IMF screening and GNSS signal reconstruction method and system enhanced by deep learning

Abstract

The invention provides an IMF screening and GNSS signal reconstruction method and system enhanced by deep learning, and belongs to the field of GNSS signal processing. The invention aims to solve the problems of single feature, threshold dependence and manual intervention of a DFA method in an IMF screening process. According to the method, the Transform deep learning model is introduced, so that complex time domain, frequency domain and energy characteristics in the IMF can be fully captured; by performing multi-dimensional feature extraction and classification on the IMF, the screening accuracy is improved, the IMF containing flicker noise is identified more accurately, and a foundation is laid for subsequent high-quality signal reconstruction; the signal is decomposed and reconstructed by combining iCEEMDAN and VMD technologies, the quality of signal reconstruction is further optimized, and the accuracy and stability of the reconstructed signal are improved, so that the quality of the GNSS signal is improved, and the precision of positioning, navigation and time synchronization application is improved.

Description

Technical Field

[0001] The present invention relates to the field of GNSS signal processing technology, and in particular to a method and system for IMF screening and GNSS signal reconstruction enhanced by deep learning. Background Art

[0002] Since GNSS signals are widely used in positioning, navigation, time synchronization and other fields, the improvement of their signal quality has always been a hot topic of research. In the prior art, iCEEMDAN (integrated set empirical mode decomposition) is widely used to decompose GNSS signals to extract multiple IMFs. However, in the IMF screening process, the traditional DFA method mainly determines whether it contains flicker noise by calculating the scaling index α of the IMF. For example, the document "A combined iCEEMDAN and VMD method formitigating the impact of ionospheric scintillation on GNSS signals" discloses a DFA-based IMF screening method, the main steps of which include calculating the scaling index α for each IMF, and screening out noise-free IMFs by setting a threshold θ (such as IMFs with α>0.5 are set to). However, the prior art has the following shortcomings:

[0003] 1. Single feature: DFA only relies on the single feature of scaling exponent α, which cannot fully capture the complex time domain and frequency domain characteristics in IMF, resulting in limited screening accuracy.

[0004] 2. Threshold dependence: DFA screening is based on a fixed threshold θ, which may need to be readjusted in different signal environments, lacking flexibility and adaptability.

[0005] 3. Human intervention: The DFA method requires experts to set the threshold, and the degree of automation of the screening process is limited, which increases the possibility of human error. Summary of the invention

[0006] The technical problems to be solved by the present invention are:

[0007] In order to solve the problems of low screening accuracy caused by the single feature of the DFA method in the IMF screening process, poor flexibility and adaptability caused by threshold dependence, and human error caused by manual intervention.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

[0009] The present invention provides an IMF screening and GNSS signal reconstruction method enhanced by deep learning, comprising the following steps:

[0010] S100, signal reading and iCEEMDAN decomposition, apply the iCEEMDAN algorithm to the noisy GNSS signal and decompose it into multiple IMFs to extract different frequency components in the signal:

[0011] S200, performing DFA feature extraction on IMFs, and extracting time domain features, frequency domain features, and energy features of IMFs at the same time, setting labels with a scaling index less than 0.5 as having flicker noise, and setting the rest as flicker-free IMFs, and finally outputting a feature vector of each IMF;

[0012] S300, using the Transformer model to classify IMFs, marking whether the feature vector obtained in step S200 contains flicker noise, and outputting the IMFS part with a label of no flicker noise;

[0013] S400, signal reconstruction and VMD decomposition, reconstruct the flicker noise-free IMFS obtained in step S300 after summing up, and then perform adaptive decomposition, optimize the modal function and the center frequency through an iterative method, gradually separate the different frequency components of the signal, and obtain K narrowband modes of adaptive decomposition and their frequency information; re-perform the DFA feature extraction of step S200 and the classification using the Transformer model of step S300 on each modal function after the adaptive decomposition, and still set the labels with a scaling index less than 0.5 as having flicker noise, screen out the modes without flicker noise, and finally obtain the reconstructed flicker noise-free signal.

[0014] Furthermore, in step S100, it specifically includes:

[0015] Assume the original signal is s(t), w (i) represents the i-th realization of the added Gaussian white noise sample, E k (·) represents the operation process of extracting the kth IMF through empirical mode decomposition, N(·) represents the operation of envelope averaging of the signal to obtain the local mean, <·> represents the averaging of all noise realizations, and the parameter β 0 ,β 1 ,β 2 ,...,β k is the weight factor for adjusting the noise scale;

[0016] S110, read the GNSS signal s(t) containing flicker noise, first add a weighted white noise term to the original signal s(t) to obtain a signal set (s (i) ):

[0017] s (i) =s+β 0 E 1 (w (i) )

[0018] S120, using the iCEEMDAN method to transform the signal set (s (i) ) is decomposed into multiple IMFs, and for each mode function IMF k , calculate the final residual r k = <N(r k-1 +β k-1 E k (w (i) ))>, Finally, we get a set of IMFS: Specifically include:

[0019] For each signal set s (i) Perform EMD to obtain its local mean and average all realizations:

[0020] r 1 = <N(s (i) )>

[0021] Then the first-order IMF is:

[0022]

[0023] In obtaining the first-order residual r 1 Then, add it to the weighted second modal noise component and average all realizations locally:

[0024] r 2 = <N(r 1 +β 1 E 2 (w (i) ))>.

[0025] Then the second-order IMF is:

[0026]

[0027] Follow the above steps to get the k-order mode and k IMFs, and then repeat the iteration until all the expected intrinsic mode function sets are obtained. The final residual is r K , no longer decompose.

[0028] Furthermore, in step S200, it specifically includes:

[0029] S210, calculate the mean of each IMF <IMF i >

[0030] Find the mean of a given signal sequence s(t):

[0031]

[0032] S220, subtract each IMF from its own mean, and then sum the errors to construct the cumulative deviation sequence Y i (t);

[0033]

[0034] S230, Y i (t) Divide the window into segments according to the length n and use a polynomial to fit the local trend Y fit,k (t), and then calculate the signal fluctuation function F k (n):

[0035]

[0036] Then change the window length n, fit n and the fluctuation function through double logarithmic coordinates, and get the scaling index α k :

[0037] F(n)~n α

[0038] At the same time, the time domain features, frequency domain features and energy features of IMFs are extracted, and the labels with a scaling index less than 0.5 are set as flicker noise, and the rest are set as flicker-free IMFs. Finally, the feature vector f of each IMF is output k .

[0039] Further, in step S300, the input feature vector X=[f 1 ,f 2 ,...,f K ], based on the existing data, mark whether the IMF contains flicker noise; through the linear mapping Q = XW Q ,K=XW K ,V=XW V And attention mechanism Z = Concat(head 1 ,head 2 ,...,head h )W O After feature classification training, all IMFs obtained in step S200 are input into the network, and the feature vector of each IMF is classified to obtain the predicted label Set the noise-free label to 0, and the final output label is the noise-free IMFs part;

[0040] Where Q is the query matrix, K is the key matrix, V is the value matrix; W Q ,W K ,W V is a trainable parameter matrix; head i =Attention(Q i ,K i,V i ) and W O Mapping parameters for output.

[0041] Furthermore, in step S400, it specifically includes:

[0042] S410, will be flicker-free Sum and reconstruct the flicker noise-free signal s clean (t);

[0043] S420, for s clean (t) Perform adaptive decomposition, set the mode number K and penalty factor α to control the bandwidth range of decomposition, and initialize the modal function i of each mode k (t) and center frequency ω k ;

[0044]

[0045] S430, optimize mode i by iterative method k (t) and center frequency ω k , gradually separate the different frequency components of the signal; in each round of iteration, adjust the center frequency and bandwidth of the mode according to the frequency domain and time domain information until the convergence condition is met, and finally obtain K narrowband modes and their frequency information of adaptive decomposition;

[0046] Solve the following constrained variational problem:

[0047]

[0048] And satisfy the constraints:

[0049]

[0050] Where j represents the imaginary unit, t represents time, δ(t) is the Dirac function, and * represents the convolution operation. is the time differential operator, ‖·‖ 2 For L 2 norm; by introducing the penalty factor α and the Lagrange multiplier, the augmented Lagrangian function is constructed:

[0051]

[0052] Using the alternating direction multiplier method, {i k},{ω k},λ are iteratively optimized. The formula is as follows. After the iteration converges, all IMFs and corresponding center frequencies are obtained, thereby completing the VMD decomposition of the signal:

[0053]

[0054] Among them, τ represents the step size parameter, which is used to control the update rate of the Lagrange multiplier; I represents the total number of modes, that is, the number of modal functions decomposed from the signal;

[0055] S440, re-perform the DFA feature extraction of step S200 and the classification using the Transformer model of step S300 for each modal function after VMD decomposition, set the labels with a scaling index less than 0.5 as having flicker noise, screen out the modes without flicker noise, and finally obtain a reconstructed flicker noise-free signal.

[0056] A system for IMF screening and GNSS signal reconstruction using deep learning enhancement, the system has a program module corresponding to the above steps, and executes the steps in the above IMF screening and GNSS signal reconstruction method using deep learning enhancement during operation.

[0057] A computer-readable storage medium stores a computer program, wherein the computer program is configured to implement the steps of an IMF screening and GNSS signal reconstruction method enhanced by deep learning when called by a processor.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The present invention discloses a method and system for IMF screening and GNSS signal reconstruction enhanced by deep learning. Compared with the traditional DFA method which only relies on the single feature of scaling index to screen IMF, the present invention introduces the Transformer deep learning model, which can fully capture the complex time domain, frequency domain and energy characteristics in IMF; by performing multi-dimensional feature extraction and classification on IMF, the accuracy of IMF screening is improved compared with the prior art, and IMF containing flicker noise is more accurately identified, laying the foundation for subsequent high-quality signal reconstruction; more accurate IMF screening removes more flicker noise components, and can better retain effective signal components during signal reconstruction; iCEEMDAN and VMD technologies are used to decompose and reconstruct the signal, which further optimizes the quality of signal reconstruction, improves the accuracy and stability of the reconstructed signal, thereby improving the quality of GNSS signal, and helps to improve the accuracy of applications such as positioning, navigation and time synchronization. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a flowchart of a method for IMF screening and GNSS signal reconstruction enhanced by deep learning in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0062] Specific implementation plan 1: Combine Figure 1 As shown, the present invention provides an IMF screening and GNSS signal reconstruction method enhanced by deep learning, comprising the following steps:

[0063] S100, signal reading and iCEEMDAN decomposition, applying the iCEEMDAN algorithm (integrated empirical mode decomposition) to the noisy GNSS signal, decomposing it into multiple IMFs to extract different frequency components in the signal, including:

[0064] Let the original signal be s(t), w (i) represents the i-th realization of the added Gaussian white noise sample (independent repeated experiments), E k (·) represents the operation process of extracting the kth mode function (IMF) through empirical mode decomposition (EMD), N(·) represents the operation of envelope averaging of the signal to obtain the local mean, <·> represents the averaging of all noise realizations, and the parameter β 0 ,β 1 ,β 2 ,...,β k is the weight factor for adjusting the noise scale;

[0065] S110, read the GNSS signal s(t) containing flicker noise, first add a weighted white noise term to the original signal s(t) to obtain a signal set (s (i) ):

[0066] s (i) =s+β 0 E 1 (w (i) )

[0067] S120, using the iCEEMDAN method to transform the signal set (s (i) ) is decomposed into multiple intrinsic mode functions (IMFs), and for each mode function IMF k , calculate the final residual r k = <N(r k-1 +β k-1 E k (w (i) ))>, Finally, we get a set of IMFS: Specifically include:

[0068] For each signal set s (i) Perform EMD to obtain its local mean and average all realizations:

[0069] r 1 = <N(s (i) )>

[0070] Then the first-order IMF is:

[0071]

[0072] In obtaining the first-order residual r 1 Then, add it to the weighted second modal noise component and average all realizations locally:

[0073] r 2 = <N(r 1 +β 1 E 2 (w (i) ))>.

[0074] Then the second-order IMF is:

[0075]

[0076] Follow the above steps to get the k-order mode and k IMFs, and then repeat the iteration until all the expected intrinsic mode function sets are obtained. The final residual is r K , no longer decompose; the IMF component containing flicker noise characteristics can be effectively separated, thus providing a basis for subsequent signal quality evaluation, flicker characteristic analysis and positioning accuracy improvement;

[0077] S200, perform DFA (Detrended Fluctuation Analysis) feature extraction on IMFs. DFA (Detrended Fluctuation Analysis) is a long-range correlation analysis method for non-stationary time series, specifically including:

[0078] S210, calculate the mean of each IMF <IMF i >

[0079] Find the mean of all given signal sequences s(t):

[0080]

[0081] S220, subtract each IMF from its own mean, and then sum the errors to construct the cumulative deviation sequence Y i (t);

[0082]

[0083] S230, Y i (t) Divide the window into segments according to the length n and use a polynomial to fit the local trend Y fit,k (t), and then calculate the signal fluctuation function F k (n):

[0084]

[0085] Then change the window length n, fit n and the fluctuation function through double logarithmic coordinates, and get the scaling index α k :

[0086] F(n)~n α

[0087] At the same time, the time domain features, frequency domain features and energy features of IMFs are extracted, and the labels with a scaling index less than 0.5 are set as flicker noise, and the rest are set as flicker-free IMFs. Finally, the feature vector f of each IMF is output k ;

[0088] S300, using the Transformer model to classify IMFs, including:

[0089] Transformer is a deep neural network structure based on the self-attention mechanism, which does not rely on the traditional RNN or CNN structure. Its core is to achieve global dependency modeling of the internal information of the input sequence through linear transformation and weighted summation of query, key and value.

[0090] Input feature vector X = [f 1 ,f 2 ,...,f K ], based on the existing data, mark whether the IMF contains flicker noise; the "existing data" refers to the data used to mark whether the IMF contains flicker noise, which is used for feature classification training and classified in the Transformer model, and finally outputs the IMF part without flicker noise; through linear mapping

[0091] Q=XW Q ,K=XW K ,V=XW V , Attention Mechanism

[0092] Z=Concat(head 1 ,head 2 ,...,head h )W O After feature classification training, all IMFs obtained in step S200 are input into the network, and the feature vectors of each IMF are classified to obtain the predicted label Set the noise-free label to 0, and the final output label is the noise-free IMFS part;

[0093] Where Q is the query matrix, K is the key matrix, V is the value matrix; WQ ,W K ,W V is a trainable parameter matrix;

[0094] head i =Attention(Q i ,K i ,V i ) and W O is the output mapping parameter; the Encoder or Decoder layer in the Transformer also includes a feed-forward neural network (FFN) and a residual connection and a layer normalization module. After multiple layers of stacked self-attention and feed-forward layers, the Transformer can obtain a high-level feature representation of the input sequence;

[0095] S400, signal reconstruction and VMD (variational mode decomposition) decomposition, specifically including,

[0096] VMD (Variational Mode Decomposition) is a technical method that adaptively decomposes a given signal into several narrowband intrinsic mode functions (IMFs) by solving a variational optimization problem.

[0097] S410, will be flicker-free Sum and reconstruct the flicker noise-free signal s clean (t);

[0098] S420, for s clean (t) Perform adaptive decomposition, set the mode number K and penalty factor α to control the bandwidth range of the decomposition,

[0099] And initialize the modal function i of each mode k (t) and center frequency ω k ;

[0100]

[0101] S430, optimize mode i by iterative method k (t) and center frequency ω k , gradually separate the different frequency components of the signal; in each round of iteration, adjust the center frequency and bandwidth of the mode according to the frequency domain and time domain information until the convergence condition is met, and finally obtain K narrowband modes and their frequency information of adaptive decomposition;

[0102] The basic idea of ​​VMD is to solve the following constrained variational problem:

[0103]

[0104] Among them, j represents the imaginary unit and t represents time;

[0105] And satisfy the constraints:

[0106]

[0107] Among them, δ(t) is the Dirac function, * represents the convolution operation, is the time differential operator, ‖·‖ 2 For L 2 norm;

[0108] By introducing the penalty factor α and the Lagrangian multiplier, the augmented Lagrangian function is constructed:

[0109]

[0110] Using the alternating direction multiplier method, {i k},{ω k},λ are iteratively optimized. The formula is shown below. After the iteration converges, all IMFs and corresponding center frequencies are obtained, thereby completing the VMD decomposition of the signal.

[0111]

[0112] Where τ represents the step size parameter (learning rate), which controls the update rate of the Lagrange multiplier; I represents the total number of modes, that is, the number of modal functions decomposed from the signal;

[0113] S440, applying the DFA+transformer model analysis again to each modal function after VMD decomposition, still setting the labels with a scaling index less than 0.5 as having flicker noise, screening out the modes without flicker noise, and finally obtaining a reconstructed flicker noise-free signal.

[0114] Specific implementation scheme 2: The present invention provides an IMF screening and GNSS signal reconstruction system enhanced by deep learning. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned IMF screening and GNSS signal reconstruction method enhanced by deep learning during operation.

[0115] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0116] Specific implementation scheme three: The present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the IMF screening and GNSS signal reconstruction method enhanced by deep learning when called by a processor.

[0117] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0118] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A method for IMF screening and GNSS signal reconstruction enhanced by deep learning, characterized in that: The following steps are involved: S100, signal reading and iCEEMDAN decomposition, apply the iCEEMDAN algorithm to the noisy GNSS signal and decompose it into multiple IMFs to extract different frequency components in the signal: S200, performing DFA feature extraction on IMFs, and extracting time domain features, frequency domain features, and energy features of IMFs at the same time, setting labels with a scaling index less than 0.5 as having flicker noise, and setting the rest as flicker-free IMFs, and finally outputting a feature vector of each IMF; S300, using the Transformer model to classify IMFs, marking whether the feature vector obtained in step S200 contains flicker noise, and outputting the IMFS part with a label of no flicker noise; S400, signal reconstruction and VMD decomposition, reconstruct the flicker noise-free IMFS obtained in step S300 after summing up, and then perform adaptive decomposition, optimize the modal function and the center frequency through an iterative method, gradually separate the different frequency components of the signal, and obtain K narrowband modes of adaptive decomposition and their frequency information; re-perform the DFA feature extraction of step S200 and the classification using the Transformer model of step S300 on each modal function after the adaptive decomposition, and still set the labels with a scaling index less than 0.5 as having flicker noise, screen out the modes without flicker noise, and finally obtain the reconstructed flicker noise-free signal.

2. The method for IMF screening and GNSS signal reconstruction using deep learning enhancement according to claim 1, characterized in that: In step S100, specifically including: Let the original signal be s(t), w (i) represents the i-th realization of the added Gaussian white noise sample, E k (·) represents the operation process of extracting the kth IMF through empirical mode decomposition, N(·) represents the operation of envelope averaging of the signal to obtain the local mean, <·> represents the averaging of all noise realizations, and the parameters β0, β1, β2, ..., β k is the weight factor for adjusting the noise scale; S110, read the GNSS signal s(t) containing flicker noise, first add a weighted white noise term to the original signal s(t) to obtain a signal set (s (i) ): s (i) =s+β0E1(w (i) ) S120, using the iCEEMDAN method to transform the signal set (s (i) ) is decomposed into multiple IMFs, and for each mode function IMF k , calculate the final residual r k = <N(r k-1 +β k-1 E k (w (i) ))>, Finally, we get a set of IMFS: Specifically include: For each signal set s (i) Perform EMD to obtain its local mean and average all realizations: r1= <N(s (i) ) Then the first-order IMF is: After obtaining the first-order residual r1, add it to the weighted second modal noise component and then take the average after taking the local mean of all realizations: r2= <N(r1+β1E2(w (i) ))>. Then the second-order IMF is: Follow the above steps to get the k-order mode and k IMFs, and then repeat the iteration until all the expected intrinsic mode function sets are obtained. The final residual is r K , no longer decompose.

3. The method of IMF screening and GNSS signal reconstruction using deep learning enhancement according to claim 2, characterized in that: In step S200, specifically including: S210, calculate the mean of each IMF <IMF i > Find the mean of a given signal sequence s(t): S220, subtract each IMF from its own mean, and then sum the errors to construct the cumulative deviation sequence Y i (t); S230, Y i (t) Divide the window into segments according to the length n and use a polynomial to fit the local trend Y fit,k (t), and then calculate the signal fluctuation function F k (n): Then change the window length n, fit n and the fluctuation function through double logarithmic coordinates, and get the scaling index α k : F(n)~n α At the same time, the time domain features, frequency domain features and energy features of IMFs are extracted, and the labels with a scaling index less than 0.5 are set as flicker noise, and the rest are set as flicker-free IMFs. Finally, the feature vector f of each IMF is output k .

4. The method of IMF screening and GNSS signal reconstruction using deep learning enhancement according to claim 3, characterized in that: In step S300, the input feature vector X=[f1,f2,...,f K ], based on the existing data, mark whether the IMF contains flicker noise; through the linear mapping Q = XW Q ,K=XW K ,V=XW V and attention mechanism Z = Concat(head1,head2,...,head h )W O After feature classification training, all IMFs obtained in step S200 are input into the network, and the feature vector of each IMF is classified to obtain the predicted label Set the noise-free label to 0, and the final output label is the noise-free IMFs part; Where Q is the query matrix, K is the key matrix, V is the value matrix; W Q ,W K ,W V is a trainable parameter matrix; head i =Attention(Q i ,K i ,V i ) and W O Mapping parameters for output.

5. The method of IMF screening and GNSS signal reconstruction using deep learning enhancement according to claim 4, characterized in that: In step S400, specifically including: S410, will be flicker-free Sum and reconstruct the flicker noise-free signal s clean (t); S420, for s clean (t) Perform adaptive decomposition, set the mode number K and penalty factor α to control the bandwidth range of decomposition, and initialize the modal function i of each mode k (t) and center frequency ω k ; S430, optimize mode i by iterative method k (t) and center frequency ω k , gradually separate the different frequency components of the signal; in each round of iteration, adjust the center frequency and bandwidth of the mode according to the frequency domain and time domain information until the convergence condition is met, and finally obtain K narrowband modes and their frequency information of adaptive decomposition; Solve the following constrained variational problem: And satisfy the constraints: Where j represents the imaginary unit, t represents time, δ(t) is the Dirac function, and * represents the convolution operation. is the time differential operator, ‖·‖2 is the L2 norm; by introducing the penalty factor α and the Lagrange multiplier, the augmented Lagrangian function is constructed: Using the alternating direction multiplier method, {i k },{ω k },λ are iteratively optimized. The formula is as follows. After the iteration converges, all IMFs and corresponding center frequencies are obtained, thereby completing the VMD decomposition of the signal: Among them, τ represents the step size parameter, which is used to control the update rate of the Lagrange multiplier; I represents the total number of modes, that is, the number of modal functions decomposed from the signal; S440, re-perform the DFA feature extraction of step S200 and the classification using the Transformer model of step S300 for each modal function after VMD decomposition, set the labels with a scaling index less than 0.5 as having flicker noise, screen out the modes without flicker noise, and finally obtain a reconstructed flicker noise-free signal.

6. A deep learning-enhanced IMF screening and GNSS signal reconstruction system, characterized in that: The system has a program module corresponding to the steps of any one of claims 1 to 5 above, and executes the steps in the above-mentioned IMF screening and GNSS signal reconstruction method enhanced by deep learning when running.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the IMF screening and GNSS signal reconstruction method enhanced by deep learning according to any one of claims 1 to 5 when called by a processor.

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