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| Analysis of the Quantized Step Distribution Mechanism ofSine Parameter Fitting Error |
| LIANG Zhiguo1,LIANG Jiayi2 |
1. National Key Laboratory of Science and Technology on Metrology and Calibration, Changcheng Institute of Metrology and Measurement, Beijing 100095, China
2. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611700, China |
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Abstract 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.
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Received: 17 January 2024
Published: 30 September 2024
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|
|
| ［2］ |
IEC 62008-2005 Performance characteristics and calibration methods for digital data acquisition systems and relevant software ［S］. 2005.
|
| ［3］ |
数字存储示波器校准规范: JJF 1057—1998［S］. 北京: 中国计量出版社,1998.
|
| ［5］ |
赵明雲, 楼嘉宇, 马 琪. 基于正弦曲线拟合的快速限流预测算法 ［J］. 太赫兹科学与电子信息技术, 2016, 14(1): 93-95.
|
| ［9］ |
王选择, 洪潭, 胡晓晖, 等. 基于移动正弦拟合的快速解包络算法 ［J］. 传感器与微系统, 2019, 38(12): 112-115, 119.
|
| ［10］ |
何丕雁, 白泰礼．一种改进的正弦拟合时基失真估计算法［J］．系统工程与电子技术, 2003, 25(3): 359-361.
|
| ［14］ |
徐志钮, 律方成, 汪佛池, 等. 用加Hanning窗插值高阶正弦拟合法测介损角 ［J］. 高电压技术, 2007, 33, (4): 50-53.
|
| ［15］ |
梁志国. 一种基于残周期正弦波拟合的相位差测量方法 ［J］. 计量学报, 2016, 37(4): 419-422.
|
| ［19］ |
汪国娇. 基于正弦拟合的ADC快速测试算法的设计与实现［D］. 南京: 东南大学, 2015.
|
|
ZHAO M Y, LOU J Y, MA Q. A quick current-limiting predicted algorithm based on sinusoidal curve fitting ［J］. Journal of Terahertz Science and Electronic Information Technology, 2016,14(1): 93-95.
|
|
LI Y B, ZENG X B, SHEN C W. Fitting algorithm of sine wave based on interpolation of parabola ［J］. Computer Engineering and Design, 2009, 30(11): 2793- 2795.
|
|
JIN J F, WANG Y, LIU Z J. The application of sine fitting method in neutral point non directly grounded systems ［J］. Water Resources and Power, 2007, 25(4): 148-151.
|
|
LIU Y, WANG C W, WANG L, et al. Method of Partial Period Sine Wave Fit in Fast North-seeking Based on Fiber Optic Gyroscope ［J］. Piezoelectrics & Acoustooptics, 2015, 37(6): 1020-1024.
|
|
HE P Y, BAI T L. An Improved Sine-Fitting Estimation Method for Time-Base Distortion ［J］. Systems Engineering and Electronics, 2003, 25(3): 359-361.
|
| ［21］ |
毛林燕, 沈晓峰．改进的正弦波拟合法评价数据采集系统通道间延时［J］．现代电子技术, 2007, 30(15): 125-127.
|
| ［25］ |
梁志国, 朱济杰, 孟晓风. 四参数正弦曲线拟合的一种收敛算法 ［J］. 仪器仪表学报, 2006, 27(11): 1513-1519.
|
| ［27］ |
齐国清, 吕健. 正弦曲线拟合若干问题探讨 ［J］. 计算机工程与设计, 2008, 29(14): 3677-3680.
|
| ［28］ |
许化龙, 袁晓峰, 陈淑红. 正弦信号波形参数拟合求解的混合优化算法 ［J］. 电子测量与仪器学报, 2004, 18(4): 1-5.
|
| ［29］ |
苏德伦, 王仕成, 张安京. 基于遗传算法的正弦波四参数曲线拟合 ［J］. 计测技术, 2005, 25(6): 18-20.
|
| ［4］ |
数据采集系统校准规范: JJF 1048—1995［S］. 北京: 中国计量出版社,1995.
|
|
WANG X Z, HONG T, HU X H, et al. Fast finding envelope algorithm based on moving sine fitting ［J］. Transducer and Microsystem Technologies, 2019, 38(12): 112-115, 119.
|
|
Liang Z G, SAO X H. The Vibration Parameters Evaluation Method Based on Partial Sinusoidal Curve-fitting ［J］. Journal of Vibration and Shock, 2013, 32(18): 91-94.
|
|
LIANG Z G, MENG X F. Measurement Uncertainty of Sinusoidal Frequency by Using Curve-fit Method ［J］. Acta Metrologica Sinica, 2009, 30(4): 358-362.
|
|
ZHANG K, ZHANG L, HU Y L, et al. Transmission line traveling wave data automatically screening method based on sine fitting ［J］. Power System Protection and Control, 2015, 43(20): 58-64.
|
|
XU Z N, LV F C, WANG F C, et al. Measurement of dielectric loss angle using high-order sine fitting method with added Hanning window interpolation ［J］. Hi Voltage Engineering, 2007, 33(4): 50-53.
|
|
LIANG Z G. The Phase Difference Evaluation Based on Total Least-square Method with Partial Period Sinusoidal Waveforms ［J］. Acta Metrologica Sinica, 2016, 37(4): 419-422.
|
|
HAN X J, DENG N M, WANG J Z, et al. Algorithm for fast north-seeking of gyrocompass based on sine curve fitting ［J］. Journal of Chinese Inertial Technology, 2012, 20(3): 253-256.
|
| ［20］ |
雍存宝．基于最小二乘算法的ADC正弦拟合测试研究与实现［D］．南京: 东南大学, 2013.
|
| ［26］ |
梁志国. 四参数正弦波组合式拟合算法 ［J］. 计量学报, 2021, 42(12): 1559-1566.
|
| ［30］ |
梁志国, 朱振宇. 非均匀采样正弦波形的最小二乘拟合算法 ［J］. 计量学报, 2014, 35(5): 494-499.
|
| ［31］ |
梁志国. 残周期正弦曲线拟合的比较研究 ［J］. 计量学报, 2023, 44(6): 948-955.
|
| ［32］ |
朱仕银, 曾涛, 龙腾. 改进的数据采集系统性能测试的正弦拟合法 ［J］. 北京理工大学学报, 2000, 20(6): 757-761.
|
| ［1］ |
IEEE Std 1057-2017, IEEE standard for digitizing waveform recorders ［S］. 2017.
|
| ［8］ |
刘宇, 王长文, 王乐, 等. 基于光纤陀螺的残周期正弦拟合快速寻北法 ［J］. 压电与声光, 2015, 37(6): 1020-1024.
|
| ［13］ |
张可, 张凌, 胡燕玲, 等. 输电线路行波测距数据的正弦拟合自动筛选方法 ［J］. 电力系统保护与控制, 2015, 43(20): 58-64.
|
|
JIA W D, LIN C S, LIN P F, et al. Calibration Method of Three-Axis Magnetometer Based on Sine Fitting ［J］. Geomatics and information science of Wuhan University, 2019, 64(9): 1328-1333, 1406.
|
| ［18］ |
王晋国, 廖祖文, 王明祥, 等. 正弦波拟合算法的薄互层解释 ［J］. 陕西师范大学学报: 自然科学版, 2005, 33(4): 40-43.
|
|
WANG J G, LIAO Z W, WANG M X, et al. Interpretation of thin inter-breeds based on SinFit algorithm ［J］. Journal of Shaanxi Normal University (Natural Science Edition), 2005, 33(4): 40-43.
|
|
MAO L Y, SHEN X F. An Improved Sine-Wave Fitting Procedure to Estimate Delay between Channels in Data Acquisition System ［J］. Modern Electronics Technique, 2007, 30(15): 125-127.
|
|
QIN S, SHEN X F. A Nicety Evaluation Method of Sine Wave Phase Difference ［J］. Measurement & Control Technology, 2008, 27(11): 22-24.
|
|
ZHANG H, SHI Y B, WANG Z G. Multi-tone sine wave fit algorithm of channel time delay in time-interleaved ADC system ［J］. Journal of Electronic Measurement and Instrumentation, 2010, 24(3):244-249.
|
| ［24］ |
陈启蒙．基于正弦拟合的时间交织ADC校准算法设计与实现［D］．南京: 东南大学, 2017.
|
|
LIANG Z G, ZHU J J, MENG X F. Convergence algorithm of four-parameter sine wave curve-fit ［J］. Chinese Journal of Scientific Instrument, 2006, 27(11): 1513-1519.
|
| ［7］ |
靳建峰, 王毅, 刘忠菁, 等. 正弦拟合法在中性点非直接接地系统中的应用 ［J］. 水电能源科学, 2007, 25(4): 148-151.
|
| ［12］ |
梁志国, 孟晓风. 拟合测量正弦信号频率的不确定度 ［J］. 计量学报, 2009, 30(4): 358-362.
|
| ［17］ |
贾文抖, 林春生, 林朋飞, 等. 基于正弦拟合的三轴磁力仪标定方法 ［J］. 武汉大学学报: 信息科学版, 2019, 64(9): 1328-1333, 1406.
|
| ［23］ |
张昊,师奕兵,王志刚. 时间交替ADC系统通道时钟延迟的多频正弦拟合算法 ［J］. 电子测量与仪器学报, 2010, 24(3): 244-249.
|
|
XU H L, YUAN X F, CHEN S H. Hybrid Optimization Algorithm for Curve-fit Model of Sinusoid Wave Parameters［J］. Journal of Electronic Measurement and Instrumentation, 2004, 18(4): 1-5.
|
|
SU D L, WANG S C, ZHANG A J. Four-parameter Sine Wave Curve-fit Based on Genetic Algorithms ［J］. Aviation Metrology & Measurement Technology, 2005, 25(6): 18-20.
|
| ［33］ |
Deyst J P, Sounders T M, Solomon O M . Bounds on least-squares four-parameter sine-fit errors due to harmonic distortion and noise ［J］. IEEE Transactions on Instrumentation & Measurement, 1995, 44(3): 637-642. DOI: 10. 1109/19. 387298.
|
| ［34］ |
梁志国. 采样序列长度及周波数对正弦参数拟合的影响 ［J］. 计量学报, 2022, 43(8): 989-1000.
|
| ［6］ |
李耀彬, 曾祥斌, 沈铖武. 基于抛物线插值的正弦波拟合算法 ［J］. 计算机工程与设计, 2009, 30(11): 2793-2795.
|
| ［11］ |
梁志国, 邵新慧. 基于残周期正弦拟合的振动参数测量 ［J］. 振动与冲击, 2013, 32(18): 91-94.
|
| ［16］ |
韩新建, 邓年茂, 王建钊, 等. 基于正弦曲线拟合法实现陀螺罗盘快速精寻北 ［J］. 中国惯性技术学报, 2012, 20(3): 253-256.
|
| ［22］ |
秦爽, 沈晓峰. 数据采集系统通道间延时的准确评价 ［J］. 测控技术, 2008, 27(11): 22-24.
|
|
QI G Q, L J. Investigation of sine wave fitting algorithms ［J］. Computer Engineering and Design, 2008, 29(14): 3677-3680.
|
|
ZHU S Y, ZEN T, LONG T. An Improved Sine Fitting Test for the Data Acquisition System ［J］. Transactions of Beijing Institute of Technology, 2000, 20(6): 757-761.
|
|
LIANG Z G . The Four-parameter Sinusoidal Curve-fit Method by Using Combination Methods ［J］. Acta Metrologica Sinica, 2021, 42(12): 1559-1566.
|
|
LIANG Z G. The Comparative Study of Curve-fit Methods for Partial Period Sine Waves ［J］. Acta Metrologica Sinica, 2023, 44(6): 948-955.
|
|
LIANG Z G, ZHU Z Y. The Sinewave Fit Algorithm Based on Total Least-square Method with Non-uniform Sampling ［J］. Acta Metrologica Sinica, 2014, 35(5): 494-499.
|
|
LIANG Z G. The Influence of Both Data Number and Signal Cycles to the Sinusoidal Parameters Error in Sine-Fit Method ［J］. Acta Metrologica Sinica, 2022, 43(8): 989-1000.
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2024, Vol. 45 
