Abstract：A combined four-parameter sinusoidal fitting method is proposed. Firstly, a three-parameter sine fitting algorithm with known frequency is used for frequency search, and a one-dimension search iterative sine fitting algorithm is constructed to obtain four parameters of amplitude, frequency, phase and DC component. Then, using it as an initial value, a four-parameter search iteration method is used to obtain the final sine fitting result. The method can be applied to multi-cycle and partial cycle sequences, with clear convergence domain, which can ensure the overall optimal convergence fitting result under any circumstances. Simulation and experimental experiments verify the effectiveness and feasibility of the proposed method.
［1］Jeng Y C, Crosby P B. Sinewave parameter estimation algorithm with application to waveform digitizer effective bits measurement［J］. IEEE Transactions on Instrumentation and Measurement, 1988, 37(4) 529-532.
［2］IEEE Std 1057-1994, IEEE standard for digitizing waveform recorders［S］. 1994
［3］Giaquninto N, Trotta A. Fast and accurate ADC testing via an enhanced sine wave fitting algorithm［J］. IEEE transactions on Instrumentation and Measurement, 1997, 46(4) 1020-1025.
［4］Zhang J, Zhao X, Xiao H, et al. Sine wave fit algorithm based on total least-squares method with application to ADC effective bits measurement［J］. IEEE Transactions on Instrumentation and Measurement, 1997, 46(4) 1026-1930.
［5］Tian S, Wang J, Yan D, et al. Base on inherit algorithmic sinusoidal parameter estimation［J］. Measurement Technique, 2005, (369): 3-5.
［6］Kollar I and Blair J J. Improved determination of the best fitting sine wave in ADC testing, IEEE Transactions on Instrumentation and Measurement, 2005, 54(5) 1978-1983
［7］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.
Liang Z G, Zhu J J, Meng X X, Convergence algorithm of four-parameter sine wave curve-fit［J］. Chinese Journal of Scientific Instrument, 2006, 27 (11): 1513-1519.
［8］Belega D, Dallet D, Petri D. A high-performance procedure for effective number of bits estimation in analog-to-digital converters［J］. IEEE Transactions on Instrumentation and Measurement, 2011, 60(5):1522-1532.
［9］Chen K F. Estimating parameters of a sine wave by separable nonlinear least squares fitting［J］. IEEE Transactions on Instrumentation and Measurement, 2010, 59(12): 3214.
［10］Sárhegyi Attila and István Kollár. Robust sine wave fitting in ADC testing［C］//IMTC 2006-Instrumentation and Measurement Technology Conference, Sorrento, Italy, 24-27.
［11］Jeng Y C. High precision sinusoidal frequency estimator based on weighted least square method［J］. IEEE Transactions on Instrumentation and Measurement, 1987, 36(2): 124-127.
［12］Vucijak N M, Saranovac L V. A simple algorithm for the estimation of phase difference between two sinusoidal voltages［J］. IEEE Transactions on Instrumentation and Measurement, 2010, 59(12): 3152.
［13］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.
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.
［14］Kuffel J, McComb T R, Malewski R. Comparative evaluation of computer methods for calculating the best-fit sinusoid to the digital record of a high-purity sine wave［J］. IEEE Transactions on Instrumentation and Measurement, 1987, 36(3): 418-422.
［15］McComb T R, Kuffel J, Le Roux B C. Acomparative evaluation of some practical algorithms used in the effective bits test of waveform recorders［J］. IEEE Transactions on Instrumentation and Measurement, 1989, 38(1): 37-42.
［16］Belega D, Dallet D, Petri D. Performance comparison of the three-parameter and the four-parameter sine-fit algorithms［C］//Instrumentation and Measurement Technology Conference (I2MTC), IEEE. 2011: 1-4.
［17］Ramos P M, Janeiro F M, Radil T. Performance comparison of three algorithms for two-channel sinewave parameter estimation［J］. Metrology and Measurement Systems XVII, 2010, (2): 255-270.
［18］Belega D, Petri D. Statistical performance of the effective-number-of-bit estimators provided by the sine-fitting algorithms［J］. IEEE Transactions on Instrumentation and Measurement, 2013, 62(3): 633-640.
［19］Handel P. Properties of the IEEE-STD-1057 Four-Parameter Sine Wave Fit Algorithm［J］. IEEE Transactions on Instrumentation and Measurement, 2000, 49(6): 1189-1193.
［20］Bilau T Z, Megyeri T, Sárhegyi A, et al. Four-parameter fitting of sine wave testing result: Iteration and convergence［J］. Computer Standards & Interfaces, 2004, 26(1): 51-56.
［21］吴义华, 杨俊峰, 程敬原, 等. 正弦信号四参数的高精度估计算法［J］. 中国科学技术大学学报, 2006, 36(6): 625-629.
Wu Y H, Yang J F, Cheng J Y, et al. High-accuracy estimation algorithm for 4 parameters of sine-wave［J］. Journal of University of Science and Technology of China, 2006, 36(6): 625-629.
［22］梁志国, 张大治, 孙璟宇, 等. 四参数正弦曲线拟合的快速算法［J］. 计测技术, 2006, 26(1): 4-7.
Liang Z G, Zhang D Z, Sun J Y, et al. A Fast Arithmetic Method of Four-parameter Sine Wave Curve fit［J］. Metrology & Measurement Technology, 2006, 26(1): 4-7.
［23］田社平, 王坚, 颜德田, 等, 基于遗传算法的正弦波信号参数提取方法［J］. 计量技术, 2005 (5): 3-5.
Tian S P, Wang J, Yan D T, et al. The Estimation Methods of Sinusoidal Parameters Based on Heredity Arithmetic［J］. Measurement Technique, 2005 (5): 3-5.
［24］梁志国, 孟晓风. 残周期正弦波形的四参数拟合［J］. 计量学报, 2009, 30(3): 245-249.
Liang Z G, Meng X F. A Curve-fit Arithmetic of Four-parameter Sine Wave for Partial Period［J］. Acta Metrologica Sinica, 2009, 30(3): 245-249.
［25］喻胜, 闫波, 陈光踽. 一种提取噪声中正弦信号的总体最小二乘法［J］. 电子测量与仪器学报, 2000, 14(2): 6-10.
Yu S, Yan B, Chen G Y. An Overall Least Mean Square Method to Pick up Sinusoidal in Noise［J］. Journal of Electronic Measurement and Instrument, 2000, 14(2): 6-10.
［26］王慧, 刘正士. 基于Hilbert-Huang变换测试A/D转换器有效位数的正弦曲线拟合法［J］. 计量学报, 2009, 30(4): 332-336.
Wang H, Liu Z S. The Sinusoid Fitting Method for Testing Effective Number of Bits of A/D Converter Based on Hilbert-Huang Transform ［J］. Acta Metrologica Sinica, 2009, 30(4): 332-336.
［27］梁志国, 朱济杰. 调相信号的一种数字化精确解调方法 ［J］. 计量学报, 2003, 24(4): 325-329.
Liang Z G, Zhu J J. A Precise Digitizing Demodulation Method for the PM Signal［J］. Acta Metrologica Sinica, 2003, 24(4): 325-329.
2021, Vol. 42 
