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
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.
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.
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.
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.
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.
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.
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.
2024, Vol. 45 
