Periodic signal modeling method, device, electronic device and storage medium

Abstract

The present application relates to the field of signal processing technology, and in particular to a modeling method, device, electronic device and storage medium for periodic signals, wherein the method comprises: obtaining a coordinate time series of a target navigation satellite system; preprocessing the coordinate time series to obtain a preprocessed coordinate time series, and correcting the preprocessed coordinate time series to obtain a corrected coordinate time series; estimating the corrected coordinate time series to obtain a sine coefficient of the periodic amplitude, a cosine coefficient of the periodic amplitude and a periodic frequency deviation; and decomposing the corrected coordinate time series to establish an initial harmonic model, and using a preset estimation strategy to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model, thereby solving the problem of systematic deviation caused by the empirical period length assumption in coordinate time series modeling, and improving the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

Description

Technical Field

[0001] The present application relates to the field of signal processing, and in particular to a method, device, electronic device and storage medium for modeling periodic signals. Background Art

[0002] Global Navigation Satellite System (GNSS) coordinate time series provide critical data support for the study of crustal deformation, post-glacial rebound, and surface loading effects by continuously recording millimeter-scale changes in the three-dimensional coordinates of observation stations. Traditional harmonic modeling methods typically treat seasonal signals (such as annual and semi-annual signals) as sinusoidal curves with fixed amplitudes and pre-set their period lengths to theoretical values ​​(such as 365.25 days and 182.5 days). However, actual geophysical processes (such as delayed response to hydrological loads and thermal expansion effects) can cause periodic signals to produce systematic frequency offsets (PO) and time-varying period lengths (PV).

[0003] While techniques such as singular spectrum analysis (SSA), Kalman filtering (KF), wavelet decomposition (WD), and Chebyshev polynomials (CP) can address the time-varying amplitude of periodic fluctuations (PAV), they still rely on empirically defined fixed period lengths. Mainstream GNSS data processing software (such as Hector, Cats, and est_noise) also default to fixed period values ​​of 365.25 days and 182.5 days. However, actual period lengths deviate significantly from these empirical values ​​(PO) and can vary dynamically over time (PV). For example, the actual period of an annual signal can be extended to 370-380 days due to delayed response to hydrological loads, while atmospheric effects can cause the standard deviation of its interannual fluctuations to reach 3 days. Furthermore, the aliasing effect of non-seasonal signals (e.g., periods of 351.2, 430, and 531 days) further complicates period modeling.

[0004] In summary, the limitations of the fixed-period assumption lead to two key problems: (1) Periodic offset (PO) leads to cumulative phase errors. Assuming a 28-year time series span, a PO of only 2 days can accumulate 56 days of phase deviation, resulting in serious errors in the estimation of the annual signal amplitude; (2) Periodic time variation (PV) distorts the noise statistics, leading to a systematic underestimation of the flicker noise spectral index κ, which in turn leads to a serious underestimation of the velocity field uncertainty. These problems are particularly prominent in sensitive areas such as the Greenland Ice Sheet, where the estimated post-glacial rebound rate can have an error of up to 0.8 mm / yr. The dynamic parameter modeling methods used in related technologies cannot adapt to the nonlinear characteristics of real geophysical processes, becoming a bottleneck for high-precision geodynamic research. Summary of the Invention

[0005] The present application provides a modeling method, device, electronic device and storage medium for periodic signals to solve the problem of systematic deviation caused by the empirical period length assumption in coordinate time series modeling, establish a harmonic model that takes into account the frequency offset and time-varying period length of the periodic signal, and significantly improve the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

[0006] The first embodiment of the present application provides a method for modeling a periodic signal, comprising the following steps:

[0007] Obtain the coordinate time series of the target navigation satellite system;

[0008] Preprocessing the coordinate time series to obtain a preprocessed coordinate time series, and correcting the preprocessed coordinate time series to obtain a corrected coordinate time series;

[0009] Using a preset weighted least squares method to estimate the corrected coordinate time series to obtain a sine coefficient of the periodic amplitude, a cosine coefficient of the periodic amplitude, and a periodic frequency deviation;

[0010] The sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation are decomposed, and an initial harmonic model is established based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the decomposed periodic frequency, and a preset estimation strategy is used to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model.

[0011] Optionally, in some embodiments, preprocessing the coordinate time series to obtain a preprocessed coordinate time series includes:

[0012] Determining whether there are abnormal values ​​and / or missing values ​​in the coordinate time series;

[0013] If the abnormal values ​​and / or the missing values ​​exist in the coordinate time series, the abnormal values ​​are cleared and / or the missing values ​​are interpolated to obtain an initial coordinate time series;

[0014] A step signal and a trend signal in the initial coordinate time series are identified, and the step signal and the trend signal are removed to obtain the preprocessed coordinate time series.

[0015] Optionally, in some embodiments, the initial harmonic model is:

[0016]

[0017] in, is the initial harmonic model, is the long-term mean of the sinusoidal coefficient of the periodic amplitude, is a zero-mean random perturbation of the sinusoidal coefficient of the periodic amplitude, is the empirical value of the periodic angular frequency, is the deviation of the periodic angular frequency, is the disturbance of periodic angular frequency, For time, is the long-term mean of the cosine coefficient of the periodic amplitude, is a zero-mean random perturbation of the cosine coefficient of the periodic amplitude.

[0018] Optionally, in some embodiments, the parameters to be estimated include: static parameters, time-varying parameters and noise parameters.

[0019] Optionally, in some embodiments, after establishing the final harmonic model according to the estimation result and the initial harmonic model, the method further includes:

[0020] Integrating multi-source geophysical time series data, and performing modeling based on the multi-source geophysical time series data to obtain a geophysical model;

[0021] A time-lag cross-correlation function is calculated based on the final harmonic model and the geophysical model, and a target analysis result is generated based on the time-lag cross-correlation function.

[0022] A second embodiment of the present application provides a periodic signal modeling device, including:

[0023] An acquisition module is used to obtain the coordinate time series of the target navigation satellite system;

[0024] a processing module, configured to preprocess the coordinate time series to obtain a preprocessed coordinate time series, and correct the preprocessed coordinate time series to obtain a corrected coordinate time series;

[0025] An estimation module, configured to estimate the corrected coordinate time series using a preset weighted least squares method to obtain a sine coefficient of the periodic amplitude, a cosine coefficient of the periodic amplitude, and a periodic frequency deviation;

[0026] Establish a module for decomposing the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation, and establish an initial harmonic model based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the decomposed periodic frequency, and use a preset estimation strategy to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model.

[0027] Optionally, in some embodiments, the processing module includes:

[0028] a judgment unit, configured to judge whether there are abnormal values ​​and / or missing values ​​in the coordinate time series;

[0029] an interpolation unit, configured to, when the abnormal values ​​and / or the missing values ​​exist in the coordinate time series, remove the abnormal values ​​and / or interpolate the missing values ​​to obtain an initial coordinate time series;

[0030] The identification unit is used to identify the step signal and the trend signal in the initial coordinate time series, and remove the step signal and the trend signal to obtain the preprocessed coordinate time series.

[0031] Optionally, in some embodiments, the initial harmonic model is:

[0032]

[0033] in, is the initial harmonic model, is the long-term mean of the sinusoidal coefficient of the periodic amplitude, is a zero-mean random perturbation of the sinusoidal coefficient of the periodic amplitude, is the empirical value of the periodic angular frequency, is the deviation of the periodic angular frequency, is the disturbance of periodic angular frequency, For time, is the long-term mean of the cosine coefficient of the periodic amplitude, is a zero-mean random perturbation of the cosine coefficient of the periodic amplitude.

[0034] Optionally, in some embodiments, the parameters to be estimated include: static parameters, time-varying parameters and noise parameters.

[0035] Optionally, in some embodiments, after establishing the final harmonic model according to the estimation result and the initial harmonic model, the establishing module includes:

[0036] a modeling unit, configured to integrate multi-source geophysical time series data and perform modeling based on the multi-source geophysical time series data to obtain a geophysical model;

[0037] A generating unit is configured to calculate a time-delay cross-correlation function based on the final harmonic model and the geophysical model, and generate a target analysis result based on the time-delay cross-correlation function.

[0038] The third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the periodic signal modeling method as described in the above embodiment.

[0039] The fourth aspect of the present application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the periodic signal modeling method as described in the above embodiment.

[0040] Thus, by obtaining the coordinate time series of the target navigation satellite system and preprocessing the coordinate time series to obtain a preprocessed coordinate time series, the preprocessed coordinate time series is corrected to obtain a corrected coordinate time series, and the corrected coordinate time series is estimated using a preset weighted least squares method to obtain the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude, and the periodic frequency deviation of the periodic amplitude, and then decomposed. An initial harmonic model is established based on the decomposed sine coefficient of the periodic amplitude, the decomposed cosine coefficient of the periodic amplitude, and the decomposed periodic frequency, and the parameters to be estimated of the initial harmonic model are estimated using a preset estimation strategy to obtain an estimation result, and a final harmonic model is established based on the estimation result and the initial harmonic model. Thus, the problem of systematic deviation caused by the empirical cycle length assumption in coordinate time series modeling is solved, and a harmonic model that takes into account the frequency offset and time-varying cycle length of the periodic signal is established, significantly improving the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

[0041] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0043] Figure 1 A flowchart of a method for modeling a periodic signal according to an embodiment of the present application;

[0044] Figure 2 A schematic diagram of the principle of a modeling method for a periodic signal provided according to one embodiment of the present application;

[0045] Figure 3 A schematic diagram of the results of periodic signal modeling of a time series synthesized by a PO with different period amplitudes and different time series lengths according to one embodiment of the present application;

[0046] Figure 4 A schematic diagram of a cycle modeling result when PV and PAV exist simultaneously according to one embodiment of the present application;

[0047] Figure 5 A schematic diagram of the modeling results of a real station and its power spectrum density diagram provided according to one embodiment of the present application;

[0048] Figure 6 A schematic diagram of statistical results of the mean and standard deviation of the cycle lengths estimated for all real measurement stations according to one embodiment of the present application;

[0049] Figure 7 Schematic diagram of a block diagram of a periodic signal modeling apparatus according to an embodiment of the present application;

[0050] Figure 8 A schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0051] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0052] The following describes a modeling method, device, electronic device and storage medium for periodic signals according to an embodiment of the present application with reference to the accompanying drawings. In response to the systematic deviation problem caused by the empirical period length assumption in the coordinate time series modeling mentioned in the above background technology, the present application provides a modeling method for periodic signals. In this method, the coordinate time series of the target navigation satellite system is obtained, and the coordinate time series is preprocessed to obtain a preprocessed coordinate time series, the preprocessed coordinate time series is corrected to obtain a corrected coordinate time series, and the corrected coordinate time series is estimated using a preset weighted least squares method to obtain the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation of the periodic amplitude, and decomposed, and an initial harmonic model is established based on the decomposed sine coefficient of the periodic amplitude, the decomposed cosine coefficient of the periodic amplitude and the decomposed periodic frequency, and a preset estimation strategy is used to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model. In this way, the problem of systematic deviation caused by the empirical period length assumption in coordinate time series modeling is solved, and a harmonic model that takes into account the frequency offset and time-varying period length of periodic signals is established, which significantly improves the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

[0053] Specifically, Figure 1 A flowchart of a method for modeling a periodic signal provided in an embodiment of the present application.

[0054] like Figure 1 As shown, the modeling method of the periodic signal includes the following steps:

[0055] In step S101 , a coordinate time series of a target navigation satellite system is obtained.

[0056] Specifically, embodiments of the present application can obtain the original GNSS coordinate time series of the target navigation satellite system from a public data source.

[0057] In step S102 , the coordinate time series is preprocessed to obtain a preprocessed coordinate time series, and the preprocessed coordinate time series is corrected to obtain a corrected coordinate time series.

[0058] Optionally, in some embodiments, the coordinate time series is preprocessed to obtain a preprocessed coordinate time series, including: determining whether there are abnormal values ​​and / or missing values ​​in the coordinate time series; if there are abnormal values ​​and / or missing values ​​in the coordinate time series, clearing the abnormal values ​​and / or interpolating the missing values ​​to obtain an initial coordinate time series; identifying step signals and trend signals in the initial coordinate time series, and removing the step signals and trend signals to obtain a preprocessed coordinate time series.

[0059] Specifically, combined Figure 2 As shown, the embodiment of the present application adopts the following process to preprocess the coordinate time series: first, abnormal signals are removed and missing data are interpolated, and the interquartile range (IQR) method is used to remove the influence of outliers in the GNSS coordinate time series and the missing data is interpolated by linear interpolation. The threshold for determining outliers is:

[0060] ;

[0061] in, is the first quartile, is the third quartile, is the interquartile range.

[0062] Linear interpolation can be expressed as:

[0063] ;

[0064] in, is the timestamp of the most recent valid data before the missing point, is the timestamp of the most recent valid data after the missing point, y is the GNSS coordinate time series value at the corresponding timestamp, t Timestamp for missing values.

[0065] Then, this embodiment of the application needs to identify and correct step signals in the coordinate time series. Specifically, information from the Jet Propulsion Laboratory (JPL), including the time when antenna or receiver replacement or technical factors such as earthquakes occur, is used to mark step signals. Using the Sequential T-Test Analysis Method (STARS), additional offsets and trend change points are further identified and marked. The expression formula for step signals and target trend signals can be:

[0066] ;

[0067] in, is the mean value before the step signal, is the mean value after the step signal, is the standard deviation, is the amount of data in the window, is the variance of the time window after the step, is the variance of the time window before the step, is the number of samples after the step, is the number of samples before the step, when It is determined that there is a potential step signal when

[0068] Then, based on the detection results and combined with the Gazeaux criterion (2013), the automatic detection results are visually corrected to eliminate false detection points.

[0069] Finally, the trend and step signals in the GNSS coordinate time series are fitted. The fitting formula of the coordinate time series can be expressed as:

[0070] ;

[0071] in, To stand The coordinate displacement at a moment can be in any direction, such as north, east, or sky; Solve the epoch (floating point year) for the day coordinates; is the position of the reference epoch of the station; is the polynomial fitting order in the GNSS coordinate time series; are the coefficients of the polynomial, if If it is 1, it has a linear trend; is the number of harmonics; is the angular frequency of the periodic signal The constant of the sine term, is the angular frequency of the periodic signal The constant of the cosine term; is the number of times the offset occurs; is the offset function; is the moment when the offset occurs; Time for sudden changes in equipment or seismic activity; is the number of categories of the random process, To observe the noise, no other special cases are considered in this formula.

[0072] After removing the trend and step signal, the preprocessed coordinate time series It only contains periodic signals and random process signals.

[0073] ;

[0074] in, is the preprocessed coordinate time series, is the angular frequency of the periodic signal The constant of the sine term, is the angular frequency of the periodic signal The constant of the cosine term, is the number of harmonics, is the number of categories of the random process, Solve for the epoch (floating point year) for day coordinates, is the observation noise, ; Usually set to the empirical frequency (Such as the anniversary signal = 1cpy), estimated by conventional weighted least squares (WLS) with a fixed cycle length and Thus, the long-term mean of the sine and cosine coefficients of the amplitude is obtained and , but ignores the change of amplitude over time (i.e. zero-mean random perturbation and ), and the actual frequency and experience points deviation.

[0075] It is understandable that the actual frequency and experience points There is a bias ,Right now The corresponding empirical values ​​and deviations of angular velocity are and , at this time the periodic displacement model is corrected to:

[0076] ;

[0077] in, For a harmonic model that considers the time-varying periodic amplitude, is the long-term mean of the cosine coefficient of the periodic amplitude, is the long-term mean of the cosine coefficient of the periodic amplitude, is the empirical value of angular velocity, is the deviation of angular velocity.

[0078] Expand and linearize the equation (when ≪0.01cpy), we can get:

[0079] ;

[0080] in, in is the PO parameter to be estimated.

[0081] In step S103, the preset weighted least square method is used to estimate the corrected coordinate time series to obtain the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation.

[0082] Specifically, due to the nonlinearity of the model, nonlinear least squares (NLS) is required for estimation. In the embodiment of the present application, it is first assumed that , the model degenerates into a linear model, and the parameters are determined by the preset weighted least squares (WLS) method and , then , as well as As the parameters to be estimated, construct the NLS minimization criterion:

[0083] ;

[0084] in, represents the NLS minimization criterion, is the length of the time series, and Estimates provided by WLS, The initial value of It can be simply set to 0cpy. The parameters are updated iteratively through the Levenberg-Marquardt algorithm. In order to correct the possible deviation of the initial value and improve the estimation accuracy, the first NLS estimation result is 、 and As the new initial value, repeat the NLS process. Calculate the final sine and cosine coefficients of the periodic amplitude 、 and periodic frequency deviation After that, the amplitude of the period is obtained by converting the equation , Phase and cycle length ;

[0085] ;

[0086] ;

[0087] .

[0088] In step S104, the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation are decomposed, and an initial harmonic model is established based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the decomposed periodic frequency, and the parameters to be estimated of the initial harmonic model are estimated using a preset estimation strategy to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model.

[0089] The parameters to be estimated include static parameters, time-varying parameters and noise parameters.

[0090] Specifically, the time-varying nature of geophysical processes causes both amplitude and frequency to vary with time. The amplitude is decomposed into a long-term mean. and and zero-mean random perturbations and , the periodic angular frequency is decomposed into empirical values ,deviation and disturbances , then the initial harmonic model taking into account the period amplitude variation (PAV), period offset (PO) and period length variation (PV) It can be expressed as:

[0091]

[0092] in, is the initial harmonic model, is the long-term mean of the sinusoidal coefficient of the periodic amplitude, is a zero-mean random perturbation of the sinusoidal coefficient of the periodic amplitude, is the empirical value of the periodic angular frequency, is the deviation of the periodic angular frequency, is the disturbance of periodic angular frequency, For time, is the long-term mean of the cosine coefficient of the periodic amplitude, is a zero-mean random perturbation of the cosine coefficient of the periodic amplitude.

[0093] Since the model has nonlinear coupling terms , a two-stage estimation strategy is required: and Estimates provided by WLS, The initial value of Can be simply set to 0cpy.

[0094] The observation matrix is:

[0095] ;

[0096] in, for The observed value at time, is the observation noise (with variance ).

[0097] The state equation is:

[0098] ;

[0099] Among them, is the state transition matrix, and Obeying the white noise model, Obey the random walk model; the state vector include 、 + as well as .

[0100] ;

[0101] , is the process noise covariance: ;

[0102] in, is the variance of the sinusoidal coefficient disturbance of the periodic amplitude (controlling the rate of change of PAV), is the variance of the cosine coefficient disturbance of the periodic amplitude, is the variance of the periodic frequency disturbance (controlling the PV change rate).

[0103] Then, the parameters to be estimated of the initial harmonic model are estimated using the preset estimation strategy to obtain the estimation results, as shown in Table 1, which is a summary table of the parameters to be estimated.

[0104] Table 1

[0105]

[0106] The amplitude of the cycle is obtained by converting the equation , Phase and cycle length :

[0107] ;

[0108] ;

[0109] ;

[0110] in, is the sinusoidal coefficient of the periodic amplitude containing disturbance, is the cosine coefficient of the periodic amplitude with disturbance, is the periodic frequency of the disturbance.

[0111] Optionally, in some embodiments, after establishing the final harmonic model based on the estimation results and the initial harmonic model, it includes: integrating multi-source geophysical time series data, modeling based on the multi-source geophysical time series data to obtain a geophysical model; calculating the time-lag cross-correlation function based on the final harmonic model and the geophysical model, and generating target analysis results based on the time-lag cross-correlation function.

[0112] Specifically, after establishing a final harmonic model that takes into account the period length with higher accuracy, it is necessary to systematically explore the possible physical sources. First, integrate multi-source geophysical time series data, including: regional precipitation series , abnormal temperature , GRACE equivalent water height and atmospheric pressure etc., build a time-varying coupling analysis framework, for the periodic signal that is successfully modeled and geophysical data , calculate the time-delayed cross-correlation function of the two:

[0113] ;

[0114] in, The standard deviation of the results of the period modeling, is the standard deviation of the geophysical data series, is the mean of the periodic signal sequence, is the mean of the geophysical data series, is the time delay (unit: day), the search range is usually ,when And corresponding When the response time matches the physical process, a causal relationship is considered to exist. is the length of the time series; is the epoch of the day coordinate solution (floating point year), where Used to distinguish and , to indicate It is to extract the corresponding frequency band time series of the GNSS coordinate time series through bandpass filtering and has no other practical significance.

[0115] The present invention has demonstrated significant advantages in periodic signal modeling through systematic verification of synthetic time series and 56 JPL station measured data. Figure 3 As shown in the figure, in the annual signal modeling for different true period amplitudes (0-15 mm) and time series lengths (1-28 years), the traditional WLS has a deviation of up to 50% when the amplitude exceeds 8 mm, and the residual standard deviation can reach 1.2 mm in short time series (<10 years); while the PO model of the embodiment of the present application controls the amplitude estimation error within 5% and reduces the residual standard deviation to 0.5 mm (a reduction of 58%) by introducing a dynamic weight strategy and multi-period harmonic compensation, showing excellent adaptability to high amplitude and long time series data. Figure 4 As shown in the figure, in the synthetic sequence of preset PV (periodic frequency variation) and PAV (periodic amplitude variation) interference, both the traditional harmonic model and the PAV model are difficult to accurately fit the change of the periodic frequency. However, by introducing the periodic frequency parameter, the embodiment of the present application reduces the maximum deviation from 2.3 mm to 0.08 mm (a decrease of 96%). Figure 5 The experimental results based on real JPL station data show that the harmonic model described in this application has higher fitting accuracy, with the highest residual standard deviation being only 2.8 mm, 40% lower than the SSA method. At the same time, within the 0.5–2.0 cpy frequency band, its peak power spectral density is much lower than that of other methods, effectively suppressing the impact of periodic signal deviation and its changes. Figure 6 The statistical results show that the period length estimates of 56 stations reveal that the period of the true annual signal deviates from the empirical value and changes over time. These characteristics are accurately captured by the embodiments of the present application, providing a high-precision period modeling method for the GNSS coordinate reference frame and laying a solid foundation for in-depth analysis of geophysical signals.

[0116] In summary, the embodiments of the present application provide a harmonic model that jointly models periodic amplitude variation (PAV), period offset (PO), and period length variation (PV). This model overcomes the technical limitation of traditional GNSS time series periodic modeling, which fixes the period length to an empirical value. Its core advantages are reflected in two aspects: First, it incorporates period length as a dynamic parameter into the modeling framework for the first time. By integrating the time-varying characteristics of PAV, PO, and PV, it truly depicts the co-evolution of amplitude and period in geophysical signals, resolving the model distortion problem caused by the fixed period assumption in traditional methods. Second, the dynamic estimation model constructed based on nonlinear least squares (NLS) and unscented Kalman filtering (UKF) has been verified to be superior in synthetic data and field measurements at global stations. Compared with traditional fixed-period models, it significantly improves the fitting accuracy and spectral fidelity of periodic signals, providing a more reliable periodic signal modeling technology for GNSS time series in geodynamic inversion and high-precision reference frame establishment. It effectively solves the problem of inconsistency between the period length parameters and the empirical period length caused by geophysical signals such as environmental load and thermal expansion effect, and significantly improves the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

[0117] According to the modeling method of the periodic signal of the embodiment of the present application, the coordinate time series of the target navigation satellite system is obtained, and the coordinate time series is preprocessed to obtain the preprocessed coordinate time series, the preprocessed coordinate time series is corrected to obtain the corrected coordinate time series, and the corrected coordinate time series is estimated using a preset weighted least squares method to obtain the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation of the periodic amplitude, and decomposed, and an initial harmonic model is established based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the decomposed periodic amplitude and the decomposed periodic frequency, and the preset estimation strategy is used to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model. Thus, the problem of systematic deviation caused by the empirical cycle length assumption in the coordinate time series modeling is solved, and a harmonic model that takes into account the frequency offset and time-varying cycle length of the periodic signal is established, which significantly improves the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

[0118] Next, a periodic signal modeling device proposed in accordance with an embodiment of the present application will be described with reference to the accompanying drawings.

[0119] Figure 7 4 is a block diagram of a device for modeling a periodic signal according to an embodiment of the present application.

[0120] like Figure 7 As shown, the periodic signal-based modeling device 10 includes: an acquisition module 100 , a processing module 200 , an estimation module 300 and a building module 400 .

[0121] The acquisition module 100 is used to acquire the coordinate time series of the target navigation satellite system.

[0122] The processing module 200 is used to preprocess the coordinate time series to obtain a preprocessed coordinate time series, and to correct the preprocessed coordinate time series to obtain a corrected coordinate time series.

[0123] The estimation module 300 is used to estimate the corrected coordinate time series using a preset weighted least square method to obtain the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation.

[0124] Establish module 400, which is used to decompose the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation, and establish an initial harmonic model based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the decomposed periodic frequency, and use a preset estimation strategy to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model.

[0125] Optionally, in some embodiments, the processing module 200 includes: a judgment unit, an interpolation unit, and an identification unit.

[0126] The judgment unit is used to judge whether there are abnormal values ​​and / or missing values ​​in the coordinate time series.

[0127] The interpolation unit is used to remove abnormal values ​​and / or interpolate missing values ​​when there are abnormal values ​​and / or missing values ​​in the coordinate time series to obtain an initial coordinate time series.

[0128] The identification unit is used to identify the step signal and the trend signal in the initial coordinate time series, and remove the step signal and the trend signal to obtain the preprocessed coordinate time series.

[0129] Optionally, in some embodiments, the initial harmonic model is:

[0130]

[0131] in, is the initial harmonic model, is the long-term mean of the sinusoidal coefficient of the periodic amplitude, is a zero-mean random perturbation of the sinusoidal coefficient of the periodic amplitude, is the empirical value of the periodic angular frequency, is the deviation of the periodic angular frequency, is the disturbance of periodic angular frequency, For time, is the long-term mean of the cosine coefficient of the periodic amplitude, is a zero-mean random perturbation of the cosine coefficient of the periodic amplitude.

[0132] Optionally, in some embodiments, the parameters to be estimated include: static parameters, time-varying parameters and noise parameters.

[0133] Optionally, in some embodiments, after the final harmonic model is established according to the estimation result and the initial harmonic model, the module 400 is established, including: a modeling unit and a generating unit.

[0134] Among them, the modeling unit is used to integrate multi-source geophysical time series data and obtain a geophysical model based on the multi-source geophysical time series data.

[0135] The generating unit is used to calculate the time-delay cross-correlation function according to the final harmonic model and the geophysical model, and generate the target analysis result according to the time-delay cross-correlation function.

[0136] According to the modeling device of the periodic signal of the embodiment of the present application, by obtaining the coordinate time series of the target navigation satellite system, and preprocessing the coordinate time series to obtain the preprocessed coordinate time series, correcting the preprocessed coordinate time series to obtain the corrected coordinate time series, and using the preset weighted least squares method to estimate the corrected coordinate time series to obtain the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation of the periodic amplitude, and decompose them, and establish an initial harmonic model based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the decomposed periodic amplitude and the decomposed periodic frequency, and use the preset estimation strategy to estimate the parameters to be estimated of the initial harmonic model to obtain the estimation results, so as to establish a final harmonic model based on the estimation results and the initial harmonic model. Thus, the problem of systematic deviation caused by the empirical cycle length assumption in the coordinate time series modeling is solved, and a harmonic model that takes into account the frequency offset and time-varying cycle length of the periodic signal is established, which significantly improves the accuracy of seasonal deformation inversion and the reliability of crustal movement rate estimation.

[0137] Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0138] A memory 801 , a processor 802 , and a computer program stored in the memory 801 and executable on the processor 802 .

[0139] When the processor 802 executes the program, the periodic signal modeling method provided in the above embodiment is implemented.

[0140] Furthermore, the electronic device further includes:

[0141] The communication interface 803 is used for communication between the memory 801 and the processor 802 .

[0142] The memory 801 is used to store computer programs that can be run on the processor 802.

[0143] The memory 801 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0144] If the memory 801, processor 802, and communication interface 803 are implemented independently, the communication interface 803, memory 801, and processor 802 can be interconnected via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. Buses can be divided into address buses, data buses, control buses, etc. For ease of representation, Figure 8 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0145] Optionally, in a specific implementation, if the memory 801, the processor 802 and the communication interface 803 are integrated on a chip, the memory 801, the processor 802 and the communication interface 803 can communicate with each other through an internal interface.

[0146] The processor 802 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0147] An embodiment of the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for modeling periodic signals.

[0148] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" 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 application. 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 can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0149] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0150] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A method for modeling a periodic signal, characterized in that: The following steps are involved: Obtain the coordinate time series of the target navigation satellite system; Preprocessing the coordinate time series to obtain a preprocessed coordinate time series, and correcting the preprocessed coordinate time series to obtain a corrected coordinate time series; Using a preset weighted least squares method to estimate the corrected coordinate time series to obtain a sine coefficient of the periodic amplitude, a cosine coefficient of the periodic amplitude, and a periodic frequency deviation; The sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation are decomposed, and an initial harmonic model is established based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the decomposed periodic angle, and a preset estimation strategy is used to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model.

2. The method according to claim 1, characterized in that The preprocessing of the coordinate time series to obtain a preprocessed coordinate time series includes: Determining whether there are abnormal values ​​and / or missing values ​​in the coordinate time series; If the abnormal values ​​and / or the missing values ​​exist in the coordinate time series, the abnormal values ​​are cleared and / or the missing values ​​are interpolated to obtain an initial coordinate time series; A step signal and a trend signal in the initial coordinate time series are identified, and the step signal and the trend signal are removed to obtain the preprocessed coordinate time series.

3. The method according to claim 1, characterized in that The initial harmonic model is: in, is the initial harmonic model, is the long-term mean of the sinusoidal coefficient of the periodic amplitude, is a zero-mean random perturbation of the sinusoidal coefficient of the periodic amplitude, is the empirical value of the periodic angular frequency, is the deviation of the periodic angular frequency, Perturbations in the periodic angular frequency, For time, is the long-term mean of the cosine coefficient of the periodic amplitude, is a zero-mean random perturbation of the cosine coefficient of the periodic amplitude.

4. The method according to claim 1, wherein The parameters to be estimated include: static parameters, time-varying parameters and noise parameters.

5. The method according to claim 1, wherein After the final harmonic model is established according to the estimation results and the initial harmonic model, it includes: Integrating multi-source geophysical time series data, and performing modeling based on the multi-source geophysical time series data to obtain a geophysical model; A time-lag cross-correlation function is calculated based on the final harmonic model and the geophysical model, and a target analysis result is generated based on the time-lag cross-correlation function.

6. A modeling device for periodic signals, characterized in that: include: An acquisition module is used to obtain the coordinate time series of the target navigation satellite system; a processing module, configured to preprocess the coordinate time series to obtain a preprocessed coordinate time series, and correct the preprocessed coordinate time series to obtain a corrected coordinate time series; An estimation module, configured to estimate the corrected coordinate time series using a preset weighted least squares method to obtain a sine coefficient of the periodic amplitude, a cosine coefficient of the periodic amplitude, and a periodic frequency deviation; Establish a module for decomposing the sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the periodic frequency deviation, and establish an initial harmonic model based on the decomposed sine coefficient of the periodic amplitude, the cosine coefficient of the periodic amplitude and the decomposed periodic frequency, and use a preset estimation strategy to estimate the parameters to be estimated of the initial harmonic model to obtain an estimation result, so as to establish a final harmonic model based on the estimation result and the initial harmonic model.

7. The device according to claim 6, characterized in that The processing module includes: a judgment unit, configured to judge whether there are abnormal values ​​and / or missing values ​​in the coordinate time series; an interpolation unit, configured to, when the abnormal values ​​and / or the missing values ​​exist in the coordinate time series, remove the abnormal values ​​and / or interpolate the missing values ​​to obtain an initial coordinate time series; The identification unit is used to identify the step signal and the trend signal in the initial coordinate time series, and remove the step signal and the trend signal to obtain the preprocessed coordinate time series.

8. The device according to claim 6, characterized in that The initial harmonic model is: in, is the initial harmonic model, is the long-term mean of the sinusoidal coefficient of the periodic amplitude, is a zero-mean random perturbation of the sinusoidal coefficient of the periodic amplitude, is the empirical value of the periodic angular frequency, is the deviation of the periodic angular frequency, is the disturbance of periodic angular frequency, For time, is the long-term mean of the cosine coefficient of the periodic amplitude, is a zero-mean random perturbation of the cosine coefficient of the periodic amplitude.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for modeling a periodic signal according to any one of claims 1 to 5.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the periodic signal modeling method according to any one of claims 1 to 5.

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