Method and device for fusing adaptive denoising, transient event recognition and parameter estimation

Abstract

The invention provides a method and equipment for fusing adaptive denoising, transient event identification and parameter estimation. The method comprises the following steps: acquiring a GNSS coordinate time sequence of an observation station; according to a scene, modeling the GNSS coordinate time sequence into a combination of more than one physical meaning components, the components being noise, long-term trend, periodic signals and / or transient signals, and each component corresponding to a mean square small characteristic, a mean square smooth characteristic, a periodic constraint characteristic and a sparsity characteristic; defining a corresponding loss function based on the characteristics of each component; an optimal solution is obtained by optimizing the sum of the loss functions of all the components; and synchronously estimating a long-term trend parameter, a periodic parameter and a transient event parameter in the GNSS coordinate time sequence based on the optimal solution. The method can effectively process modeling and detection of long-term slow change events, has good accuracy and reliability, and is suitable for earthquake monitoring and disaster prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS data precision processing, and specifically relates to a technical solution for fusion adaptive denoising, transient event recognition and parameter estimation of GNSS coordinate time series. Background Art

[0002] GNSS station coordinate time series contain a wealth of information, including long-term trends (velocities), periodic signals, transient signals, and noise. Long-term trends (velocities) reflect phenomena such as tectonic movement, fault stress accumulation, and glacial isostatic adjustments, providing fundamental data for geophysical research. Periodic signals reflect cyclical variations caused by geophysical phenomena such as surface mass loading and thermal expansion (Blewitt and Lavallée, 2002; Penna, 2003; Yan et al., 2009; Bos et al., 2010; Williams and Penna, 2011; Fang et al., 2018). However, the aliasing effect of complex periodic signals in GNSS coordinate time series can reduce the reliability of station velocities and their uncertainties. Furthermore, spurious signals caused by non-geophysical factors such as imperfect GNSS solution strategies and satellite constellations (Ray et al., 2008; Amiri-Simkooei et al., 2013) can also lead to biased velocity estimates. Furthermore, transient anomalies (often manifesting as steps) caused by factors such as earthquakes, equipment replacement, and poor observation conditions can further reduce the accuracy of station velocity. GNSS coordinate time series can also experience varying degrees of discontinuity due to unpredictable factors. In summary, parameter estimation using GNSS coordinate time series is susceptible to multiple influences, including discontinuities (interruptions), aliasing of periodic signals, and noise.

[0003] Currently, methods commonly used to address the multiple impacts of sequence discontinuities (interruptions), periodic signal aliasing, and noise involve multiple steps. Specifically, data interruptions are addressed using interpolation or segmentation; periodic signal aliasing is addressed by modeling and fitting the anniversary / semi-anniversary period and its harmonics; and noise is typically addressed based on an established mathematical model, with the corresponding model values ​​deducted before noise analysis. These approaches face the following challenges: low automation and operational efficiency in parameter calculation, as well as low reliability in parameter estimation. Therefore, the present invention breaks with conventional techniques by proposing a simple, automated, and one-step GNSS coordinate time series parameter estimation solution. Summary of the Invention

[0004] Conventional parameter estimation methods rely on prior assumptions and often use multi-step analysis methods to achieve denoising, step detection and parameter estimation, which is inefficient. The present invention provides a new technical solution to establish a framework that can simultaneously denoise, detect steps and estimate parameters. Based on this framework, it is possible to solve parameters such as velocity and periodic terms in GNSS station coordinate time series without relying on prior assumptions.

[0005] The above technical problems of the present invention are mainly solved by the following technical solutions: A method integrating adaptive denoising, transient event recognition and parameter estimation includes the following steps: Get the time series of GNSS coordinates of the measuring station; Based on the scenario, the GNSS coordinate time series is modeled as a combination of one or more physically meaningful components, wherein the components are noise, long-term trends, periodic signals, and / or transient signals, where each component corresponds to a mean square small characteristic, a mean square smooth characteristic, a periodic constraint characteristic, and a sparsity characteristic; and a corresponding loss function is defined based on the characteristics of each component; The optimal solution is obtained by optimizing the sum of the loss functions of each component; Based on the optimal solution, long-term trend parameters, periodic parameters and transient event parameters in the GNSS coordinate time series are synchronously estimated.

[0006] Moreover, the loss function includes a mean square error loss function corresponding to the noise component, a low-order differential mean square smoothing loss function corresponding to the long-term trend component, a periodic constrained mean square smoothing loss function corresponding to the periodic signal component, and / or a sparsity constrained loss function corresponding to the transient signal component.

[0007] Moreover, the problem of minimizing the sum of the loss functions of each component is iteratively solved based on the alternating direction multiplier method.

[0008] Moreover, the mask matrix is ​​used in the iterative solution process to handle missing data values ​​and align the dimensions of the observed data and the estimated values.

[0009] Moreover, the solution is achieved through the augmented Lagrangian function.

[0010] Furthermore, the transient events include step signals caused by earthquakes, equipment replacement or abnormal observation conditions.

[0011] Moreover, the long-term trend parameter includes the station speed, the periodic parameter includes the period length, and the transient event parameter includes the time when the transient event occurs.

[0012] On the other hand, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the method of integrating adaptive denoising, transient event identification, and parameter estimation as described above is implemented.

[0013] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method of integrating adaptive denoising, transient event identification, and parameter estimation as described above.

[0014] On the other hand, the present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method for integrating adaptive denoising, transient event identification, and parameter estimation as described above.

[0015] To address the complex periodic signals, difficult-to-quantify noise, and sequence discontinuities in GNSS coordinate time series, this paper proposes a solution for simultaneously denoising discontinuous coordinate time series and estimating both periodic signals and long-term trends. This solution decomposes GNSS time series signals containing missing values ​​into components with distinct characteristics (smoothness, sparsity, and periodicity), transforming this into an optimal signal decomposition problem. This approach enables simultaneous denoising, transient signal detection, and parameter estimation for GNSS coordinate time series with missing data.

[0016] Compared with the existing technology, the present invention provides an optimization-based signal decomposition method that can effectively handle the modeling and detection of long-term slowly changing events, has good accuracy and reliability, and is suitable for earthquake monitoring and disaster prediction.

[0017] The solution of the present invention is simple and convenient to implement and has strong practicality. It solves the problems of low practicality and inconvenience in actual application existing in related technologies, can improve user experience, and has important market value. DETAILED DESCRIPTION

[0018] The following will further illustrate the concept, specific structure and technical effects of the present invention in conjunction with embodiments, so as to fully understand the purpose, characteristics and effects of the present invention.

[0019] The embodiment provides a method for integrating adaptive denoising, transient event recognition, and parameter estimation, including the following steps: Step 1: Obtain several station GNSS coordinate time series from public datasets or self-calculation, where any station GNSS time series is denoted as ; in, Represents any moment, is the total length of the sequence, Represents the coordinate value of the measuring station at any time t.

[0020] Step 2: Model the global navigation satellite system (GNSS) time series as a combination of smooth signals and sparse events, considering that long-term linear trends show slow changes and transient signals show sparsity in the time domain from the perspective of mathematical properties.

[0021] In the embodiment, first define as follows: Convert GNSS coordinate time series Modeled as ingredients The sum of Represents a component with physical meaning. , is the total number of components. is the field of real numbers, is the total length of the sequence, but due to data interruption and other reasons, the data is missing, and the actual length of the observed data is .

[0022] Different from the previous mathematical model fitting based on anniversary and semi-anniversary signals, the present invention regards the position information in the GNSS coordinate time series as a combination of several physical components and satisfies the consistency constraint assumption based on the signal decomposition problem, that is, the sum of the estimated values ​​of each component is equal to the input at the known point, which is expressed as (1) in, for The mask matrix can rearrange the known elements of the estimate in the order of observation and "mask" or ignore the unknown values.

[0023] Based on the above definition, make the following specific settings: According to the general modeling of GNSS coordinate time series, the embodiment preferably models the GNSS coordinate time series into four types of signals, namely, noise, long-term trend, periodic signal and transient signal, that is, K=4. These four types of signals have obvious physical and mathematical characteristics, namely, noise corresponds to the mean square small characteristic (the first component below), the long-term surface motion trend corresponds to the mean square smoothing (the second component below), the periodic signal has periodic repeatability and therefore corresponds to the mean square smoothing component with periodic constraints (the third component below), and the transient signal corresponds to sparsity (the fourth component below).

[0024] 1) Example First, assume that the objective function of the first component of the model satisfies the mean square error convergence constraint, which is called the "mean square small class" and is expressed as follows: (2) in, To satisfy The loss function under the condition, is the input value, is an actual non-null input value, It is the root mean square sum of the input values ​​under the quadratic norm.

[0025] This type of component is very effective in separating Gaussian distribution noise. is interpreted as the approximation residual, and is the mean square error of observation. That is, this type of component Explainable fitting residuals, which exhibit random error characteristics and correspond to hyperparameters Fixed to 1.

[0026] 2) Since the long-term deformation of the surface is characterized by slow changes, it is defined as a mean square smoothing component. The loss function of this type of component is defined as of The mean square sum of the order derivatives satisfies the following formula: (3) in, is the corresponding hyperparameter, is the i-order difference matrix, Can be interpreted as of Derivative. When i≤ 3, has a clear physical meaning; only considering the case of i ≤ 2, then It can be deduced that the ) and a slowly changing slope ( )of Estimated value. The component loss function corresponding to long-term deformation is second order ( ) is the mean square of the differences, where is a second-order difference matrix, and its calculation result is usually a smooth curve.

[0027] 3) Existing research generally uses sine waves to model anniversary and semi-annual periodic signals. However, these two types of periodicity are not the only ones encountered in real data processing. To increase the versatility of the model, this paper proposes using a mean square smoothing component with a period constraint to further isolate periodic signals.

[0028] Assume that the integer period is The signal satisfies the constraint , ( , The meaning is the same as before), the indicator function form of the period constraint can be expressed as: (4) in, To meet the cycle A periodic signal, assuming that every interval period , corresponding to Taking the same value, and combining it with any loss function, we can get periodic signals with different characteristics.

[0029] Since only the periodicity is constrained, the periodic signal can be extended from the sinusoidal form to a wider range and the estimated value of the non-sinusoidal form can be obtained.

[0030] 4) Signals may exhibit sparse characteristics in a certain transformation domain (such as time domain, frequency domain or wavelet domain), that is, after a certain transformation, they contain only a very small number of non-zero coefficients. This invention regards signals with transient characteristics such as dynamic rupture as piecewise constant sequences with sparse change points, and uses Norm (Sum of Absolute Values) and Difference Matrix Quantification The time domain sparse features, its loss function is written as: (5) in, for norm, is the corresponding hyperparameter.

[0031] Components The estimated value of is usually a pulse signal ( ), piecewise constant signal ( ) or piecewise linear signal ( ).

[0032] Step 3: Use components in different scenarios Any one or more of them form a description scheme, the number of components of this scheme is ,but ≤ , where the components can be combined arbitrarily, e.g. combination, or For ease of notation, the selected components are denoted as When implementing it, you can formulate multiple solutions based on different scenarios. Choose the solution based on the actual situation. Use the corresponding loss function Describes several components corresponding to the selected scheme, which can be interpreted as estimated values The smaller the value, the more credible it is.

[0033] In specific scenarios (the scenarios here refer to slow slip state, strong periodic characteristic state, low rate state, dynamic rupture state, etc.), under the condition of satisfying formula (1), the component The estimated value of will be achieved by solving the following optimization problem: (6) in, ,..., Corresponding to different components The loss function of the formula shows that when different components are selected, the optimal solution is solved by optimizing the sum of the loss functions of the components.

[0034] Step 4, based on the alternating direction multiplier method, gives an iterative solution to the optimization problem in step 3. During the iteration process, the mask operator and its inverse Used to align dual variables with the estimated value dimensions and insert zeros in the place of missing values, thereby relaxing the consistency constraints during the optimization process.

[0035] Therefore, by constructing the augmented Lagrangian function, the solution to formula (6) is as follows:

[0036] (7) in, is a positive parameter, is the scaled dual variable, the component Scale the dual variables accordingly ; One point needs to be explained: It has nothing to do with k, so it can be uniformly expressed by the second formula in formula (7); therefore, and The second formula in formula (7) can be used ( ) is brought in to represent, n is the iteration cycle, In the iterative formula, its function is to align the dual variables with the estimated value dimension, which means that the consistency constraint of the optimization problem is relaxed at the missing value position, and the missing value does not need to meet this constraint. (8) is an approximate point operator = A variant of .

[0037] Where v is the input of the proximal operator. and its inverse In actual calculations, it mainly works on coordinate time series with missing values. By introducing masks, it avoids problems such as additional errors introduced by common methods such as polynomial interpolation.

[0038] In summary, the present invention provides a parameter estimation method that can be completed in one step: 1) flexibly introducing different numbers of components based on the research objectives; 2) constructing a new framework based on the mathematical properties of the components. For example, when the rigid block of the research object has slow motion characteristics, component 2 is used; when studying reservoir deformation, considering the periodicity of pumping and drainage, component 3 is used; 3) constructing the objective function and estimating the selected components at the same time, completing the estimation of all parameters represented by the components in one step.

[0039] In specific implementation, the long-term trend parameters in the parameter estimation include the station speed, and the periodic parameters include the period length (i.e., the integer period ), the transient event parameters include the time when the transient event occurs, and all parameters are output synchronously through a single optimization framework.

[0040] To facilitate understanding of the technical effects of the present invention, comparative results are presented below, as detailed in Table 1. The results demonstrate that the method described in this invention can detect more small slip events than the classic Bi-LSTM and RSI methods when detecting slow slip events in the Cascadia region, and its recall rate is significantly higher than the other two methods.

[0041] Table 1 Detection effects of different methods

[0042] In specific implementation, the method proposed in the technical solution of the present invention can be automatically run by those skilled in the art using computer software technology. System devices that implement the method, such as computer-readable storage media that store the corresponding computer program of the technical solution of the present invention and computer equipment that runs the corresponding computer program, should also be within the scope of protection of the present invention.

[0043] The electronic device provided by the present invention that integrates adaptive denoising, transient event recognition and parameter estimation is described below. The electronic device that integrates adaptive denoising, transient event recognition and parameter estimation described below and the method that integrates adaptive denoising, transient event recognition and parameter estimation described above can be referenced to each other.

[0044] The electronic device may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may call logic instructions in the memory to execute the method for integrating adaptive denoising, transient event identification, and parameter estimation, which mainly includes the software processing portion of the above steps.

[0045] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0046] On the other hand, the present invention also provides a computer program product, which includes a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the software processing part of the method of integrating adaptive denoising, transient event identification and parameter estimation provided by the above-mentioned methods.

[0047] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the software processing portion of the method of integrating adaptive denoising, transient event identification and parameter estimation provided by the above-mentioned methods.

[0048] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0049] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method integrating adaptive denoising, transient event recognition, and parameter estimation, characterized by: Including the following process, Get the time series of GNSS coordinates of the measuring station; Based on the scenario, the GNSS coordinate time series is modeled as a combination of one or more physically meaningful components, wherein the components are noise, long-term trends, periodic signals, and / or transient signals, where each component corresponds to a mean square small characteristic, a mean square smooth characteristic, a periodic constraint characteristic, and a sparsity characteristic; and a corresponding loss function is defined based on the characteristics of each component; The optimal solution is obtained by optimizing the sum of the loss functions of each component; Based on the optimal solution, long-term trend parameters, periodic parameters and transient event parameters in the GNSS coordinate time series are synchronously estimated.

2. The method of integrating adaptive denoising, transient event recognition and parameter estimation according to claim 1, characterized in that: The loss function includes a mean square error loss function corresponding to the noise component, a low-order difference mean square smoothing loss function corresponding to the long-term trend component, a periodic constrained mean square smoothing loss function corresponding to the periodic signal component, and / or a sparsity constrained loss function corresponding to the transient signal component.

3. The method according to claim 1, wherein: The problem of minimizing the sum of loss functions of each component is iteratively solved based on the alternating direction multiplier method.

4. The method according to claim 3, wherein: During the iterative solution process, the mask matrix is ​​used to handle missing data values ​​and align the dimensions of the observed data and the estimated values.

5. The method according to claim 3, wherein: The solution is achieved through augmented Lagrangian function.

6. The method according to claim 1, wherein: The transient events include step signals caused by earthquakes, equipment replacement or abnormal observation conditions.

7. The method according to claim 1, wherein: The long-term trend parameter includes the station speed, the periodic parameter includes the period length, and the transient event parameter includes the time when the transient event occurs.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for integrating adaptive denoising, transient event recognition and parameter estimation as described in any one of claims 1 to 7 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for integrating adaptive denoising, transient event recognition and parameter estimation as claimed in any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program, characterized in that: When the computer program is executed by a processor, the method for integrating adaptive denoising, transient event recognition and parameter estimation as claimed in any one of claims 1 to 7 is implemented.

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