A Time Scale Fusion Method of Complementary Wavelet Transform

Abstract

The present application belongs to the field of time-frequency technology. The present application provides a time scale fusion method of complementary wavelet transform. The disclosed embodiment can decompose the atomic time into a combination of a series of wavelet functions, effectively extract the frequency domain and time domain localization features of the same atomic time or different atomic times, and then perform atomic time fusion based on the multi-scale and multi-feature analysis results, which is reasonable and effective, and further reduces the influence of experience and subjective factors. Extracting high-frequency information can achieve noise reduction to a certain extent, retain actual useful information, further reduce the disturbance of noise to atomic time, and thus enhance the stability of atomic time.

Description

Technical Field

[0001] The disclosed embodiments relate to the field of time-frequency technology, and in particular to a time-scale fusion method of complementary wavelet transform. Background Art

[0002] Atomic time is a more stable, uniform and reliable time standard compared to a single atomic clock, and is one of the most important contents in the research of timekeeping technology. The calculation of atomic time can provide a reference for the long-term and short-term control of the frequency source of the master clock of the timekeeping system, and also provide a reference for the abnormal detection of atomic clocks. Common atomic time calculation methods include ALGOS algorithm, AT1 algorithm, Kalman algorithm, ARIMA algorithm, etc.

[0003] A single atomic time calculation model often cannot simultaneously meet the needs of improving the short-term and long-term stability of atomic time. Therefore, it is necessary to study atomic time fusion methods. In the study of fused atomic time, Jiang Meng, Bai Shanshan and other scholars conducted atomic time fusion research based on the Vondark-Cepek method. One is based on the atomic time of the fusion of hydrogen and cesium atomic clocks, and the other is based on the atomic time of the fusion of cesium fountain clocks and hydrogen atomic clocks. The study pointed out that the traditional fusion method uses the same method to weight data from different types of atomic clocks, which has certain limitations for the optimal use of the long-term and short-term stability of different types of atomic clocks. The Vondrak-Cepek combined filter is used to carry out atomic time calculations, and the atomic time of the combination of all-cesium clocks and all-hydrogen clocks or hydrogen clocks and cesium fountain clocks is weighted according to different smoothing factors, which can improve the overall atomic time performance.

[0004] Conventional atomic time fusion methods that require determination of smoothing factors often calculate smoothing factors for phase and frequency separately. In this fusion method, the phase smoothing factor has a greater impact, while the frequency smoothing factor has a smaller impact. The essence of this fusion is to assign weights, which has a certain subjective tendency.

[0005] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0006] It should be noted that this section is intended to provide background or context for the technical solutions of the present disclosure stated in the claims. The description herein is not admitted to be prior art by virtue of being included in this section. Summary of the invention

[0007] The purpose of the embodiments of the present disclosure is to provide a time scale fusion method of complementary wavelet transform, thereby overcoming one or more problems caused by the limitations and defects of related technologies at least to a certain extent.

[0008] According to an embodiment of the present disclosure, a time scale fusion method of complementary wavelet transform is provided, the method comprising:

[0009] Acquire atomic clock comparison data and preprocess the atomic clock comparison data;

[0010] Two different types of time scale models are used to perform time scale calculations on the preprocessed atomic clock comparison data to obtain the first atomic time and the second atomic time;

[0011] The ALLAN variance was calculated for the first atomic time and the second atomic time, respectively, to evaluate the stability of the first atomic time and the stability of the second atomic time;

[0012] Determine a wavelet function and a wavelet decomposition layer number, and perform wavelet decomposition on the first atomic time and the second atomic time respectively to obtain a first high-frequency coefficient and a first low-frequency coefficient of the first atomic time, and a second high-frequency coefficient and a second low-frequency coefficient of the second atomic time;

[0013] Based on the stability of the first atomic hour and the stability of the second atomic hour, combining the first high frequency coefficient, the second high frequency coefficient, the first low frequency coefficient and the second low frequency coefficient to obtain a third high frequency coefficient and a third low frequency coefficient;

[0014] Wavelet reconstruction is performed based on the wavelet function, the third high frequency coefficient and the third low frequency coefficient to obtain the fusion atomic time and evaluate the stability of the fusion atomic time.

[0015] Furthermore, the step of obtaining atomic clock comparison data and preprocessing the atomic clock comparison data includes:

[0016] The integrity of the atomic clock comparison data is checked according to the time scale. If the time scale is missing, the data is missing. The missing atomic clock comparison data is obtained by fitting a linear model based on historical data.

[0017] Anomaly detection is performed on the atomic clock comparison data. When the absolute residual difference between the atomic clock comparison data and the fitting data is greater than 3 When , the atomic clock comparison data is judged to be abnormal, and the abnormal data is replaced by the fitting data; is the variance of the residuals of the atomic clock comparison data and the fitting data.

[0018] Further, the step of using two different types of time scale models to perform time scale calculation on the preprocessed atomic clock comparison data to obtain the first atomic time and the second atomic time includes:

[0019] selecting two first time scale models and second time scale models with different stability characteristics;

[0020] Setting a calculation cycle, and using the first time scale model to perform atomic clock calculation on the preprocessed time scale comparison data to obtain the first atomic time;

[0021] The second time scale model is used to perform time scale calculation on the preprocessed atomic clock comparison data to obtain the second atomic time.

[0022] Furthermore, the first atomic time model is an AT1 algorithm based on short-term stability optimization, and the second atomic time model is an ALGOS-like algorithm based on long-term stability optimization.

[0023] Furthermore, the expression of ALLAN variance is:

[0024]

[0025] in, is the ALLAN variance, is the sampling interval, In a sampling period is the number of samples in the sampling interval, For the i Phase data interval, For the i +1 phase data interval, For the i +2 phase data intervals, is the number of consecutive measurements.

[0026] Further, the steps of determining the wavelet function and the wavelet decomposition layer number, and performing wavelet decomposition on the first atomic time and the second atomic time respectively to obtain the first high-frequency coefficient and the first low-frequency coefficient of the first atomic time, and the second high-frequency coefficient and the second low-frequency coefficient of the second atomic time include:

[0027] Select biorwavf wavelet function as wavelet function;

[0028] The traversal method is used to determine the optimal number of wavelet decomposition layers;

[0029] The first atomic time and the second atomic time are decomposed by using discrete wavelet multi-scale to obtain a first high frequency coefficient and a first low frequency coefficient of the first atomic time, and a second high frequency coefficient and a second low frequency coefficient of the second atomic time.

[0030] Furthermore, the expression of discrete wavelet multi-scale decomposition is:

[0031]

[0032] in, For atoms, i =1 is the first atomic hour, i =2 is the second atomic time; is the biorwavf wavelet function, is the scale parameter of the biorwavf wavelet function, is the translation parameter of the biorwavf wavelet function, t for t time.

[0033] Further, based on the stability of the first atomic hour and the stability of the second atomic hour, the step of combining the first high frequency coefficient, the second high frequency coefficient, the first low frequency coefficient and the second low frequency coefficient to obtain the third high frequency coefficient and the third low frequency coefficient includes:

[0034] Based on the stability of the first atomic time and the stability of the second atomic time, selecting the coefficient with better long-term stability from the first low-frequency coefficient and the second low-frequency coefficient as the third low-frequency coefficient;

[0035] The first high frequency coefficient and the second high frequency coefficient are fused using wavelet variance to obtain a third high frequency coefficient.

[0036] Furthermore, the expression of the third high frequency coefficient is:

[0037]

[0038] in, is the first high frequency coefficient, is the second high frequency coefficient, weight normalization model , , is the number of high-frequency coefficients, n is the number of wavelet decomposition layers, D is the number of time scale models.

[0039] The technical solution provided by the embodiments of the present disclosure may have the following beneficial effects:

[0040] In the embodiments of the present disclosure, through the time scale fusion method of the complementary wavelet transform, on the one hand, the atomic time is decomposed into a combination of a series of wavelet functions, and the frequency domain and time domain localization features of the same atomic time or different atomic times are effectively extracted, and then the atomic time is fused according to the multi-scale and multi-feature analysis results, which is reasonable and effective, and further reduces the influence of experience and subjective factors. Extracting high-frequency information can achieve noise reduction to a certain extent, retain actual useful information, and further reduce the disturbance of noise to atomic time, thereby enhancing the stability of atomic time. On the other hand, the selection of smoothing factors is not considered to avoid the fusion deviation caused by the absolute advantage of a single model. The uncertainty of the system and the subjectivity of the selection of model parameters are reduced, and the advantages of the extracted data themselves are emphasized. The short-term stability of the fused atomic time result obtained is close to and better than that of a single model with good short-term stability, and the long-term stability is better than that of any single model atomic time. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0042] Figure 1 A diagram showing the steps of a time scale fusion method of complementary wavelet transform in an exemplary embodiment of the present disclosure;

[0043] Figure 2 A specific flow chart showing a time scale fusion method of complementary wavelet transform in an exemplary embodiment of the present disclosure;

[0044] Figure 3 A schematic diagram showing the atomic time TA1 obtained by the ALGOS-like model in an exemplary embodiment of the present disclosure;

[0045] Figure 4 A schematic diagram showing the atomic time TA2 obtained by the AT1 atomic time model in an exemplary embodiment of the present disclosure;

[0046] Figure 5 A diagram showing a stability comparison result of the atomic time TA1, the atomic time TA2 and the fusion atomic time in an exemplary embodiment of the present disclosure;

[0047] Figure 6 A schematic diagram showing TAw when fusing atoms in an exemplary embodiment of the present disclosure. DETAILED DESCRIPTION

[0048] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0049] In addition, the accompanying drawings are only schematic illustrations of the embodiments of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated descriptions will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0050] This example embodiment provides a time scale fusion method for complementary wavelet transform. Figure 1 As shown in , the time scale fusion method of complementary wavelet transform may include: step S101 to step S106.

[0051] Step S101: Acquire atomic clock comparison data and pre-process the atomic clock comparison data;

[0052] Step S102: using two different types of time scale models to perform time scale calculation on the preprocessed atomic clock comparison data to obtain a first atomic time and a second atomic time;

[0053] Step S103: calculating the ALLAN variance for the first atomic time and the second atomic time respectively, so as to evaluate the stability of the first atomic time and the stability of the second atomic time;

[0054] Step S104: determining a wavelet function and a wavelet decomposition layer number, and performing wavelet decomposition on the first atomic time and the second atomic time respectively to obtain a first high-frequency coefficient and a first low-frequency coefficient of the first atomic time, and a second high-frequency coefficient and a second low-frequency coefficient of the second atomic time;

[0055] Step S105: Based on the stability of the first atomic time and the stability of the second atomic time, the first high frequency coefficient, the second high frequency coefficient, the first low frequency coefficient and the second low frequency coefficient are combined to obtain a third high frequency coefficient and a third low frequency coefficient;

[0056] Step S106: performing wavelet reconstruction based on the wavelet function, the third high frequency coefficient and the third low frequency coefficient to obtain the fused atomic time and evaluate the stability of the fused atomic time.

[0057] Through the time scale fusion method of complementary wavelet transform, on the one hand, the atomic time is decomposed into a combination of a series of wavelet functions, and the frequency domain and time domain localization features of the same atomic time or different atomic times are effectively extracted. Then, the atomic time is fused according to the multi-scale and multi-feature analysis results, which is reasonable and effective, and further reduces the influence of experience and subjective factors. The extraction of high-frequency information can achieve noise reduction to a certain extent, retain actual useful information, and further reduce the disturbance of noise to atomic time, thereby enhancing the stability of atomic time. On the other hand, the selection of smoothing factors is not considered to avoid the fusion deviation caused by the absolute advantage of a single model. The uncertainty of the system and the subjectivity of the selection of model parameters are reduced, and the advantages of the extracted data themselves are emphasized. The short-term stability of the fused atomic time result is close to and better than that of a single model with good short-term stability, and the long-term stability is better than that of any single model atomic time.

[0058] Next, we will refer to Figures 1 to 6 Each step of the time scale fusion method of complementary wavelet transform in this example implementation is described in more detail.

[0059] In step S101, atomic clock comparison data is acquired and preprocessed.

[0060] Specifically, the integrity of the atomic clock comparison data is checked according to the time scale. If the time scale is missing, the data is missing. The missing atomic clock comparison data is obtained by fitting a linear model based on historical data.

[0061] Anomaly detection is performed on the atomic clock comparison data. When the absolute residual difference between the atomic clock comparison data and the fitting data is greater than 3 When , the atomic clock comparison data is judged to be abnormal, and the abnormal data is replaced by the fitting data; is the variance of the residuals of the atomic clock comparison data and the fitting data.

[0062] More specifically, the experimental data (i.e. the atomic clock comparison data of the timekeeping system) is preprocessed. This includes two aspects: one is data integrity check, which is carried out based on the time scale. If the time scale is missing, the data is missing. The missing data is fitted based on a linear model based on historical data. The other is data anomaly detection. When the absolute value residual of the measured data and the fitted data is greater than 3 (In the normal distribution table, the data is within ±3 The probability is 99.73%), which is considered abnormal. is the variance of the residuals of the measured and fitted data.

[0063] In step S102, two different types of time scale models are used to perform time scale calculations on the preprocessed atomic clock comparison data to obtain a first atomic time and a second atomic time.

[0064] Specifically, two first time scale models and second time scale models with different stability characteristics are selected; a calculation cycle is set, and the first time scale model is used to perform time scale calculation on the preprocessed atomic clock comparison data to obtain the first atomic time; and the second time scale model is used to perform time scale calculation on the preprocessed atomic clock comparison data to obtain the second atomic time.

[0065] More specifically, the atomic time is calculated based on the preprocessed experimental data. First, two atomic time models are selected to calculate the atomic time separately. It should be noted here that the two atomic time models need to have different characteristics, and fusion is meaningful. If the performance is similar, the fusion effect cannot be reflected. Therefore, taking AT1 and ALGOS-like methods as examples, the AT1 atomic time algorithm, its rate and weight parameters are calculated based on the exponential average of the atomic clock's short-term data and iterative prediction, so the algorithm as a whole has good short-term stability. For the ALGOS-like algorithm, the calculation of rate and weight takes into account the long-term changes of the atomic clock, so the algorithm as a whole shows good long-term stability. The overall calculation ideas of AT1 and ALGOS-like are weighted average, and the principles are as follows:

[0066] (1)

[0067] in, , Represents atomic clock The difference with the integrated atom, Indicates the clock He Zhong Phase difference data, Indicates the number of atomic clocks, No. The weight of the atomic clock, the clock error prediction term is: ,in express time, is the frequency drift term, That is, frequency prediction. To correspond to the comparison period of the timekeeping system (1 hour interval), the calculation interval of the exponential AT1 atomic time is set to 1 hour, and the calculation period of the ALGOS-like algorithm is also 1 hour. The first atomic time TA1 is obtained based on the ALGOS-like algorithm, and the first atomic time TA2 is obtained based on the AT1 algorithm.

[0068] In step S103, ALLAN variance is calculated for the first atomic time and the second atomic time respectively to evaluate the stability of the first atomic time and the stability of the second atomic time.

[0069] Specifically, the ALLAN variance is calculated for the two atomic times and the stability is analyzed. The ALLAN variance calculation formula is as follows:

[0070] (2)

[0071] in, It is Phase data interval, Indicates the number of consecutive measurements. is the sampling interval.

[0072] In step S104, the wavelet function and the wavelet decomposition layer number are determined, and the first atomic time and the second atomic time are respectively subjected to wavelet decomposition to obtain the first high frequency coefficient and the first low frequency coefficient of the first atomic time, and the second high frequency coefficient and the second low frequency coefficient of the second atomic time.

[0073] Specifically, the biorwavf wavelet function is selected as the wavelet function; the traversal method is used to determine the optimal number of wavelet decomposition layers; the discrete wavelet multi-scale decomposition is used to decompose the first atomic time and the second atomic time to obtain the first high-frequency coefficient and the first low-frequency coefficient of the first atomic time, and the second high-frequency coefficient and the second low-frequency coefficient of the second atomic time.

[0074] More specifically, the first atomic time TA1 and the second atomic time TA2 are decomposed by wavelet multiscale. First, the wavelet function to be selected is determined. Daubechies (dbN) wavelet, Symlet (symN) wavelet and Biorwavf (bior N,M) are commonly used wavelet functions, which perform well in denoising. The essence of our main research on atomic time is the atomic clock noise relationship, and these three wavelet functions are initially selected as research objects. In theory, the symN wavelet is an improvement on the dbN wavelet (lack of symmetry), with better symmetry, which can reduce the phase distortion when analyzing and reconstructing the signal to a certain extent. However, the bior N,M wavelet is a biorthogonal wavelet, which has better symmetry and linear phase characteristics than symN, and avoids phase distortion under reconstruction conditions. It is suitable for data scenarios under linear phase. The commonly used analysis data of the timekeeping system is phase data. Therefore, the bior N,M wavelet has good applicability, and the biorwavf wavelet function is finally selected as the research basis.

[0075] As for the number of decomposition layers, the more decomposition layers there are, the finer the decomposition will be. However, this is not always the case, as it is affected by the distortion of high-frequency coefficients and the limitation of the length of experimental data (usually , is the length of the experimental data, Indicates the number of decomposition layers), and the impact of real-time performance needs to be considered. This application uses the traversal method to determine that the optimal number of decomposition layers is 7 layers.

[0076] Perform wavelet decomposition. Since atomic time is discrete data, the two atomic times obtained are Using discrete wavelet multi-scale decomposition, the discretized wavelet coefficients are obtained as follows:

[0077] (3)

[0078] in, Represents discrete wavelet function, here is the biorwavf function obtained by analysis, where , They represent the scale parameter and translation parameter of the wavelet function respectively.

[0079] In step S105, based on the stability of the first atomic hour and the stability of the second atomic hour, the first high frequency coefficient, the second high frequency coefficient, the first low frequency coefficient and the second low frequency coefficient are combined to obtain a third high frequency coefficient and a third low frequency coefficient.

[0080] Specifically, based on the stability of the first atomic time and the stability of the second atomic time, the first low-frequency coefficient and the second low-frequency coefficient with good long-term stability are selected as the third low-frequency coefficient; the first high-frequency coefficient and the second high-frequency coefficient are fused using wavelet variance to obtain the third high-frequency coefficient.

[0081] More specifically, the high-frequency and low-frequency coefficients of the wavelet function are extracted and wavelet fusion is performed. In order to provide more comprehensive detail information for the fused atomic time, the fused high-frequency coefficients are obtained by weighted combination of the wavelet variance of the high-frequency coefficients of the first atomic time TA1 and the second atomic time TA2. Assume that the high-frequency coefficients of the first atomic time TA1 and the second atomic time TA2 are , , then the fused high-frequency coefficient (ie, the third high-frequency coefficient) is expressed as:

[0082] (4)

[0083] Where D represents the number of models involved in the fusion. There are two atomic time models here. . In the formula, the weight normalization model is as follows:

[0084] (5)

[0085] (6)

[0086] in, Indicates the number of high-frequency coefficients.

[0087] Assuming that TA1 has good long-term stability, it means that its overall trend is relatively good. By extracting and reconstructing low-frequency coefficients, the key information of the signal can be retained while removing noise and redundant information. Therefore, its low-frequency coefficients are used as the low-frequency coefficients of the reconstructed signal. Thus, a new wavelet structure is obtained.

[0088] In step S106, wavelet reconstruction is performed based on the wavelet function, the third high frequency coefficient and the third low frequency coefficient to obtain the fused atomic time, and the stability of the fused atomic time is evaluated.

[0089] Specifically, based on the new wavelet structure, wavelet multi-scale reconstruction is performed using the same wavelet function as the wavelet decomposition.

[0090] The stability index of the fused atom after reconstruction (i.e., after fusion) is analyzed and compared with the stability index of the single atom.

[0091] In a specific embodiment, the measured phase comparison data of several hydrogen atomic clocks in the timekeeping laboratory for one month are arbitrarily selected as the research object. First, the measured data are preprocessed, the time scale is observed, and the data is intact. Then, outlier detection is performed. Since hydrogen atomic clocks often have frequency drift terms, quadratic least squares fitting is used to perform outlier detection and replacement. When the absolute value residual of the measured data and the fitted data is greater than 3 times the variance of the residual of the measured data and the fitted data, it is judged as abnormal and replaced with the quadratic least squares fitting value. Then the calculation of atomic time is started. The flowchart of the whole method is as follows. Figure 2 shown.

[0092] Based on the processed data, two atomic time models are selected to calculate the atomic time. One is the ALGOS-like model. The calculated atomic time TA1 is as follows: Figure 3 As shown, it can be seen that the short-term fluctuation of TA1 atomic time is large, but the overall trend term is small; the other is the AT1 atomic time model, and the atomic time TA2 is calculated, such as Figure 4 As shown, it can be seen that TA2 has a small short-term fluctuation, so it is relatively smooth. This is the result of the exponential filtering effect of its calculation model. However, as time goes by, it has an obvious trend term. The ALLAN variance of the two atomic times is calculated using formula (2) respectively, as follows: Figure 5 The middle icon shows the lines of atomic time TA1 (star dotted line) and atomic time TA2 (circle dotted line). It can be seen that the short-term stability of atomic time TA1 is worse than that of atomic time TA2, but its long-term stability is better than that of atomic time TA2. Figure 3 and Figure 4 The analysis results are consistent.

[0093] Formula (3) is used to perform wavelet multi-scale decomposition on atomic time TA1 and atomic time TA2. Here, bior wavelet and 7-scale decomposition are used to obtain the high-frequency coefficient and low-frequency coefficient of atomic time TA1 and the high-frequency coefficient and low-frequency coefficient of atomic time TA2 respectively.

[0094] The high and low frequency coefficients of the wavelet function are extracted. Atomic time TA1 has good long-term stability. Its low frequency coefficient is extracted as the fused low frequency coefficient. At the same time, the high frequency coefficients of atomic time TA1 and atomic time TA2 are extracted and fused using wavelet variance. That is, formulas (4), (5) and (6) are used to calculate the combined high frequency coefficient as the fused high frequency coefficient.

[0095] The obtained fused low-frequency coefficients and high-frequency coefficients are combined into a new wavelet structure, and the bior wavelet is used for wavelet reconstruction to obtain the fused atomic time TAw, such as Figure 6 As shown in . It can be seen that when fusing atoms, TAw has small short-term fluctuations and a small overall trend term.

[0096] When fusion atoms are involved, the ALLAN variance is calculated using formula (2), as follows: Figure 5 (Triangle dotted line), the smaller the ALLAN variance is, the higher the stability is. The short-term stability of fusion atomic time TAw is close to and better than atomic time TA2, and the long-term stability is better than any single atomic time model.

[0097] Through the time scale fusion method of complementary wavelet transform, on the one hand, the atomic time is decomposed into a combination of a series of wavelet functions, and the frequency domain and time domain localization features of the same atomic time or different atomic times are effectively extracted. Then, the atomic time is fused according to the multi-scale and multi-feature analysis results, which is reasonable and effective, and further reduces the influence of experience and subjective factors. The extraction of high-frequency information can achieve noise reduction to a certain extent, retain actual useful information, and further reduce the disturbance of noise to atomic time, thereby enhancing the stability of atomic time. On the other hand, the selection of smoothing factors is not considered to avoid the fusion deviation caused by the absolute advantage of a single model. The uncertainty of the system and the subjectivity of the selection of model parameters are reduced, and the advantages of the extracted data themselves are emphasized. The short-term stability of the fused atomic time result is close to and better than that of a single model with good short-term stability, and the long-term stability is better than that of any single model atomic time.

[0098] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0099] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0100] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A time scale fusion method of complementary wavelet transform, characterized in that: The method includes: Acquire atomic clock comparison data and preprocess the atomic clock comparison data; Two different types of time scale models are used to perform time scale calculations on the preprocessed atomic clock comparison data to obtain the first atomic time and the second atomic time; The ALLAN variance was calculated for the first atomic time and the second atomic time, respectively, to evaluate the stability of the first atomic time and the stability of the second atomic time; Determine a wavelet function and a wavelet decomposition layer number, and perform wavelet decomposition on the first atomic time and the second atomic time respectively to obtain a first high-frequency coefficient and a first low-frequency coefficient of the first atomic time, and a second high-frequency coefficient and a second low-frequency coefficient of the second atomic time; Based on the stability of the first atomic hour and the stability of the second atomic hour, combining the first high frequency coefficient, the second high frequency coefficient, the first low frequency coefficient and the second low frequency coefficient to obtain a third high frequency coefficient and a third low frequency coefficient; Wavelet reconstruction is performed based on the wavelet function, the third high frequency coefficient and the third low frequency coefficient to obtain the fusion atomic time and evaluate the stability of the fusion atomic time.

2. The time scale fusion method of complementary wavelet transform according to claim 1, characterized in that: The steps of obtaining atomic clock comparison data and preprocessing the atomic clock comparison data include: The integrity of the atomic clock comparison data is checked according to the time scale. If the time scale is missing, the data is missing. The missing atomic clock comparison data is obtained by fitting a linear model based on historical data. Anomaly detection is performed on the atomic clock comparison data. When the absolute residual difference between the atomic clock comparison data and the fitting data is greater than 3 When , the atomic clock comparison data is judged to be abnormal, and the abnormal data is replaced by the fitting data; is the variance of the residuals of the atomic clock comparison data and the fitting data.

3. The time scale fusion method of complementary wavelet transform according to claim 2 is characterized in that: The steps of using two different types of time scale models to perform time scale calculation on the pre-processed atomic clock comparison data to obtain the first atomic time and the second atomic time include: selecting two first time scale models and second time scale models with different stability characteristics; Setting a calculation cycle, and using the first time scale model to perform time scale calculation on the preprocessed atomic clock comparison data to obtain the first atomic time; The second time scale model is used to perform time scale calculation on the preprocessed atomic clock comparison data to obtain the second atomic time.

4. The time scale fusion method of complementary wavelet transform according to claim 3 is characterized in that: The first atomic time model is the AT1 algorithm based on short-term stability optimization, and the second atomic time model is the ALGOS-like algorithm based on long-term stability optimization.

5. The time scale fusion method of complementary wavelet transform according to claim 3 is characterized in that: The expression of ALLAN variance is: in, is the ALLAN variance, is the sampling interval, In a sampling period is the number of samples in the sampling interval, For the i Phase data interval, For the i +1 phase data interval, For the i +2 phase data intervals, is the number of consecutive measurements.

6. The time scale fusion method of complementary wavelet transform according to claim 5, characterized in that: The steps of determining a wavelet function and a wavelet decomposition layer number, and performing wavelet decomposition on the first atomic time and the second atomic time respectively to obtain a first high frequency coefficient and a first low frequency coefficient of the first atomic time, and a second high frequency coefficient and a second low frequency coefficient of the second atomic time, include: Select biorwavf wavelet function as wavelet function; The traversal method is used to determine the optimal number of wavelet decomposition layers; The first atomic time and the second atomic time are decomposed by using discrete wavelet multi-scale to obtain a first high frequency coefficient and a first low frequency coefficient of the first atomic time, and a second high frequency coefficient and a second low frequency coefficient of the second atomic time.

7. The time scale fusion method of complementary wavelet transform according to claim 6, characterized in that: The expression of discrete wavelet multi-scale decomposition is: in, For atoms, i =1 is the first atomic hour, i =2 is the second atomic time; is the biorwavf wavelet function, is the scale parameter of the biorwavf wavelet function, is the translation parameter of the biorwavf wavelet function, t for t time.

8. The time scale fusion method of complementary wavelet transform according to claim 7 is characterized in that: The step of combining the first high frequency coefficient, the second high frequency coefficient, the first low frequency coefficient and the second low frequency coefficient based on the stability of the first atomic hour and the stability of the second atomic hour to obtain the third high frequency coefficient and the third low frequency coefficient includes: Based on the stability of the first atomic time and the stability of the second atomic time, selecting the coefficient with better long-term stability from the first low-frequency coefficient and the second low-frequency coefficient as the third low-frequency coefficient; The first high frequency coefficient and the second high frequency coefficient are fused using wavelet variance to obtain a third high frequency coefficient.

9. The time scale fusion method of complementary wavelet transform according to claim 8, characterized in that: The expression of the third high frequency coefficient is: in, is the first high frequency coefficient, is the second high frequency coefficient, weight normalization model , , is the number of high-frequency coefficients, n is the number of wavelet decomposition layers, D is the number of time scale models.

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