitting Error

作　　者：梁志国[1] 梁家奕 LIANG Zhiguo;LIANG Jiayi(National Key Laboratory of Science and Technology on Metrology and Calibration,Changcheng Institute of Metrology and Measurement,Beijing 100095,China;School of Information and Software Engineering,University of Electronic Science and Technology of China,Chengdu,Sichuan 611700,China)

机构地区：[1]北京长城计量测试技术研究所计量与校准技术国家重点实验室,北京100095 [2]电子科技大学信息与软件工程学院,四川成都611700

出　　处：《计量学报》2024年第10期1555-1561,共7页Acta Metrologica Sinica

基　　金：国家重点研发计划(2017YFF0206202)。

摘　　要：量化误差对正弦曲线拟合参数误差界的影响,伴随着采样序列长度的增加呈等间隔阶梯状跳变下降规律。该规律与此前认为的拟合误差随序列长度增加呈单调下降的经验截然不同。为此进行了深入的机理分析和讨论,给出了该现象的数理解释,包括拟合参数误差界的阶梯状跳变机理,误差阶梯缓慢增大机理,第1个误差阶梯的马鞍形状机理,幅度拟合误差无跳变原因等。对于理解、掌握和充分利用这一规律获得更高的拟合参数准确度,具有较大的意义和价值。The impact of quantization error on the error bound of sine wave curve fitting parameters follows a step like jump with equal intervals as the length of the sampling sequence increases,which is completely different from the previous experience of monotonic decrease in fitting error with increasing sequence length.In response to this phenomenon,this article conducted in-depth mechanism analysis and discussion,and provided a mathematical explanation for the phenomenon,including the step like jump mechanism of fitting parameter error bounds,the slow increase mechanism of error steps,the saddle shape mechanism of the first error step,and the reason for no jump in amplitude fitting error.It is of great significance and value to understand,master,and fully utilize this law to obtain higher accuracy of fitting parameters.

关 键 词：无线电计量 量化误差 正弦波 曲线拟合 误差界 评价 

分 类 号：TB973[一般工业技术—计量学]