A method for separating time-frequency overlapping signals based on instantaneous phase discontinuity

Abstract

The present invention provides a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, which uses a variational mode extraction algorithm to extract momentum wheel interference signals that may contain time-frequency overlapping areas, thereby realizing a primary separation of natural signals and interference signals; constructing a complex analytical form of the interference signal to obtain its phase function and envelope; analyzing the mutation and discontinuity points of the phase function, identifying and marking the time-frequency overlapping areas and non-overlapping areas; constraining the bandwidth of the overlapping area to be consistent with the non-overlapping area, and reconstructing the interference signal of the overlapping area; subtracting the reconstructed interference signal from the marked mixed signal of the overlapping area to realize a secondary separation of the natural signal; and finally merging the primary and secondary natural signal separation results to realize lossless separation of the natural signal. Based on the discontinuity of the instantaneous phase, the present invention can solve the problem of lossy separation when the traditional method processes the time-frequency overlapping area, thereby maintaining the integrity of the natural signal.

Description

Technical Field

[0001] The invention relates to the field of measurement and testing technology, and in particular to a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity. Background Art

[0002] Space magnetic field observation is of great significance for understanding space physics phenomena and revealing space physics laws. However, due to the influence of various complex electromagnetic interferences of spacecraft, it is quite difficult to obtain high-quality observation results. For example, spacecraft equipment such as momentum wheels, magnetic torquers and rotating mechanisms will generate magnetic field interference, thereby reducing the quality of observation data. Among these devices, satellite momentum wheels are normally open devices, mainly used for satellite attitude adjustment. Their working process is accompanied by a large number of electromagnetic harmonics, resulting in significant interference to magnetic field measurements. And it is found in the observation data that there is often a time-frequency overlap between the interference signal (the multi-harmonic signal generated by the momentum wheel in the present invention) and the natural signal (the magnetic field signal in nature in the present invention). This time-frequency overlap makes it difficult to observe and analyze the natural signal covered by the interference, which makes it difficult to observe space physics phenomena and analyze scientific laws in the observation data. Therefore, separating the interference signal generated by the momentum wheel and solving the time-frequency overlap problem are crucial to improving the quality of detection data and ensuring the reliability of scientific discoveries in space observations. However, the separation of time-frequency overlapping signals is one of the difficult problems in the field of signal processing. Because the separation problem of time-frequency overlapping signals is usually mathematically underdetermined. In many cases, it may not be possible to accurately separate signals due to incomplete or ambiguous information. In addition, the similarity or sameness of the frequency components of the signals in the overlapping area makes the mixed signal appear as a complex mixture of multiple frequency components. The frequency and amplitude of the mixture show irregular changes, which makes it more difficult to separate the signals.

[0003] In order to separate the interference generated by the momentum wheel, predecessors have proposed a variety of algorithms, such as blind source separation, independent component analysis, and multi-channel singular spectrum analysis. However, these algorithms have limitations when separating the momentum wheel interference, which are specifically reflected in the following two aspects: (1) These algorithms usually have adaptive characteristics and are prone to modal aliasing, resulting in the loss of some natural signals mixed into the mode during the separation of multi-order harmonic interference; (2) These algorithms cannot effectively identify and separate the time-frequency overlapping areas, and the natural signals in the overlapping areas are often mistakenly identified as interference signals for separation. In short, although the existing satellite momentum wheel interference separation algorithms have certain effects, they often fail to take into account the damage to the natural signals after separation, resulting in reduced quality of scientific data.

[0004] Patent application CN107607065A discloses an impact echo signal analysis method based on variational modal decomposition. The acquired signal is decomposed into multiple modes using the variational modal decomposition (VMD) method, and the center frequency of the mode is adaptively obtained. However, when a higher noise level is involved, the decomposition result may be interfered by the noise, and the processing time is relatively long, so the integrity of the natural signal cannot be maintained.

[0005] Patent application CN107679199A discloses a single-channel radio mixed signal separation method based on variational modal decomposition. The single-channel radio mixed signal is separated by a variational modal decomposition algorithm with optimized parameters, and each separated radio signal is then subjected to a second separation in turn by using a variational modal decomposition algorithm with optimized parameters. This method still uses the variational modal decomposition method, and although it also uses a penalty factor for optimization, it still cannot accurately separate the natural signal.

[0006] Therefore, it is necessary to propose a new method that can effectively separate the multi-harmonic interference generated by the satellite momentum wheel and realize the separation of time-frequency overlapping signals while maintaining the integrity of the natural signal, so as to improve the quality and reliability of space magnetic field measurements. Summary of the invention

[0007] The present invention aims to solve the problems of removing multi-harmonic interference from the momentum wheel of a spacecraft and separating the time-frequency overlap of interference and natural signals, and provides a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, which can not only remove the multi-harmonic interference caused by the momentum wheel in scientific data, but also separate the time-frequency overlap area of ​​interference and natural signals, thereby realizing lossless separation of natural signals.

[0008] The present invention provides a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, comprising the following steps:

[0009] S1. Extract mixed signals using variational mode extraction algorithm The sub-signal with adjustable bandwidth near the center frequency obtains the mode and the residual signal. The mode is the interference signal after one separation. s mode ( t ), the remaining signal is the natural signal after one separation f r ( t ), interference signal after one separation s mode ( t ) is an interference signal with time-frequency overlap. After one separation, the natural signal f r ( t ) is a natural signal of the presence of loss;

[0010] S2, according to the interference signal after one separation s mode ( t ) is used in complex analytical form to obtain the phase function and envelope ;

[0011] S3. By analyzing the phase function The mutation and discontinuity in the interference signal are separated once s mode ( t ) to identify and mark the time-frequency overlapping and non-overlapping regions;

[0012] S4, constraining the bandwidth of the time-frequency overlapping region to be the same as that of the non-overlapping region and making the frequency band of the interference signal in the time-frequency overlapping region the same as that of the natural signal, and then combining the envelope characteristics of the interference signal in the non-overlapping region to obtain the reconstructed interference signal in the overlapping region;

[0013] S5. Based on the same bandwidth, the interference signal reconstructed in the overlapping area is subtracted from the mixed signal in the time-frequency overlapping area to perform secondary separation of the natural signal in the overlapping area to obtain the natural signal in the overlapping area. ;

[0014] S6, the natural signal after the first separation f r ( t ) and the natural signal in the overlapping area Merge and reconstruct to get natural signal , a time-frequency overlapping signal separation method based on instantaneous phase discontinuity is completed.

[0015] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity described in the present invention is, as a preferred embodiment, step S1 comprises the following steps:

[0016] S11, get mixed signal , mixed signal By interference signal and natural signals s g ( t )composition;

[0017] S12, mixed signal Perform short-time Fourier transform to obtain the time-frequency joint distribution of the received signal spectrum S ( t , f );

[0018] S13, setting a threshold, from the time-frequency joint distribution of the received signal spectrum S ( t ,f ) to determine the interference signal The center frequency and bandwidth;

[0019] S14. Based on the center frequency and bandwidth, a sub-signal with an adjustable bandwidth near the center frequency is extracted using variational mode to obtain a mode and a residual signal, and perform a primary separation of the natural signal.

[0020] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity described in the present invention is, as a preferred embodiment, in step S12,

[0021] ;

[0022] in, j is the imaginary part, f is the frequency, is the window length of STFT, Intercept global signal for window function The short-term signal around time t, t is the center time, the center position of the current time window, τ is a time variable at any time within the window time range.

[0023] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity of the present invention is preferably implemented in step S11, wherein the mixed signal Interference signal in It is the interference signal of the spacecraft momentum wheel.

[0024] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity described in the present invention is, as a preferred embodiment, step S2 comprises the following steps:

[0025] S21, interference signal after separation s mode ( t ) is subjected to Hilbert transform to obtain the complex analytical form:

[0026] ;

[0027] in,

[0028] ;

[0029] and They are the interference signals after one separation s mode ( t )’s amplitude and phase;

[0030] ;

[0031] in, HT [ * ] represents the Hilbert transform, PV is the Cauchy principal value; is the interference signal after separation s mode ( t ) at time τ The value of τ is the integration variable;

[0032] S22, interference signal after primary separation s mode ( t )’s phase function and envelope are:

[0033] .

[0034] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity described in the present invention is, as a preferred embodiment, step S3 comprises the following steps:

[0035] S31, phase function Unwrapping to obtain the unwrapped phase function :

[0036] ;

[0037] in, , , sgn(*) is the sign function;

[0038] S32, judging the time-frequency overlapping area and the non-overlapping area according to the phase function and the envelope and dividing them; the phase function after unwrapping It shows continuous change in the non-overlapping area; the phase function after unwrapping A sudden change occurs at the boundary of the time-frequency overlapping region; a sudden change occurs in the trend of the phase function in the time-frequency overlapping region;

[0039] When the phase function of the mode to be analyzed changes linearly, the phase function is:

[0040] ;

[0041] The entire time region of the modality is marked as non-overlapping region, where f I Interference signal frequency, Interference signal Initial phase;

[0042] When the phase function of the mode to be analyzed has a nonlinear trend, the phase function is:

[0043] ;

[0044] The time region [t1, t2] of the modal is marked as the time-frequency overlapping region, and the other time regions are non-overlapping regions, where: a I Interference signal Amplitude, For natural signals Amplitude, For natural signals Initial phase.

[0045] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity described in the present invention is, as a preferred embodiment, in step S32, the mode of the time-frequency overlapping region is:

[0046] ;

[0047] in,

[0048] ;

[0049] ;

[0050] R For the overlapping area [ t 1, t 2] The composite envelope of the overlapping signals, is the phase of the overlapping signals.

[0051] The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity described in the present invention is, as a preferred embodiment, step S4 comprises the following steps:

[0052] S41. Use the variational mode extraction algorithm and increase the penalty factor value of the overlapping area to enhance the bandwidth of the constrained time-frequency overlapping area:

[0053] .

[0054] in, is the increased penalty factor, which is used to constrain the bandwidth of the time-frequency overlap region. α 0 is the initial penalty factor for variational mode extraction, BW overlap is the bandwidth of the time-frequency overlapping region, BW non-overlap is the bandwidth of the non-overlapping area;

[0055] Penalty factor based on constraints and center frequencies in the frequency domain using variational mode extraction from mixed signals The interference signal in the time-frequency overlapping region is re-extracted to obtain the mode after the frequency band is constrained. The frequency band of the interference signal in the time-frequency overlapping region is the same as that of the natural signal.

[0056] S42, by statistically analyzing the interference envelope characteristics of the non-overlapping area and combining the phase function, the complex analytical form of the reconstructed interference signal in the overlapping area is obtained:

[0057] ;

[0058] in,

[0059] ;

[0060] ;

[0061] Reconstruct the phase function of the interfering signal for the overlap region, The envelope of the interfering signal is reconstructed for the overlap region.

[0062] The present invention discloses a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, as a preferred embodiment, in step S5, the complex analytical form of the reconstructed interference signal in the overlapping area is subjected to an inverse Hilbert transform to obtain the real signal form of the reconstructed interference signal in the overlapping area; based on the same bandwidth, the real signal of the reconstructed interference signal in the overlapping area is subtracted from the marked mixed signal in the time-frequency overlapping area to perform secondary separation of the natural signal in the time-frequency overlapping area, and obtain the natural signal in the overlapping area. ;

[0063] Natural signal in overlapping area for:

[0064] ;

[0065] In step S6,

[0066] .

[0067] The time-frequency overlapping signal separation method based on instantaneous phase discontinuity described in the present invention, as a preferred mode, uses a spacecraft momentum wheel interference signal separation system to separate the time-frequency signal overlapping area of ​​momentum wheel interference and natural signal;

[0068] The spacecraft momentum wheel interference signal separation system includes a natural signal primary separation module, a phase function acquisition module, a time-frequency overlapping area division and identification module, an overlapping area interference signal reconstruction module, an overlapping area natural signal secondary separation module and a natural signal merging and reconstruction module which are sequentially connected;

[0069] The primary separation module of natural signals extracts mixed signals through variational mode extraction algorithm The momentum wheel interference signal in the image is obtained by separating the interference signal s mode ( t ) and the natural signal after one separation f r ( t );

[0070] The phase function acquisition module is based on the interference signal after the first separation. s mode ( t ) to obtain the phase function and envelope ;

[0071] The time-frequency overlapping area division and marking module identifies and divides the time-frequency overlapping area and the non-overlapping area in the interference signal after separation by analyzing the mutations and discontinuities in the phase function;

[0072] The overlapping area interference signal reconstruction module constrains the bandwidth of the overlapping area to be the same as that of the non-overlapping area so that the interference signal in the overlapping area has the same frequency band as the natural signal, and then combines the envelope characteristics of the interference signal in the non-overlapping area to obtain the reconstructed interference signal in the overlapping area;

[0073] The overlapping area natural signal secondary separation module subtracts the reconstructed interference signal in the overlapping area from the mixed signal in the time-frequency overlapping area based on the same bandwidth to perform secondary separation of the natural signal in the overlapping area, and obtains the overlapping area natural signal. ;

[0074] The natural signal merging and reconstruction module combines the natural signal after separation f r ( t ) and the natural signal in the overlapping area Merge and reconstruct to get natural signal .

[0075] For the multi-harmonic interference generated by the momentum wheel mixed into the natural signal, the natural magnetic field signal is non-stationary, that is, the frequency and amplitude of the natural signal will change over time. Although the multi-harmonic interference generated by the momentum wheel has multiple harmonic frequencies, these harmonic frequencies fluctuate within a certain range and can be considered as an approximately stationary signal, that is, the frequency and amplitude are almost unchanged. According to Ville's definition of instantaneous frequency, the instantaneous frequency of a non-stationary signal is the derivative of the phase function of its analytical signal. Phase information is very sensitive to signal mutations and can be used to observe the detailed features and mutations of the signal. For example, in the field of image processing, the phase consistency criterion detects the edge of the image by calculating the phase consistency of the image, which can effectively suppress the influence of local illumination changes while retaining information such as corners, lines and textures in the image. In the field of fault diagnosis, the phase function can also be used as an effective tool to describe the time-varying dynamic system of structural waves. For an approximately stationary interference signal, the first-order derivative of its phase function is a constant value and the phase function is a linear trend; for a non-stationary signal, the first-order derivative of the phase function is its instantaneous frequency. If a certain area in the interference signal contains a non-stationary signal due to time-frequency overlap, it will inevitably appear as a non-constant value and a sensitive change with a nonlinear trend in the instantaneous phase of the interference signal. Based on the above analysis, the present invention utilizes the sensitive characteristics of the instantaneous phase to the change of signal frequency, and uses the phase to characterize the difference in frequency between the quasi-stationary signal and the non-stationary signal. By analyzing the instantaneous phase of the extracted quasi-stationary momentum wheel interference, the non-stationary natural signal overlapping area in the interference is identified, and an effective solution is proposed to solve the problem of time-frequency overlapping areas. Based on this idea, the present invention proposes a time-frequency overlap separation method based on instantaneous phase discontinuity to separate satellite momentum wheel interference.

[0076] A method for separating time-frequency overlapping signals based on instantaneous phase discontinuity comprises the following steps: S1. for a mixed signal containing momentum wheel interference and a magnetic field signal of natural variation, a variational mode extraction algorithm is used to extract the approximately stable momentum wheel interference signal in the mixed signal, and an interference signal that may have time-frequency overlap and a natural signal that may be damaged are obtained, thereby achieving a one-time separation of the natural signal and the interference signal;

[0077] S2. construct a complex analytical form of the interference signal that may have time-frequency overlap to obtain its phase function and envelope;

[0078] S3. By analyzing the mutations and discontinuities in the phase function, the time-frequency overlapping area and the non-overlapping area in the interference signal are identified and marked;

[0079] S4. constrain the bandwidth of the overlapping area to be consistent with the non-overlapping area, so that the interference signal in the overlapping area has the same frequency band as the natural signal, and then combine the envelope characteristics of the interference signal in the non-overlapping area to reconstruct the interference signal in the marked overlapping area;

[0080] S5. Based on the same bandwidth, the reconstructed interference signal is subtracted from the mixed signal of the marked overlapping area to achieve secondary separation of the natural signal in the overlapping area;

[0081] S6. The natural signals after the two separations are merged and reconstructed, and finally the lossless separation of the natural signal and the interference signal is achieved.

[0082] The primary separation process of natural signals (step S1) includes:

[0083] 1a) obtaining a mixed signal to be processed containing the interference of the momentum wheel of the spacecraft, wherein the mixed signal includes a magnetic field signal with natural changes and a momentum wheel interference signal with multi-harmonic and approximately stable characteristics;

[0084] 1b) Perform time-frequency transformation on the mixed signal to obtain the time-frequency joint distribution of the mixed signal spectrum;

[0085] 1c) based on the time-frequency joint distribution of the mixed signal spectrum, determining the center frequency and bandwidth of the interference signal from the time-frequency joint distribution using a threshold method;

[0086] 1d) Based on the center frequency and bandwidth of the interference signal, the interference signal with the specified center frequency and bandwidth is extracted in the frequency domain to obtain the interference signal that may have time-frequency overlap and the natural signal that may be incomplete, thereby achieving a one-time separation of the natural signal.

[0087] The process of obtaining the phase function (step S2) includes:

[0088] 2a) Based on the approximate stationary characteristics of the spacecraft interference signal, the interference signal extracted in step S1 is subjected to Hilbert transform, and a complex analytical form of the interference signal is constructed;

[0089] 2b) Based on the complex analytical form of the interference signal, a phase function and an envelope of the interference signal are calculated and obtained.

[0090] The process of determining the time-frequency overlapping area (step S3) includes:

[0091] 3a) Unwrapping the phase function to characterize the frequency variation of the entire interference signal over time;

[0092] 3b) If there is a time-frequency overlap region of the mixed natural signal, based on the approximate stationary characteristics of the spacecraft interference signal, the phase function after unwrapping shows a continuous change in the non-overlapping region; while the phase function after unwrapping changes suddenly at the boundary of the time-frequency overlap region, and the change trend of the phase function changes in the time-frequency overlap region;

[0093] 3c) By analyzing the sudden changes and discontinuous points in the phase function after unwrapping, the time-frequency overlapping and non-overlapping areas in the interference signal can be identified and marked.

[0094] The interference signal reconstruction process in the overlapped area (step S4) includes:

[0095] 4a) constraining the bandwidth of the time-frequency overlapping region, and re-extracting the interference signal in the overlapping region from the mixed signal in the frequency domain based on the constrained bandwidth and the above-mentioned center frequency, so as to remove the frequency components outside the center frequency, so that the interference signal in the overlapping region has the same frequency band as the natural signal;

[0096] 4b) The interference envelope characteristics of the non-overlapping area are statistically analyzed and combined with the phase function to reconstruct the complex analytical form of the interference signal in the time-frequency overlapping area.

[0097] The natural signal separation process in the overlapping area (step S5) includes:

[0098] 5a) Performing an inverse Hilbert transform on the complex analytical form of the interference signal in the time-frequency overlapping region reconstructed in step S4 to obtain a real signal form of the reconstructed interference signal.

[0099] 5b) Based on the same bandwidth, the reconstructed interference signal is subtracted from the mixed signal in the marked overlapping area to achieve a secondary separation of the natural signal in the overlapping area.

[0100] The natural signal merging and reconstruction process (step S6) includes:

[0101] The possibly incomplete natural signal after the primary separation obtained in step S1 and the natural signal in the overlapping area after the secondary separation obtained in step S5 are combined and reconstructed, thereby finally achieving lossless separation of the natural signal and the interference signal.

[0102] The present invention has the following advantages:

[0103] (1) Based on the discontinuity of instantaneous phase, the present invention analyzes the phase function of the extracted momentum wheel interference signal, uses the instantaneous phase to characterize the difference in frequency between the approximate stationary signal and the non-stationary signal, identifies and marks the overlapping area of ​​non-stationary natural signals in the interference signal, and thus proposes an effective solution to the problem of time-frequency overlapping areas.

[0104] (2) The present invention can solve the lossy separation problem of traditional methods in dealing with time-frequency overlapping regions, thus maintaining the integrity of natural signals. In addition, the present invention is also widely applicable to the time-frequency overlapping separation scenarios of approximately stationary signals and time-varying signals, and has wide versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1It is a flow chart of a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity;

[0106] Figure 2 A mixed signal time domain waveform diagram of an embodiment of a method for overlapping and separating time-frequency signals with instantaneous phase discontinuity;

[0107] Figure 3 A mixed signal power spectral density (PSD) time-frequency representation diagram of an embodiment of a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity;

[0108] Figure 4 A method for separating time-frequency overlapping signals based on instantaneous phase discontinuity is provided. f r ( t )’s PSD time-frequency representation diagram;

[0109] Figure 5 The invention is an embodiment of a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, wherein the interference signal containing the time-frequency overlapping area after one separation is s mode ( t )’s PSD time-frequency representation diagram;

[0110] Figure 6 It is a time-frequency representation diagram of a lossless natural signal PSD after secondary separation in an embodiment of a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity;

[0111] Figure 7 It is a PSD time-frequency representation diagram of an interference signal after secondary separation in an embodiment of a method for separating time-frequency overlapping signals based on instantaneous phase discontinuity;

[0112] Figure 8 The figure is a schematic diagram of the structure of a spacecraft momentum wheel interference signal separation system based on a time-frequency overlapping signal separation method based on instantaneous phase discontinuity. DETAILED DESCRIPTION

[0113] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Example 1

[0114] A method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, in this embodiment 1, the on-board magnetic field waveform data of the ELF band of the induction magnetometer (SCM) of the Zhangheng-1 electromagnetic monitoring satellite (CSES) is used as the signal to be processed, and a natural signal for testing is added to illustrate the effect of the present invention. The satellite platform is equipped with four momentum wheels with a maximum rotation speed of 2400rpm.

[0115] The application principle of the present invention is further described below in conjunction with the accompanying drawings.

[0116] like Figure 1 As shown, the time-frequency overlapping signal separation method based on instantaneous phase discontinuity provided by the embodiment of the present invention includes the following steps:

[0117] S1. Obtain the mixed signal of the on-board scientific data including the CSES SCM ELF band that is interfered by the momentum wheel, extract the approximately stable momentum wheel interference signal in the mixed signal, obtain the interference signal that may have time-frequency overlap and the natural signal that may be incomplete, and realize the primary separation of the natural signal;

[0118] The primary separation process of natural signals is as follows:

[0119] 1a) In this embodiment, the model of the mixed signal is:

[0120] ;

[0121] in, is the interference signal, s g ( t ) is a natural signal. The present invention assumes that the interference signal is an approximately stable signal, that is, the frequency and amplitude of the interference signal fluctuate only in a small range, and can be approximately equivalent to a frequency component and a constant amplitude:

[0122] .

[0123] Among them, the amplitude a I and frequency f I can be regarded as constants. is the initial phase. The natural signal is a general non-stationary signal, and its model is:

[0124] .

[0125] a g ( t )and are all arbitrary time-varying functions, representing amplitude and phase respectively.

[0126] 1b) For the mixed signal of this embodiment s mix ( t ) Perform short-time Fourier transform (STFT) to obtain the time-frequency joint distribution of the received signal spectrum S ( t , f ); the short-time Fourier transform is:

[0127] .

[0128] in, f is the frequency, is the window length of STFT, s mix ( τ ) is the window function to intercept the global signal s mix ( t ) is a short-term signal around time t, t is the center time, indicating the center position of the current time window. τ is any time, representing a time variable within the window time range.

[0129] The sampling rate of the CSES SCM ELF band signal is 10240S / s, and the frequency resolution of the STFT is 2.5Hz. Figure 2 As shown in FIG. 1 , it is a time domain waveform representation diagram of a mixed signal in an embodiment of the present application. Figure 3 As shown, it is a time-frequency characterization diagram of the power spectrum density of the mixed signal of the embodiment of the present application. Two relatively significant horizontal gray bands can be observed, which are caused by the harmonic interference generated by the momentum wheel. In addition, there are also multiple natural signals in the form of whistle waves in the figure, among which some whistle waves have time-frequency overlapping areas with the above-mentioned harmonic interference.

[0130] 1c) Based on the time-frequency joint distribution of the received signal spectrum. Figure 3 In the example, 28 Hz and 140 Hz are selected from bottom to top as the center frequencies of the harmonic interference of the momentum wheel. A threshold of appropriate size is set, and the bandwidth corresponding to the center frequency of the harmonic interference signal is determined from the time-frequency joint distribution, thereby determining the initial penalty factor.

[0131] 1d) Based on the center frequency and bandwidth of the interference signal, the signal with the specified center frequency and bandwidth is extracted using the frequency domain signal extraction algorithm. The frequency domain signal extraction algorithm used in this embodiment is variational mode extraction, which can extract a sub-signal with an adjustable bandwidth near the center frequency each time. After multiple extractions, an interference signal with time-frequency overlap is obtained. s mode ( t) and possibly incomplete natural signals f r ( t ). The extracted interference signal is also called mode, and the corresponding one is the residual signal.

[0132] Right now: .

[0133] Figure 4 This is a natural signal that is lost after one separation in the embodiment of the present application. f r ( t )’s PSD time-frequency representation. Figure 5 The interference signal containing the time-frequency overlapping area after the first separation in the embodiment of the present application s mode ( t )’s PSD time-frequency representation.

[0134] S2, constructing a complex analytical form of the interference signal that may have time-frequency overlap to obtain its phase function and envelope;

[0135] The specific method of obtaining the phase function process is:

[0136] 2a) Perform Hilbert transform on the interference signal extracted in step S1. The complex analytical form of the interference signal is:

[0137] First, write the extracted interference signal into a general form:

[0138] ;

[0139] in, a mode (t) and φ mode (t) represent the amplitude and phase of the mode respectively. The mode contains the interference signal of the momentum wheel and the possible natural signal. Because the interference signal of the momentum wheel is approximately stable, and the possible natural signal can be regarded as a narrowband signal after the variational mode extraction (which can be regarded as a Wiener filter). Therefore, when the extracted mode is Hilbert transformed, the analytical condition is satisfied:

[0140] ;

[0141] in, A ( f )and G ( f ) respectively represent a mode ( t ) amplitude and cosine function cos φ mode ( t), a and b is an arbitrary constant. Then the extracted interference signal can be Hilbert transformed:

[0142] ;

[0143] in, HT [ * ] represents Hilbert transform;

[0144] For real signals s mode ( t ), whose Hilbert transform is:

[0145] ;

[0146] in, PV is the Cauchy principal value.

[0147] Interference signal z mode ( t ) is in the form of complex analysis:

[0148] ;

[0149] 2b) Based on the complex analytical form of the interference signal, calculate the phase function and envelope of the interference signal:

[0150] ;

[0151] S3, by analyzing the mutations and discontinuities in the phase function, the time-frequency overlapping area and the non-overlapping area in the interference signal are identified and marked;

[0152] The process of determining the time-frequency overlapping area is:

[0153] 3a) Unwrapping the phase function to characterize the change of the frequency component of the entire interference signal over time:

[0154] ;

[0155] in, , , sgn(*) is the sign function.

[0156] 3b) If there is no time-frequency overlap in the interference signal, the phase function and envelope of the interference signal (mode) are expressed as:

[0157] .

[0158] At this time, the phase function changes linearly, indicating that there is no time-frequency overlapping area in the interference signal.

[0159] If the interference signal overlaps in time and frequency within a certain period of time, the natural signal in the overlapping area can also be approximated as a stationary signal because the bandwidth is limited to a small range after frequency domain extraction. The natural signal in the overlapping area has multiple frequency components. In an ideal case, if the natural signal in the overlapping area is expressed as:

[0160] ;

[0161] The mode is now:

[0162] .

[0163] in,

[0164] ;

[0165] .

[0166] R Indicates the overlapping area[ t 1, t 2] The composite envelope of the overlapping signals, Indicates the phase of the overlapping signals.

[0167] 3c) The phase function of the mode is:

[0168] .

[0169] In the time period [ t 1, t 2], due to the mixing of natural signals, the change trend of the phase function is nonlinear, that is, the discontinuous area. The discontinuity is caused by the phase difference and the amplitude of the natural signal. Generally speaking, the overlapping area has more natural signal frequency components mixed in, and the nonlinear characteristics of the change trend of its phase function are more obvious. In the case of white noise, the phase function of the overlapping area will also fluctuate due to the influence of white noise, but when the intensity of white noise is less than that of the natural signal, the nonlinear change trend of the phase function caused by the natural signal is more obvious. Therefore, the discontinuous area of ​​the phase function can determine the time-frequency overlapping area in the interference signal, and there is a mixed natural signal in this area. Figure 4 The range marked with dotted lines is the time-frequency overlapping area identified and divided by the discontinuous change characteristics of the phase function.

[0170] S4, constraining the bandwidth of the overlapping area to be consistent with the non-overlapping area, so that the frequency band of the interference signal in the overlapping area is the same as that of the natural signal, and then combining the envelope characteristics of the interference signal in the non-overlapping area to reconstruct the interference signal in the overlapping area;

[0171] The reconstruction process of the interference signal in the overlapping area is as follows:

[0172] 4a) Constraining the bandwidth of the time-frequency overlapping region. This embodiment uses a variational mode extraction algorithm to enhance bandwidth constraints to achieve this goal, that is, to increase the penalty factor value of the overlapping region. The method of increasing the penalty factor in this embodiment is:

[0173] .

[0174] in, α 0 is the initial penalty factor for variational mode extraction, BW overlap is the bandwidth of the overlapping area, BW non-overlap is the bandwidth of the non-overlapping area.

[0175] Based on the constrained bandwidth and the above-mentioned center frequency, the interference signal in the overlapping area is re-extracted from the mixed signal using variational mode extraction in the frequency domain to remove frequency components outside the center frequency to meet the narrowband condition;

[0176] 4b) Based on the mode after constraining the frequency band, the natural signal mixed in the mode has the same frequency band as the interference signal; by statistically analyzing the envelope characteristics of the interference signal in the non-overlapping area, the complex analytical form of the interference signal in the time-frequency overlapping area is reconstructed in combination with the phase function:

[0177] ;

[0178] in,

[0179] .

[0180] .

[0181] S5. Based on the same bandwidth, the reconstructed interference signal is subtracted from the mixed signal in the overlapping area to achieve secondary separation of the natural signal in the overlapping area;

[0182] Natural signal separation process in overlapping areas:

[0183] 5a) Perform an inverse Hilbert transform on the complex analytical form of the interference signal in the time-frequency overlap region reconstructed above:

[0184]

[0185] The real analytical form of the reconstructed interference signal is obtained s correct ( t ).

[0186] 5b) Based on the same bandwidth, the reconstructed interference signal is subtracted from the mixed signal in the overlapping area to achieve secondary separation of the natural signal in the overlapping area. The reconstructed interference signal is separated from the overlapping area to obtain the natural signal in the overlapping area:

[0187] .

[0188] S6. The natural signals after the two separations are merged and reconstructed, and finally lossless separation of the natural signal and the interference signal is achieved.

[0189] The natural signal merging and reconstruction process is as follows:

[0190] The possibly incomplete natural signal obtained in step S1 and the natural signal in the overlapping area obtained in step S3 are combined to obtain a lossless natural signal:

[0191] .

[0192] Figure 6 This is a PSD time-frequency representation diagram of a lossless natural signal reconstructed after secondary separation according to an embodiment of the present application. Figure 7 This is a PSD time-frequency representation diagram of the interference signal reconstructed after secondary separation in an embodiment of the present application.

[0193] like Figure 8 As shown, a time-frequency overlapping area separation system based on instantaneous phase discontinuity includes: a primary separation module of natural signals, a phase function acquisition module, a time-frequency overlapping area division marking module, an overlapping area interference signal reconstruction module, an overlapping area natural signal secondary separation module and a natural signal merging and reconstruction module.

[0194] The primary separation module of natural signals is used to extract the approximately stable momentum wheel interference signal from the mixed signal containing the spacecraft momentum wheel interference, obtain the interference signal that may have time-frequency overlap and the natural signal that may be incomplete, and realize the primary separation of the natural signal;

[0195] The phase function acquisition module is used to construct a complex analytical form of an interference signal that may have time-frequency overlap to obtain its phase function and envelope;

[0196] The time-frequency overlapping area division and marking module realizes the identification and division of the time-frequency overlapping area and the non-overlapping area in the interference signal by analyzing the mutations and discontinuities in the phase function;

[0197] The overlapping area interference signal reconstruction module is used to constrain the bandwidth of the overlapping area to be consistent with the non-overlapping area, so that the frequency band of the interference signal in the overlapping area is the same as that of the natural signal, and then combine the envelope characteristics of the interference signal in the non-overlapping area to reconstruct the interference signal in the overlapping area;

[0198] The overlapping area natural signal secondary separation module subtracts the reconstructed interference signal from the mixed signal in the overlapping area based on the same bandwidth to achieve secondary separation of the natural signal in the overlapping area;

[0199] The natural signal merging and reconstruction module merges and reconstructs the natural signals after two separations, and finally achieves lossless separation of natural signals and interference signals.

[0200] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for separating time-frequency overlapping signals based on instantaneous phase discontinuity, characterized in that: The following steps are involved: S1. Extract mixed signals using variational mode extraction algorithm The sub-signal with adjustable bandwidth near the center frequency obtains the mode and the residual signal, and the mode is the interference signal after the first separation. s mode ( t ), the remaining signal is the natural signal after one separation f r ( t ), the interference signal after the first separation s mode ( t ) is an interference signal with time-frequency overlap, and the natural signal after the first separation f r ( t ) is a natural signal of the presence of loss; S2, according to the interference signal after the first separation s mode ( t ) is used in complex analytical form to obtain the phase function and envelope ; S3, by analyzing the phase function The mutations and discontinuities in the s mode ( t ) Identification and marking of overlapping and non-overlapping regions in time and frequency; S4, constraining the bandwidth of the time-frequency overlapping region to be the same as that of the non-overlapping region and making the frequency band of the interference signal in the time-frequency overlapping region the same as that of the natural signal, and then combining the envelope characteristics of the interference signal in the non-overlapping region to obtain a reconstructed interference signal in the overlapping region; S5, based on the same bandwidth, subtract the reconstructed interference signal in the overlapping area from the mixed signal in the time-frequency overlapping area to perform secondary separation of the natural signal in the overlapping area to obtain the natural signal in the overlapping area ; S6, the natural signal after the primary separation f r ( t ) and the natural signal in the overlapping area Merge and reconstruct to get natural signal , a time-frequency overlapping signal separation method based on instantaneous phase discontinuity is completed.

2. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 1, characterized in that: Step S1 includes the following steps: S11, obtaining the mixed signal , the mixed signal By interference signal and natural signals s g ( t )composition; S12, the mixed signal Perform short-time Fourier transform to obtain the time-frequency joint distribution of the received signal spectrum S ( t , f ); S13, setting a threshold, from the time-frequency joint distribution of the received signal spectrum S ( t , f ) to determine the interference signal The center frequency and bandwidth; S14, based on the center frequency and the bandwidth, using variational mode to extract a sub-signal with adjustable bandwidth near the center frequency to obtain a mode s mode ( t ) and the remaining signal f r ( t ) to perform a primary separation of natural signals.

3. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 2, characterized in that: In step S11, the interference signal It is the interference signal of the spacecraft momentum wheel.

4. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 2, characterized in that: In step S12, ； in, j is the imaginary part, f is the frequency, is the window length of STFT, Intercepting mixed signals for window functions The short-term signal around time t, t is the center time, the center position of the current time window, τ is a time variable at any time within the window time range.

5. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 1, characterized in that: Step S2 includes the following steps: S21, the interference signal after the first separation s mode ( t ) is subjected to Hilbert transform to obtain the complex analytical form: ； in, ； and are the interference signals after the first separation s mode ( t )’s amplitude and phase; ； in, HT [ * ] represents the Hilbert transform, PV is the Cauchy principal value; is the interference signal after separation s mode ( t ) at time τ The value of τ is the integration variable; S22, the interference signal after the first separation s mode ( t )’s phase function and envelope are: 。 6. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 1, characterized in that: Step S3 includes the following steps: S31, the phase function Unwrapping to obtain the unwrapped phase function : ； in, , , sgn(*) is the sign function; S32, judging the time-frequency overlapping area and the non-overlapping area according to the phase function of the mode and dividing them; the phase function after unwrapping In the non-overlapping region, it shows a continuous change; the phase function after unwrapping A sudden change occurs at the boundary of the time-frequency overlapping region; When the phase function of the mode to be analyzed changes linearly in the entire time region, the phase function is: ； The entire time region of the modality is marked as a non-overlapping region, where f I Interference signal The frequency, Interference signal The initial phase of When the phase function of the mode to be analyzed changes nonlinearly in a certain time region, the phase function is: ； The temporal region of the modality t 1, t 2] intervals are marked as time-frequency overlapping areas, and other time areas are non-overlapping areas; among them, a I Interference signal The amplitude of For natural signals The amplitude of For natural signals The initial phase.

7. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 6, characterized in that: In step S32, the mode containing the time-frequency overlapping area is: ； in, ； ； R For the overlapping area [ t 1, t 2] The composite envelope of the overlapping signals, is the phase of the overlapping signals.

8. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 1, characterized in that: Step S4 includes the following steps: S41, using a variational mode extraction algorithm and increasing the penalty factor value of the overlapping area, thereby enhancing the bandwidth constraining the time-frequency overlapping area: ； in, is the increased penalty factor, which is used to constrain the bandwidth of the time-frequency overlap region. α 0 is the initial penalty factor for variational mode extraction, BW overlap is the bandwidth of the time-frequency overlapping region, BW non-overlap is the bandwidth of the non-overlapping area; Based on the penalty factor after the constraint and center frequency, and extract the mixed signal from the mixed signal using variational mode extraction in the frequency domain Re-extracting the interference signal in the time-frequency overlapping area to obtain a mode after constraining the frequency band, wherein the frequency band of the interference signal in the time-frequency overlapping area is the same as that of the natural signal; S42, obtaining the complex analytical form of the reconstructed interference signal in the overlapping area by statistically analyzing the interference envelope characteristics of the non-overlapping area and combining the phase function: ； in, ； ； reconstructing a phase function of the interference signal for the overlap region, An envelope of the interfering signal is reconstructed for the overlap region.

9. The method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to claim 1, characterized in that: In step S5, the complex analytical form of the reconstructed interference signal in the overlapping area is subjected to an inverse Hilbert transform to obtain the real signal form of the interference signal after the reconstruction of the overlapping area; based on the same bandwidth, the real signal of the reconstructed interference signal in the overlapping area is subtracted from the marked mixed signal of the time-frequency overlapping area to perform a secondary separation of the natural signal in the time-frequency overlapping area to obtain the natural signal of the overlapping area. ; The overlapping area natural signal for: ； In step S6, 。 10. A method for separating time-frequency overlapping signals based on instantaneous phase discontinuity according to any one of claims 1 to 9, characterized in that: Use the spacecraft momentum wheel interference signal separation system to separate the time-frequency overlapping area between momentum wheel interference and natural signals; The spacecraft momentum wheel interference signal separation system comprises a natural signal primary separation module, a phase function acquisition module, a time-frequency overlapping area division marking module, an overlapping area interference signal reconstruction module, an overlapping area natural signal secondary separation module and a natural signal merging and reconstruction module, which are connected in sequence; The primary separation module of the natural signal extracts the mixed signal through a variational mode extraction algorithm The momentum wheel interference signal in the first separation is obtained s mode ( t ) and the natural signal after the first separation f r ( t ); The phase function acquisition module obtains the interference signal according to the first separation s mode ( t ) to obtain the phase function and the envelope ; The time-frequency overlapping region division and marking module identifies and marks the time-frequency overlapping region and the non-overlapping region in the interference signal after the first separation by analyzing the mutation and discontinuity points in the phase function; The overlapping region interference signal reconstruction module constrains the bandwidth of the overlapping region to be the same as that of the non-overlapping region so that the frequency band of the interference signal in the overlapping region is the same as that of the natural signal, and then combines the envelope characteristics of the interference signal in the non-overlapping region to obtain the overlapping region reconstructed interference signal; The overlapping area natural signal secondary separation module subtracts the overlapping area reconstructed interference signal from the mixed signal of the time-frequency overlapping area based on the same bandwidth to perform secondary separation of the natural signal in the overlapping area to obtain the overlapping area natural signal. ; The natural signal merging and reconstruction module combines the natural signal after the first separation f r ( t ) and the natural signal in the overlapping area Merge and reconstruct the natural signal .

Images