Voltage amplitude calculation method and system based on full data weighting

Abstract

The invention discloses a voltage amplitude calculation method and system based on full data weighting, and belongs to the technical field of voltage measurement, and the method comprises the steps: collecting a time sequence data set corresponding to each voltage step value from a step wave quantum voltage signal; acquiring a fundamental wave Fourier coefficient corresponding to each time sequence data group according to a preset fundamental wave Fourier matrix so as to calculate a fitting fundamental wave amplitude corresponding to each time sequence data group; obtaining a sine fitting voltage value corresponding to each voltage signal point according to the fitting fundamental wave amplitude, and obtaining a residual data set corresponding to each time sequence data set according to the sine fitting voltage values and the voltage signal points; and obtaining a weight coefficient corresponding to each voltage step value according to the residual data set, so as to obtain the fundamental wave amplitude of the step wave quantum voltage signal according to the fitting fundamental wave amplitude corresponding to each time sequence data set. Therefore, by implementing the method and the device, the problem of low voltage amplitude calculation accuracy caused by data errors in the prior art can be solved.

Description

Technical Field

[0001] This invention relates to the field of voltage measurement technology, and in particular to a method and system for calculating voltage amplitude based on full data weighting. Background Technology

[0002] In the field of AC voltage quantization measurement, calculating the quantum voltage amplitude by outputting a stepped-wave quantum voltage signal based on the Programmable Josephson Voltage Standard (PJVS) and then calculating the amplitude of this stepped-wave quantum voltage signal has become a widely studied research direction. However, during the amplitude calculation using the stepped-wave quantum voltage signal output by the PJVS, there is a transient transition process lasting approximately several microseconds at the beginning and end of each voltage step. This phenomenon causes the sampled data at both ends of the step to deviate significantly from the preset quantum voltage value. Studies have shown that only in the stable middle region after removing the beginning and end transition regions of each voltage step does the sampled data fully meet the quantum precision requirements.

[0003] In existing technologies, algorithms such as the statistical 3σ criterion or segmented sampling techniques are used to accurately identify and distinguish the stable region and transition region of the quantum voltage step. Then, data is sampled based on the distinction of the regions, and the amplitude is calculated using the sampled data.

[0004] The aforementioned method of using region division for data sampling to calculate amplitude relies on the accuracy of data sampling to ensure the accuracy of amplitude calculation. The accuracy of data sampling, in turn, depends on preset criteria to identify and classify the stable and transition regions of the quantum voltage step. In this process, the accuracy of region identification is limited by the setting of threshold parameters, which leads to the inability to guarantee the accuracy of sampling. For example, if the stability judgment threshold is set too low, although the quantum precision of the data can be ensured, the amount of effective sampled data will be greatly reduced, directly affecting the completeness of amplitude calculation. Conversely, if the threshold is set too high, it is difficult to completely eliminate the interference of transition region data. The participation of this data containing systematic errors in amplitude calculation will significantly increase the uncertainty of the final calculation result and affect the accuracy of amplitude calculation. Summary of the Invention

[0005] This invention provides a voltage amplitude calculation method based on full data weighting, which can solve the problem of low accuracy in voltage amplitude calculation caused by data errors in the prior art.

[0006] This invention discloses a method for calculating voltage amplitude based on full data weighting, comprising:

[0007] Multiple voltage signal points corresponding to each voltage step value are collected from the acquired step wave quantum voltage signal to obtain a time series data group corresponding to each voltage step value;

[0008] The fundamental Fourier coefficients corresponding to each time series data group are obtained according to the preset fundamental Fourier matrix, and the fitted fundamental amplitude corresponding to each time series data group is obtained according to the fundamental Fourier coefficients.

[0009] Based on the amplitude of the fitted fundamental wave, obtain the sinusoidal fitted voltage value corresponding to each voltage signal point, and obtain the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point;

[0010] The weighting coefficients corresponding to each voltage step value are obtained from the residual data set, and the fundamental amplitude of the stepped quantum voltage signal is obtained from the weighting coefficients and the fitted fundamental amplitude of each time series data set.

[0011] This invention discloses a voltage amplitude calculation method based on full data weighting. By weighting each voltage signal point in the acquired step-wave quantum voltage signal, the influence of data screening errors on the calculation results is eliminated, thus improving the accuracy of voltage amplitude calculation. First, a time-series data set is constructed by collecting all voltage signal points for each voltage step, avoiding information loss caused by manually removing data from the transition region. Second, the fundamental wave coefficient is fitted using the fundamental wave Fourier matrix, accurately extracting the fundamental wave component from the noisy raw data. Then, the residual between the sinusoidal fitted value and the actual value of each data point is calculated to objectively reflect the reliability differences of data from different steps. Finally, weighting coefficients are generated based on the statistical characteristics of the residuals, achieving enhanced weighting of high-reliability data and suppressed weighting of low-reliability data. This achieves adaptive suppression of error data while retaining all sampled data, overcoming the contradiction between data utilization and calculation accuracy caused by the reliance on fixed thresholds in traditional methods. Furthermore, the final fundamental wave amplitude is calculated using the weighting coefficients corresponding to each voltage signal point in the step-wave quantum voltage signal, improving the accuracy of amplitude calculation.

[0012] As a preferred example, the step of acquiring multiple data points corresponding to each voltage step value from the acquired step wave quantum voltage signal to obtain a time-series data group corresponding to each voltage step value includes:

[0013] The sinusoidal stepped quantum voltage signal output by PJVS is calibrated to obtain the stepped quantum voltage signal to be processed.

[0014] Multiple voltage step values ​​of the stepped wave quantum voltage signal are obtained, and multiple voltage signal points corresponding to each voltage step value are obtained from the stepped wave quantum voltage signal to construct a time series data group corresponding to the voltage step value; wherein, each voltage signal point includes a sampling time and a sampling voltage consistent with the voltage step value.

[0015] In the above scheme, by calibrating the original signal output by PJVS, systematic errors and biases in the signal are eliminated, ensuring that the data basis for subsequent processing has quantum precision. By dividing the voltage step values ​​and extracting the voltage signal points corresponding to each step, the signals in the originally mixed transition region and the stable region are classified according to the voltage step values ​​to form independent time series data groups. The voltage signal points in each time series data group contain the sampling time and the voltage value consistent with the step value, which not only preserves the time series information, but also excludes the transition region data through voltage consistency, thereby providing a high-precision and interference-free original data set for subsequent fundamental amplitude calculation.

[0016] As a preferred example, the calibration of the sinusoidal step wave quantum voltage signal output by the PJVS to obtain the step wave quantum voltage signal to be processed includes:

[0017] The voltage sample value of the sinusoidal stepped quantum voltage signal is obtained, and the voltage sample value is linearly fitted with the voltage setting value of the PJVS to obtain the gain coefficient and bias voltage.

[0018] The sinusoidal stepped quantum voltage signal is corrected and compensated according to the gain coefficient and the bias voltage to obtain the stepped quantum voltage signal to be processed.

[0019] In the above scheme, precise calibration of the PJVS output signal is achieved by establishing a linear error model and a dynamic compensation mechanism. First, by linearly fitting the actual voltage sample values ​​with the theoretical set values, the gain and bias errors of the PJVS system can be accurately quantified. This parameter calibration method based on measured data effectively avoids the limitations of traditional fixed compensation parameters. Then, the original signal is corrected and compensated based on the fitted gain coefficient and bias voltage, directly implementing inverse correction on the mathematical representation of the PJVS system error. This eliminates distortion in signal transmission while maintaining the temporal integrity of the quantum voltage signal, balancing calibration accuracy and computational efficiency.

[0020] As a preferred example, the step of obtaining the fundamental Fourier coefficients corresponding to each time series data group according to a preset fundamental Fourier matrix, and obtaining the fitted fundamental amplitude value corresponding to each time series data group according to the fundamental Fourier coefficients, includes:

[0021] For any one of the aforementioned time-series data groups;

[0022] The number of voltage signal points in the time series data group is obtained, and the characteristic fundamental Fourier matrix corresponding to the time series data group is obtained according to the number and the preset fundamental Fourier matrix; wherein, the fundamental Fourier matrix is ​​the Fourier matrix corresponding to the fundamental obtained after fitting the time series data group.

[0023] The time series data set is converted into a time series data matrix, and the time series data matrix is ​​multiplied by the characteristic fundamental Fourier matrix to obtain the fundamental Fourier coefficients corresponding to the time series data set; wherein, the fundamental Fourier coefficients are the Fourier coefficients corresponding to the fundamental obtained after fitting the time series data set.

[0024] The fitted fundamental amplitude value corresponding to the time series data group is obtained based on the fundamental Fourier coefficients.

[0025] In the above scheme, the fundamental wave component is accurately extracted by constructing a Fourier matrix that matches a single time-series data set. First, the dimension of the fundamental wave Fourier matrix is ​​dynamically adjusted according to the number of actual voltage signal points in the time-series data set, ensuring that the matrix operation is fully adapted to the spatiotemporal characteristics of the sampled data. Second, after converting the original time-series data into matrix form, matrix multiplication is performed with the characteristic fundamental wave Fourier matrix. This linear algebraic method directly extracts the Fourier coefficients characterizing the fundamental wave component, avoiding the dependence on transition region data in traditional thresholding methods. Finally, the fitted fundamental wave amplitude is directly calculated based on the Fourier coefficients. The fundamental wave parameters are obtained through mathematical transformation rather than physical region division, preserving the integrity of all valid data while eliminating the impact of transition region identification errors on the calculation results.

[0026] As a preferred example, the expression for calculating the fitted fundamental amplitude is:

[0027] YF=C

[0028]

[0029] C = [a, b]

[0030]

[0031] Wherein, Y represents the time-series data matrix corresponding to the time-series data group; F represents the fundamental Fourier matrix; C represents the fundamental coefficient matrix composed of the fundamental Fourier coefficients; N1 represents the number of voltage signal points in the time-series data group; a and b represent the fundamental Fourier coefficients; and A... i The a represents the fitted basis amplitude value corresponding to the i-th time series data group; i b i This represents the fundamental Fourier coefficient corresponding to the i-th time series data group.

[0032] In the above scheme, a fundamental frequency coefficient matrix is ​​obtained by multiplying the time-series data matrix with the fundamental Fourier matrix using a matrix-based mathematical expression, and then the fitted fundamental frequency amplitude is directly calculated. The time-series data matrix Y fully preserves the temporal characteristics of the original sampled data, the fundamental Fourier matrix F constructs a mathematical framework for data fitting using a pre-defined fundamental frequency model, and the solution process for the fundamental frequency coefficient matrix C achieves full weighted processing of the original data. The Fourier coefficients of parameters a and b accurately characterize the amplitude characteristics of the fundamental frequency component, and the application of the number of voltage points in the time-series data ensures adaptability to different data scales. This analytical method based on matrix operations avoids the subjective setting of traditional threshold criteria, directly extracting fundamental frequency characteristic parameters through mathematical modeling, thus improving the accuracy and efficiency of amplitude calculation while ensuring data integrity.

[0033] As a preferred example, the step of obtaining the sinusoidal fitted voltage value corresponding to each voltage signal point based on the fitted fundamental amplitude, and obtaining the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point, includes:

[0034] Obtain the signal frequency of the stepped-wave quantum voltage signal;

[0035] For any one of the aforementioned time-series data groups;

[0036] Phase-locked loop is applied to the timing data group to obtain the corresponding phase.

[0037] Based on the phase, the fitted fundamental amplitude and the signal frequency of the time series data group, a sine fit is performed on each voltage signal point to obtain the sine fitted voltage value corresponding to each voltage signal point.

[0038] The difference between each sinusoidal fitted voltage value and the voltage step value corresponding to the time series data group is obtained respectively, so as to obtain the residual data group corresponding to the time series data group based on the difference.

[0039] In the above scheme, a dynamic sinusoidal fitting mechanism based on signal frequency, phase, and the amplitude of the fitted fundamental wave is introduced to construct a sinusoidal fitted voltage value that matches the time-series characteristics of the original voltage signal points, thereby generating a residual data set reflecting the deviation between the actual sampled data and the ideal quantum voltage value. Specifically, firstly, the signal frequency is obtained to determine the periodicity of the sinusoidal waveform, providing basic parameters for subsequent fitting; secondly, phase-locked processing is performed on the time-series data set to accurately capture its phase information, ensuring the time synchronization between the sinusoidal fitted waveform and the original signal; then, combining the fitted fundamental wave amplitude, phase, and frequency parameters, a sinusoidal fitted voltage value with quantum precision characteristics is generated for each voltage signal point, which includes both the fundamental wave component and retains time correlation; finally, by calculating the difference between the sinusoidal fitted voltage value and the actual voltage step value, the deviation between each sampling point and the ideal quantum voltage value is directly quantified, forming a residual data set. This technique avoids the limitations of traditional methods that rely on fixed thresholds to divide data regions, instead using residual analysis involving all data to characterize the error distribution, providing an objective basis for subsequent weighted calculations based on weight coefficients.

[0040] As a preferred example, the expression for calculating the sinusoidal fitted voltage value is as follows:

[0041] U i,j (t)=A i sin(2πft+φ i )+ε

[0042] Wherein, the U i,j (t) represents the sinusoidal fitted voltage value corresponding to the j-th voltage signal point in the i-th time series data group; t represents the sampling time corresponding to the j-th voltage signal point in the i-th time series data group; f represents the signal frequency; φ i The ε represents the phase corresponding to the i-th time series data group; the ε represents the residual term.

[0043] In the above scheme, sinusoidal fitting and residual calculation of voltage signal points are achieved by establishing mathematical expressions. Specifically, using the signal frequency and phase parameters obtained from phase-locking, combined with the amplitude of the fitted fundamental wave, a sinusoidal function model is performed on the voltage value at each sampling time point to generate the corresponding sinusoidal fitted voltage value. The difference between the actual sampled voltage and the sinusoidal fitted value is defined as the residual term, forming a residual data set. This mathematical modeling method based on dynamic phase and frequency avoids relying on fixed thresholds for region division, directly reflecting the data deviation in the transition region through the goodness of fit of the data itself, providing a quantitative basis for subsequent weight allocation based on residuals, thereby eliminating the uncertainty caused by threshold setting.

[0044] As a preferred example, the step of obtaining the weighting coefficients corresponding to each voltage step value based on the residual data set, and obtaining the fundamental amplitude of the stepped quantum voltage signal based on the weighting coefficients and the fitted fundamental amplitude of each time series data set, includes:

[0045] For any given voltage step value, calculate the standard deviation corresponding to the voltage step value based on the residual data set corresponding to the voltage step value, and obtain the weighting coefficient corresponding to the voltage step value based on the standard deviation.

[0046] Based on the weighting coefficients and fitted fundamental amplitude values ​​corresponding to each voltage step value, the fundamental amplitude value corresponding to the stepped quantum voltage signal is obtained through a weighted average algorithm.

[0047] In the above scheme, weighting coefficients are dynamically calculated using residual data, and the fundamental amplitude is accurately calculated based on a weighted average. First, the standard deviation is calculated for the residual data set of each voltage step. The standard deviation reflects the degree of dispersion of the data from the fitted fundamental amplitude; a smaller standard deviation indicates higher data reliability. Therefore, it is used as the basis for calculating the weighting coefficients, giving high-precision data a higher weight in the final amplitude calculation. Second, a weighted average algorithm is used to comprehensively calculate the fitted fundamental amplitude of all voltage steps. This avoids the sampling errors caused by traditional methods that rely on fixed thresholds to divide the stable and transition regions. Simultaneously, the weights are dynamically adjusted based on the statistical characteristics of the data itself, preserving the effective information of the entire dataset while suppressing interference from abnormal data in the transition region. This improves the accuracy and anti-interference capability of amplitude calculation without the need for preset thresholds.

[0048] As a preferred example, the expression for calculating the fundamental amplitude is as follows:

[0049]

[0050]

[0051] Wherein, A represents the fundamental amplitude corresponding to the stepped quantum voltage signal; w i The weighting coefficients represent the voltage step values ​​corresponding to the i-th time series data group; M represents the number of voltage step values; σ i The standard deviation of the voltage step value corresponding to the i-th time series data group; the U i This represents the voltage step value corresponding to the i-th time series data group.

[0052] In the above scheme, a weighting coefficient model based on the inverse proportional relationship of standard deviation is established to quantify the residual fluctuation characteristics of each voltage step into weight parameters, thereby achieving dynamic evaluation of data quality. Specifically, the calculation of standard deviation transforms the dispersion of the residual data set into an objective statistical indicator. The larger the standard deviation, the greater the deviation of the step data from the ideal quantum value; therefore, a smaller weighting coefficient is assigned to suppress the influence of error. A weighted average algorithm is used to fuse the fitted fundamental amplitude values ​​of each step according to the weighting coefficients. This retains the effective information of the entire step data while automatically weakening the interference of abnormal data in the transition zone through the weighting allocation mechanism, eliminating the need for manually setting thresholds for data screening. This scheme transforms the transition zone identification problem into statistical weight calculation through mathematical modeling, fundamentally avoiding sampling errors caused by threshold setting deviations in traditional methods, and achieving high-precision amplitude calculation without manual intervention.

[0053] Another embodiment of the present invention provides a voltage amplitude calculation system based on full data weighting, including a voltage division module, a fitting amplitude module, a residual calculation module, and an amplitude calculation module;

[0054] The voltage division module is used to collect multiple voltage signal points corresponding to each voltage step value from the acquired step wave quantum voltage signal, and obtain the time series data group corresponding to each voltage step value;

[0055] The fitting amplitude module is used to obtain the fundamental Fourier coefficients corresponding to each time series data group according to the preset fundamental Fourier matrix, and to obtain the fitting fundamental amplitude corresponding to each time series data group according to the fundamental Fourier coefficients.

[0056] The residual calculation module is used to obtain the sinusoidal fitted voltage value corresponding to each voltage signal point based on the fitted fundamental amplitude value, so as to obtain the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point;

[0057] The amplitude calculation module is used to obtain the weighting coefficient corresponding to each voltage step value based on the residual data group, and to obtain the fundamental amplitude corresponding to the step wave quantum voltage signal based on the weighting coefficient and the fitted fundamental amplitude corresponding to each time series data group.

[0058] This invention discloses a voltage amplitude calculation system based on full data weighting. By weighting each voltage signal point in the acquired step-wave quantum voltage signal, the system eliminates the influence of data screening errors on the calculation results, thereby improving the accuracy of voltage amplitude calculation. First, a time-series data set is constructed by collecting all voltage signal points for each voltage step, avoiding information loss caused by manually removing data from the transition region. Second, the fundamental wave coefficient is fitted using the fundamental wave Fourier matrix, accurately extracting the fundamental wave component from the noisy raw data. Then, the residual between the sinusoidal fitted value and the actual value of each data point is calculated, objectively reflecting the reliability differences of data from different steps. Finally, weighting coefficients are generated based on the statistical characteristics of the residuals, achieving enhanced weighting of high-reliability data and suppressed weighting of low-reliability data. This achieves adaptive suppression of error data while retaining all sampled data, overcoming the contradiction between data utilization and calculation accuracy caused by the reliance on fixed thresholds in traditional methods. Finally, the final fundamental wave amplitude is calculated using the weighting coefficients corresponding to each voltage signal point in the step-wave quantum voltage signal, improving the accuracy of amplitude calculation. Attached Figure Description

[0059] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0060] Figure 1 This is a flowchart illustrating a voltage amplitude calculation method based on full data weighting provided in an embodiment of the present invention;

[0061] Figure 2 This is a schematic diagram of a voltage amplitude calculation system based on full data weighting provided in an embodiment of the present invention;

[0062] Figure 3 This is a waveform diagram of a stepped-wave quantum voltage signal provided in an embodiment of the present invention;

[0063] Figure 4 This is a schematic diagram of a fundamental frequency amplitude calculation process provided in an embodiment of the present invention;

[0064] Figure 5 This is a schematic diagram of the fitted fundamental amplitude of a voltage step value provided in an embodiment of the present invention;

[0065] Figure 6 This is a schematic diagram of the weighting coefficients for voltage step values ​​provided in an embodiment of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0067] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0068] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0069] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0070] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0071] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).

[0072] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0073] See Figure 1 To address the problem of low accuracy in voltage amplitude calculation due to data errors in existing technologies, an embodiment of the present invention provides a voltage amplitude calculation method based on full data weighting, mainly including:

[0074] Step 101: Collect multiple voltage signal points corresponding to each voltage step value from the acquired step wave quantum voltage signal to obtain the time series data group corresponding to each voltage step value.

[0075] Step 102: Obtain the fundamental Fourier coefficients corresponding to each time series data group according to the preset fundamental Fourier matrix, and obtain the fitted fundamental amplitude value corresponding to each time series data group according to the fundamental Fourier coefficients.

[0076] Step 103: Obtain the sinusoidal fitted voltage value corresponding to each voltage signal point based on the fitted fundamental amplitude, so as to obtain the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point.

[0077] Step 104: Obtain the weighting coefficient corresponding to each voltage step value based on the residual data set, and obtain the fundamental amplitude value corresponding to the step wave quantum voltage signal based on the weighting coefficient and the fitted fundamental amplitude value corresponding to each time series data set.

[0078] In this first embodiment, when obtaining the time-series data group corresponding to each voltage step value from the stepped wave quantum voltage signal in step 101, in order to improve the accuracy of the amplitude calculation of the stepped wave quantum voltage signal, in this first embodiment, step 101 can construct the time-series data group through the following steps, so as to improve the accuracy of the construction of the time-series data group and thus improve the final voltage amplitude. Specifically, step 101 includes:

[0079] Step 1011: The sinusoidal stepped quantum voltage signal output by the PJVS is calibrated to obtain the stepped quantum voltage signal to be processed; wherein, the voltage sampling value of the sinusoidal stepped quantum voltage signal is obtained, and the voltage sampling value is linearly fitted with the voltage setting value of the PJVS to obtain the gain coefficient and the bias voltage; the sinusoidal stepped quantum voltage signal is corrected and compensated according to the gain coefficient and the bias voltage to obtain the stepped quantum voltage signal to be processed.

[0080] Step 1012: Obtain multiple voltage step values ​​of the stepped wave quantum voltage signal, and obtain multiple voltage signal points corresponding to each voltage step value from the stepped wave quantum voltage signal to construct a time series data group corresponding to the voltage step value; wherein, each voltage signal point includes a sampling time and a sampling voltage consistent with the voltage step value.

[0081] In this embodiment, the PJVS is a high-precision voltage standard based on the Josephson effect, which generates a step-wave quantum voltage signal under microwave excitation through programmable control and a Josephson array. Specifically, the waveform of the step-wave quantum voltage signal is as follows: Figure 3 As shown. (Refer to...) Figure 3 It can be seen that the voltage of the stepped wave quantum voltage signal has multiple voltage step values, such as u=0, u=0.5, u=-0.5, etc.

[0082] After obtaining the stepped quantum voltage signal output by the PJVS, to avoid errors in signal amplitude calculation caused by signal transmission errors of the PJVS itself, the following can be done: Figure 4 The diagram illustrates precise calibration of the output voltage signal to eliminate the influence of gain error and bias voltage in the PJVS system. Specifically, the stepped-wave quantum voltage signal can be precisely calibrated by acquiring the actual sampled value of the stepped-wave quantum voltage signal and the set value of the PJVS itself, so that the signal amplitude can be calculated using the calibrated stepped-wave quantum voltage signal.

[0083] Specifically, to ensure the accuracy of the calibration, in this embodiment, when calibrating the stepped-wave quantum voltage signal, a precision data acquisition card PXI5922 with 24-bit resolution can be used to sample the voltage of the sinusoidal stepped-wave quantum voltage signal output by PJVS, obtaining the actual sampled value. Then, a linear fit is performed between the actual sampled value obtained by PXI5922 and the preset output voltage value of PJVS at the factory, yielding the gain coefficient and bias voltage. The stepped-wave quantum voltage signal is then corrected and compensated based on the gain coefficient and the bias voltage. It should be noted that when sampling the signal output by PJVS, the acquisition card used for sampling is not limited to any particular type; any sampling card with a high-precision sampling rate can be used to sample data to ensure calibration accuracy. When performing a linear fit between the actual sampled value and the preset value, taking PXI5922 as an example, UPXI5922 = xUPJVS + y can be set to obtain the gain coefficient x and the bias voltage y. Subsequently, the voltage value in the corrected step wave quantum voltage signal is calculated by substituting the measured voltage into the fitted formula.

[0084] Furthermore, after obtaining the calibrated step-wave quantum voltage signal, multiple voltage signal points corresponding to each voltage step value can be selected from the step-wave quantum voltage signal by using multiple preset voltage step values ​​or by acquiring multiple voltage step values ​​from the step-wave quantum voltage signal. These voltage signal points are then sorted according to the sampling time corresponding to each voltage signal point to obtain a time-series data group corresponding to each voltage step value. It should be noted that the sinusoidal step-wave quantum voltage signal output by the PJVS system will have multiple voltage steps, each with a certain voltage value. The specific implementation of obtaining or presetting the voltage step values ​​is prior art and not an inventive point of this invention, and will not be elaborated upon here.

[0085] In this first embodiment, it is assumed that the sinusoidal stepped quantum voltage signal output by the PJVS system has 40 different voltage step values, including u = -1, u = -0.5, etc. Taking u = -1 as an example, there are n voltage signal points with u = -1 in the sinusoidal stepped quantum voltage signal. The multiple voltage signal points with u = -1 are structured to obtain the time-series data group corresponding to the voltage step value of -1. At this time, the multiple voltage signal points in the time-series data group have the same voltage value but different sampling times, and are sorted according to the sampling time. Specifically, as follows... Figure 4 As shown, multiple voltage signal points with the same voltage step value (i.e., the same step position) are extracted and constructed into a time series data group U.i , (i = 1, 2, ..., N); where, the U i The voltage step value corresponding to the i-th time data group is represented by N; N represents the number of voltage signal points in the i-th time data group.

[0086] In this embodiment, the above steps first involve linearly fitting the actual voltage sampled values ​​with the theoretical set values, which accurately quantifies the gain and bias errors of the PJVS system. This parameter calibration method based on measured data effectively avoids the limitations of traditional fixed compensation parameters. Subsequently, the original signal is corrected and compensated based on the fitted gain coefficient and bias voltage, directly implementing inverse correction on the mathematical representation of the PJVS system error. This eliminates distortion in signal transmission while maintaining the temporal integrity of the quantum voltage signal, balancing calibration accuracy and computational efficiency. Secondly, by dividing the voltage step values ​​and extracting the voltage signal points corresponding to each step, the signals in the originally mixed transition and stable regions are classified according to the voltage step values, forming independent time-series data groups. The voltage signal points in each time-series data group contain the sampling time and the voltage value consistent with the step value, which not only preserves the time series information but also excludes transition region data through voltage consistency, thereby providing a high-precision, interference-free original data set for subsequent fundamental amplitude calculation.

[0087] In this embodiment, step 102 can improve the accuracy of the fitted fundamental amplitude by obtaining the fitted fundamental amplitude corresponding to each time series data group through the following steps, thereby improving the calculation accuracy of the stepped wave quantum voltage signal amplitude. Specifically, the steps include:

[0088] Step 1021: For any of the time series data groups; obtain the number of voltage signal points in the time series data group, and obtain the characteristic fundamental Fourier matrix corresponding to the time series data group according to the number and the preset fundamental Fourier matrix; wherein, the fundamental Fourier matrix is ​​the Fourier matrix corresponding to the fundamental obtained after fitting the time series data group.

[0089] Step 1022: Convert the time series data set into a time series data matrix, and multiply the time series data matrix with the characteristic fundamental Fourier matrix to obtain the fundamental Fourier coefficients corresponding to the time series data set; wherein, the fundamental Fourier coefficients are the Fourier coefficients corresponding to the fundamental obtained after fitting the time series data set.

[0090] Step 1023: Obtain the fitted fundamental amplitude value corresponding to the time series data group based on the fundamental Fourier coefficients.

[0091] Specifically, in this embodiment, after extracting data with consistent voltage step values ​​to construct time-series data groups, in order to perform sine fitting on each time-series data group and determine the weighting coefficients corresponding to each time-series data group based on the error between the fitted value and the actual value, the fundamental amplitude value of the fitted signal after sine fitting for each time-series data group is first determined before sine fitting. Specifically, during sine fitting, the matrix Y formed by converting the time-series data group corresponding to each voltage step value, the matrix C composed of the Fourier coefficients of the fundamental wave of the signal obtained after sine fitting of the time-series data group, and the Fourier matrix F corresponding to the fundamental wave satisfy the following relationship: YF = C; and the Fourier coefficients in matrix C can be calculated as follows:

[0092]

[0093] Based on the above relationship, the Fourier coefficients of the fundamental frequency can be obtained, and then the fitted fundamental frequency amplitude corresponding to each time series data group can be calculated according to the Fourier coefficients; wherein, the calculation expression of the fitted fundamental frequency amplitude is as follows:

[0094] Wherein, Y represents the time-series data matrix corresponding to the time-series data group; F represents the fundamental Fourier matrix; C represents the fundamental coefficient matrix composed of the fundamental Fourier coefficients; N1 represents the number of voltage signal points in the time-series data group; a and b represent the fundamental Fourier coefficients; and A... i The a represents the fitted basis amplitude value corresponding to the i-th time series data group; i b i This represents the fundamental Fourier coefficient corresponding to the i-th time series data group.

[0095] Specifically, with Figure 3 Taking the stepped-wave quantum voltage signal shown as an example, when calculating the fitted fundamental amplitude corresponding to each voltage step value in the stepped-wave quantum voltage signal according to the fitted fundamental amplitude calculation expression described in this embodiment, the fitted fundamental amplitude corresponding to each voltage step value is as follows: Figure 5 As shown. In Figure 5 In the fitted basis amplitude graph shown, the horizontal axis represents the sampling points on the step. There are multiple sampling points on a step, and these sampling points are numbered from 1 to 100. The horizontal axis represents these numbers. The vertical axis represents the fitted basis amplitude value corresponding to each sampling point.

[0096] In this embodiment, the above steps achieve accurate extraction of the fundamental wave component by constructing a Fourier matrix that matches a single time-series data set. First, the dimension of the fundamental wave Fourier matrix is ​​dynamically adjusted according to the number of actual voltage signal points in the time-series data set, ensuring that the matrix operation is fully adapted to the spatiotemporal characteristics of the sampled data. Second, after converting the original time-series data into matrix form, matrix multiplication is performed with the characteristic fundamental wave Fourier matrix. This linear algebra method directly extracts the Fourier coefficients characterizing the fundamental wave component, avoiding the dependence on transition region data in traditional thresholding methods. Finally, the fitted fundamental wave amplitude is directly calculated based on the Fourier coefficients. The fundamental wave parameters are obtained through mathematical transformation rather than physical region division, preserving the integrity of all valid data while eliminating the impact of transition region identification errors on the calculation results.

[0097] In this embodiment, when step 103 performs sine fitting on each voltage signal point based on the fitted fundamental amplitude to obtain the residual data set corresponding to each time series data set, the following steps can be used to perform sine fitting and obtain the residual data set, thereby improving the accuracy of fitting and the accuracy of residual data set acquisition, and thus improving the accuracy of amplitude calculation. Specifically, the steps are as follows:

[0098] Step 1031: Obtain the signal frequency of the step wave quantum voltage signal; for any one of the time series data groups; perform phase locking on the time series data group to obtain the phase corresponding to the time series data group;

[0099] Step 1032: Perform sinusoidal fitting on each voltage signal point according to the phase, fitted fundamental amplitude and signal frequency corresponding to the time series data group to obtain the sinusoidal fitted voltage value corresponding to each voltage signal point; obtain the difference between each sinusoidal fitted voltage value and the voltage step value corresponding to the time series data group, so as to obtain the residual data group corresponding to the time series data group based on the difference.

[0100] Specifically, refer to Figure 4 As can be seen, in this embodiment, when processing the sinusoidal stepped quantum voltage signal output by PJVS, it is necessary to process data groups with the same voltage step value, i.e., U... i ,

[0101] Phase-locked loop (PJVS) processing is performed on the data sets (i = 1, 2, ..., N), which is a crucial step in ensuring the accuracy of sine curve fitting. The core purpose of PJVS operation is to maintain strict phase synchronization among all fitted curves, thereby eliminating systematic errors caused by phase deviations. This technical requirement stems from the unique properties of the PJVS system output signal: firstly, the sinusoidal stepped wave generated by PJVS has definite phase characteristics; secondly, each sine curve to be fitted has a clear phase correlation with the reference signal. By implementing precise PJVS control, the phase consistency of each data set during the fitting process can be ensured, laying the foundation for subsequent accurate quantitative analysis. Therefore, this embodiment performs PJVS on the time-series data set corresponding to each voltage step value to obtain the phase corresponding to the time-series data set. It should be noted that the implementation of PJVS is prior art and not the inventive point of this invention, and will not be elaborated upon here.

[0102] Reference Figure 4 It can be seen that when performing sine fitting on the time series data group after phase-locking, the sine fitting can be achieved through a preset sine function; wherein, the sine function is:

[0103] U i,j (t)=A i sin(2πft+φ i )+ε

[0104] Wherein, the U i,j (t) represents the sinusoidal fitted voltage value corresponding to the j-th voltage signal point in the i-th time series data group; t represents the sampling time corresponding to the j-th voltage signal point in the i-th time series data group; f represents the signal frequency; φ i The ε represents the phase corresponding to the i-th time series data group; the ε represents the residual term.

[0105] Next, taking any time series data set as an example, refer to... Figure 4 It can be seen that after obtaining the sinusoidal fitted voltage value corresponding to each voltage signal point in the time series data group, the difference between the sinusoidal fitted voltage value and the voltage step value corresponding to the time series data group, i.e., the residual, can be calculated, so as to construct the residual data group corresponding to the time series data group based on the multiple differences corresponding to multiple voltage signal points in the time series data group.

[0106] In this embodiment, the above steps introduce a dynamic sinusoidal fitting mechanism based on signal frequency, phase, and the amplitude of the fitted fundamental wave to construct a sinusoidal fitted voltage value that matches the time-series characteristics of the original voltage signal points, thereby generating a residual data set reflecting the deviation between the actual sampled data and the ideal quantum voltage value. Specifically, firstly, the signal frequency is obtained to determine the periodicity of the sinusoidal waveform, providing basic parameters for subsequent fitting; secondly, phase-locked processing is performed on the time-series data set to accurately capture its phase information, ensuring the time synchronization between the sinusoidal fitted waveform and the original signal; then, combined with the fitted fundamental wave amplitude, phase, and frequency parameters, a sinusoidal fitted voltage value with quantum precision characteristics is generated for each voltage signal point, which includes both the fundamental wave component and retains time correlation; finally, by calculating the difference between the sinusoidal fitted voltage value and the actual voltage step value, the deviation between each sampling point and the ideal quantum voltage value is directly quantified, forming a residual data set. This technique avoids the limitations of traditional methods that rely on fixed thresholds to divide data regions, instead using residual analysis involving all data to characterize the error distribution, providing an objective basis for subsequent weighted calculations based on weight coefficients.

[0107] In this embodiment, step 104, during the calculation of the fundamental amplitude corresponding to the stepped-wave quantum voltage signal, calculates the weighting coefficients corresponding to each time-series data group through the following steps, so as to obtain the amplitude based on the weighting coefficients and improve the amplitude calculation result. Specifically, the steps include:

[0108] Step 1041: For any voltage step value, calculate the standard deviation corresponding to the voltage step value based on the residual data set corresponding to the voltage step value, and obtain the weighting coefficient corresponding to the voltage step value based on the standard deviation;

[0109] Step 1042: Based on the weighting coefficients and fitted fundamental amplitude values ​​corresponding to each voltage step value, the fundamental amplitude value corresponding to the stepped quantum voltage signal is obtained through a weighted average algorithm.

[0110] Specifically, in this embodiment, refer to Figure 4 It can be seen that, for any given time series data set, the standard deviation of the voltage step value of each time series data set is obtained by calculating the statistical characteristics of the residual data set of that time series data set. This standard deviation characterizes the dispersion of the voltage step value, i.e., the sampling point location. The expression for calculating the standard deviation is:

[0111]

[0112] M represents the number of voltage step values; σ i The standard deviation of the voltage step value corresponding to the i-th time series data group; the U iThis represents the voltage step value corresponding to the i-th time-series data group. This step achieves a quantitative characterization of the time-domain features of the quantum voltage signal, laying the foundation for subsequent weighted optimization.

[0113] Next, weighting coefficients for each voltage step value, i.e., the sampling point location, are defined based on the standard deviation; wherein, the calculation expression for the weighting coefficient is:

[0114]

[0115] Wherein, A represents the fundamental amplitude corresponding to the stepped quantum voltage signal; w i The weighting coefficients represent the voltage step values ​​corresponding to the i-th time series data group; the steady-state data are affected by σ. i Smaller values ​​automatically receive higher weights; the contribution of transition zone data increases with σ. i It increases and then decays exponentially.

[0116] In this embodiment one implementation, refer to Figure 3 The quantum voltage signal shown and Figure 5 The weighting coefficients corresponding to each voltage step value obtained from the fitted basis amplitude are shown below. Figure 6 As shown, in Figure 6 In this diagram, the horizontal axis refers to the sampling points on the steps. There are multiple sampling points on a single step, and these sampling points are numbered from 1 to 100. The horizontal axis represents these numbers. The vertical axis represents the proportion of each number in the overall data, expressed as a percentage (%). For example, if the vertical axis of a certain number is 10, it means that this data has a weight of 10% in the overall data.

[0117] Finally, the high-precision fundamental amplitude of the stepped-wave quantum voltage signal is obtained through full-data weighted fusion and high-precision amplitude estimation. Specifically, a fitted amplitude matrix A corresponding to the stepped-wave quantum voltage signal can be constructed based on the fitted fundamental amplitude of each time-series data group, and a weighting coefficient matrix w can be constructed based on the weighting coefficients of each time-series data group. Where: A = [A1, A2, A3, ..., A...]. M ], w = [w1, w2, w3, ..., w M Next, a weighted average algorithm is used to estimate the final fundamental amplitude. The expression for calculating the fundamental amplitude is as follows:

[0118]

[0119] In this embodiment, the above steps dynamically calculate weighting coefficients using residual data and achieve accurate calculation of the fundamental amplitude based on weighted averaging. First, the standard deviation is calculated for the residual data set of each voltage step. The standard deviation reflects the degree of dispersion of the step data from the fitted fundamental amplitude; a smaller standard deviation indicates higher data reliability. Therefore, it is used as the basis for calculating the weighting coefficients, giving high-precision data a higher weight in the final amplitude calculation. Second, a weighted averaging algorithm is used to comprehensively calculate the fitted fundamental amplitude of all voltage steps. This avoids the sampling errors caused by traditional methods that rely on fixed thresholds to divide the stable and transition regions. Simultaneously, the weights are dynamically adjusted based on the statistical characteristics of the data itself, preserving the effective information of the entire dataset while suppressing interference from abnormal data in the transition region. This improves the accuracy and anti-interference capability of amplitude calculation without the need for preset discrimination thresholds.

[0120] like Figure 2 As shown, based on the above method embodiments, corresponding device embodiments are provided; one embodiment of the present invention provides a voltage amplitude calculation system based on full data weighting, including a voltage division module 201, a fitting amplitude module 202, a residual calculation module 203 and an amplitude calculation module 204.

[0121] The voltage division module 201 is used to collect multiple voltage signal points corresponding to each voltage step value from the acquired step wave quantum voltage signal, and obtain a time series data group corresponding to each voltage step value.

[0122] The fitting amplitude module 202 is used to obtain the fundamental Fourier coefficients corresponding to each time series data group according to the preset fundamental Fourier matrix, and to obtain the fitting fundamental amplitude corresponding to each time series data group according to the fundamental Fourier coefficients.

[0123] The residual calculation module 203 is used to obtain the sinusoidal fitted voltage value corresponding to each voltage signal point according to the fitted fundamental amplitude, so as to obtain the residual data group corresponding to each time series data group according to the sinusoidal fitted voltage value and the voltage signal point.

[0124] The amplitude calculation module 204 is used to obtain the weighting coefficient corresponding to each voltage step value according to the residual data group, and to obtain the fundamental amplitude corresponding to the step wave quantum voltage signal according to the weighting coefficient and the fitted fundamental amplitude corresponding to each time series data group.

[0125] It is understood that the above-described device embodiments correspond to the method embodiments of the present invention, and can implement the voltage amplitude calculation method based on full data weighting provided by any of the above-described method embodiments of the present invention.

[0126] It should be noted that the device embodiments described above are merely illustrative, and some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can specifically be implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0127] This embodiment provides a voltage amplitude calculation method and system based on full data weighting, which differs from previous sinusoidal voltage calibration methods. It overcomes the limitations of traditional methods that require manual setting of criteria to distinguish between transition and stable regions, eliminating measurement uncertainty introduced by improper threshold settings (too high thresholds cause interference in the transition region, too low thresholds result in loss of effective data). The method and system do not require algorithmic design for identifying transition and stable regions. Automatic optimization is achieved through adaptive methods and data-driven approaches, utilizing all step data. This avoids increased uncertainty caused by excessively high or low threshold settings during identification. Furthermore, the inverse variance weighting principle from statistical estimation theory is applied to weight the data at each step position. This weighting assigns weights to all data, representing the contribution of each position's data to the fitting process. For the identified stable and transition region data, the stable region data has a larger weight, while the transition region data has a smaller weight. This weighting calculation enables more efficient utilization of the full sampling data of each quantum voltage step in the PJVS output step wave quantum voltage signal, thereby achieving more accurate measurement and calibration of the sinusoidal voltage signal.

[0128] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for calculating voltage amplitude based on full data weighting, characterized in that, include: Multiple voltage signal points corresponding to each voltage step value are collected from the acquired step wave quantum voltage signal to obtain a time series data group corresponding to each voltage step value; The fundamental Fourier coefficients corresponding to each time series data group are obtained according to the preset fundamental Fourier matrix, and the fitted fundamental amplitude corresponding to each time series data group is obtained according to the fundamental Fourier coefficients. Based on the amplitude of the fitted fundamental wave, obtain the sinusoidal fitted voltage value corresponding to each voltage signal point, and obtain the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point; The weighting coefficients corresponding to each voltage step value are obtained from the residual data set, and the fundamental amplitude of the stepped quantum voltage signal is obtained from the weighting coefficients and the fitted fundamental amplitude of each time series data set.

2. The voltage amplitude calculation method based on full data weighting according to claim 1, characterized in that, The process of acquiring multiple data points corresponding to each voltage step value from the obtained step wave quantum voltage signal to obtain a time-series data group corresponding to each voltage step value includes: The sinusoidal stepped quantum voltage signal output by PJVS is calibrated to obtain the stepped quantum voltage signal to be processed. Multiple voltage step values ​​of the stepped wave quantum voltage signal are obtained, and multiple voltage signal points corresponding to each voltage step value are obtained from the stepped wave quantum voltage signal to construct a time series data group corresponding to the voltage step value; wherein, each voltage signal point includes a sampling time and a sampling voltage consistent with the voltage step value.

3. The voltage amplitude calculation method based on full data weighting according to claim 2, characterized in that, The calibration of the sinusoidal step wave quantum voltage signal output by PJVS to obtain the step wave quantum voltage signal to be processed includes: The voltage sample value of the sinusoidal stepped quantum voltage signal is obtained, and the voltage sample value is linearly fitted with the voltage setting value of the PJVS to obtain the gain coefficient and bias voltage. The sinusoidal stepped quantum voltage signal is corrected and compensated according to the gain coefficient and the bias voltage to obtain the stepped quantum voltage signal to be processed.

4. The voltage amplitude calculation method based on full data weighting according to claim 1, characterized in that, The step of obtaining the fundamental Fourier coefficients corresponding to each time series data group according to the preset fundamental Fourier matrix, and obtaining the fitted fundamental amplitude value corresponding to each time series data group according to the fundamental Fourier coefficients, includes: For any one of the aforementioned time-series data groups; The number of voltage signal points in the time series data group is obtained, and the characteristic fundamental Fourier matrix corresponding to the time series data group is obtained according to the number and the preset fundamental Fourier matrix; wherein, the fundamental Fourier matrix is ​​the Fourier matrix corresponding to the fundamental obtained after fitting the time series data group. The time series data set is converted into a time series data matrix, and the time series data matrix is ​​multiplied by the characteristic fundamental Fourier matrix to obtain the fundamental Fourier coefficients corresponding to the time series data set; wherein, the fundamental Fourier coefficients are the Fourier coefficients corresponding to the fundamental obtained after fitting the time series data set. The fitted fundamental amplitude value corresponding to the time series data group is obtained based on the fundamental Fourier coefficients.

5. The voltage amplitude calculation method based on full data weighting according to claim 4, characterized in that, The expression for calculating the amplitude of the fitted fundamental wave is as follows: YF=C C = [a, b] Wherein, Y represents the time-series data matrix corresponding to the time-series data group; F represents the fundamental Fourier matrix; C represents the fundamental coefficient matrix composed of the fundamental Fourier coefficients; N1 represents the number of voltage signal points in the time-series data group; a and b represent the fundamental Fourier coefficients; and A... i The a represents the fitted basis amplitude value corresponding to the i-th time series data group; i b i This represents the fundamental Fourier coefficient corresponding to the i-th time series data group.

6. The voltage amplitude calculation method based on full data weighting according to claim 4, characterized in that, The step of obtaining the sinusoidal fitted voltage value corresponding to each voltage signal point based on the fitted fundamental amplitude, and obtaining the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point, includes: Obtain the signal frequency of the stepped-wave quantum voltage signal; For any one of the aforementioned time-series data groups; Phase-locked loop is applied to the timing data group to obtain the corresponding phase. Based on the phase, the fitted fundamental amplitude and the signal frequency of the time series data group, a sine fit is performed on each voltage signal point to obtain the sine fitted voltage value corresponding to each voltage signal point. The difference between each sinusoidal fitted voltage value and the voltage step value corresponding to the time series data group is obtained respectively, so as to obtain the residual data group corresponding to the time series data group based on the difference.

7. The voltage amplitude calculation method based on full data weighting according to claim 6, characterized in that, The expression for calculating the sinusoidal fitted voltage value is as follows: U i,j (t)=A i sin(2πft+φ i )+e Wherein, the U i,j (t) represents the sinusoidal fitted voltage value corresponding to the j-th voltage signal point in the i-th time series data group; t represents the sampling time corresponding to the j-th voltage signal point in the i-th time series data group; f represents the signal frequency; φ i The ε represents the phase corresponding to the i-th time series data group; the ε represents the residual term.

8. The voltage amplitude calculation method based on full data weighting according to claim 6, characterized in that, The step of obtaining the weighting coefficients corresponding to each voltage step value based on the residual data set, and obtaining the fundamental amplitude of the stepped quantum voltage signal based on the weighting coefficients and the fitted fundamental amplitude of each time series data set, includes: For any given voltage step value, calculate the standard deviation corresponding to the voltage step value based on the residual data set corresponding to the voltage step value, and obtain the weighting coefficient corresponding to the voltage step value based on the standard deviation. Based on the weighting coefficients and fitted fundamental amplitude values ​​corresponding to each voltage step value, the fundamental amplitude value corresponding to the stepped quantum voltage signal is obtained through a weighted average algorithm.

9. The voltage amplitude calculation method based on full data weighting according to claim 8, characterized in that, The formula for calculating the fundamental frequency amplitude is as follows: Wherein, A represents the fundamental amplitude corresponding to the stepped quantum voltage signal; w i The weighting coefficients represent the voltage step values ​​corresponding to the i-th time series data group; M represents the number of voltage step values; σ i The standard deviation of the voltage step value corresponding to the i-th time series data group; the U i This represents the voltage step value corresponding to the i-th time series data group.

10. A voltage amplitude calculation system based on full data weighting, characterized in that, It includes a voltage division module, a fitting amplitude module, a residual calculation module, and an amplitude calculation module; The voltage division module is used to collect multiple voltage signal points corresponding to each voltage step value from the acquired step wave quantum voltage signal, and obtain the time series data group corresponding to each voltage step value; The fitting amplitude module is used to obtain the fundamental Fourier coefficients corresponding to each time series data group according to the preset fundamental Fourier matrix, and to obtain the fitting fundamental amplitude corresponding to each time series data group according to the fundamental Fourier coefficients. The residual calculation module is used to obtain the sinusoidal fitted voltage value corresponding to each voltage signal point based on the fitted fundamental amplitude value, so as to obtain the residual data group corresponding to each time series data group based on the sinusoidal fitted voltage value and the voltage signal point; The amplitude calculation module is used to obtain the weighting coefficient corresponding to each voltage step value based on the residual data group, and to obtain the fundamental amplitude corresponding to the step wave quantum voltage signal based on the weighting coefficient and the fitted fundamental amplitude corresponding to each time series data group.

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