A polarization matched filter based vertical ionospheric map O / X wave separation method

Abstract

This invention discloses a method for separating O / X waves in a vertical ionization map based on polarization matched filtering, comprising: acquiring dual-channel complex signals and incoherently accumulating them to obtain the echo intensity; generating a mask using an OS-CFAR detector and morphological processing; calculating the phase difference based on the mask and fitting the characteristic phases of the O and X waves using a dual Gaussian mixture model; estimating the complex polarization ratio; constructing a polarization matched filter weight vector and multiplying it with the dual-channel signals to separate the O / X wave complex signal matrices; and generating a separated ionization map through amplitude calculation and detection. This invention does not rely on the circular polarization assumption, can directly estimate the actual polarization parameters, and achieves high-precision separation through polarization matched filtering, improving robustness and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of shortwave ionospheric vertical detection technology, specifically a method for O / X wave separation of vertical ionosphere based on polarization matched filtering. Background Technology

[0002] To date, vertical ionospheric sounding remains one of the most fundamental and reliable technologies in ionospheric scientific research and radio wave propagation and application studies. Its working principle involves transmitting high-frequency pulse signals vertically upwards and receiving reflected echoes from various layers of the ionosphere. By measuring the echo delay, the virtual height of the ionosphere is obtained, leading to a frequency-virtual height relationship curve, i.e., a frequency-height map (or vertical ionospheric map). Based on the frequency-height map, key parameters such as the critical frequencies of each layer can be extracted, and the vertical distribution profile of ionospheric electron concentration can be retrieved. Vertical ionospheric sounding has irreplaceable practical value in scientific research, national defense, communications, navigation, and other fields.

[0003] Due to the presence of the Earth's magnetic field, vertically incident radio waves undergo magneto-ion splitting when propagating in the ionosphere, forming two ellipticized components: ordinary waves (O-waves) and unusual waves (X-waves). These two waves have different refractive properties and propagation paths, resulting in them appearing as two separate echo traces on the frequency-height map. The correct separation of O-waves and X-waves is crucial for interpreting vertical ionosphere maps and directly affects the accuracy of ionospheric parameter measurements. Achieving high-precision separation of these two characteristic wave traces is a necessary condition for accurately extracting ionospheric characteristic parameters and realizing high-precision electron density vertical distribution profile inversion, and is also an important link in enhancing the application value of ionospheric detection data.

[0004] However, in actual detection, due to many factors such as environmental radio noise, shortwave radio interference, ionospheric time-varying, dispersion, dissipation and multimode multipath propagation, and the technical limitations of the detection equipment itself (such as antenna orthogonality, amplitude and phase consistency of different channels, and antenna placement), achieving accurate separation of O / X waves is extremely difficult.

[0005] Existing O / X wave separation methods mainly revolve around three major directions: digital image processing, deep learning, and polarization information processing.

[0006] Digital image processing-based methods use morphology, graph theory, and other techniques to separate traces from the morphology of ionosphere images. However, their performance is heavily dependent on image integrity and lacks robustness in scenarios with severe noise, interference, or complex overlapping traces caused by ionospheric disturbances.

[0007] Deep learning-based methods achieve end-to-end separation by training neural networks and perform well on standard data. However, under complex physical conditions such as time-varying ionospheric and dispersion, their generalization ability and stability are still limited, and they cannot physically describe the polarization characteristics of OX waves.

[0008] The O / X wave separation method based on polarization information processing directly utilizes the amplitude and phase relationship of two orthogonally polarized received signals, possessing a clear physical meaning for ionospheric wave propagation. Traditional methods typically assume that the O wave and X wave exhibit ideal left-handed and right-handed circular polarization, respectively, achieving separation by applying a theoretical ±90° fixed phase shift between the two signals. However, ionospheric wave propagation is not ideally circularly polarized due to various factors. Furthermore, the orthogonality of the antenna system, amplitude and phase consistency, antenna placement (strictly aligned with the geomagnetic north-south and east-west directions), and phase noise generated by the environment and the equipment itself often cause the actual received signal's polarization to deviate from the theoretical circular polarization, exhibiting elliptical polarization characteristics. Moreover, the phase difference between the two signals is not a constant ±90°, accompanied by amplitude imbalance. To adapt to practical situations, researchers have proposed a series of improved methods: The Australian PRIME (Portable Remote Ionospheric Monitoring Equipment) performs histogram statistics on the phase differences of all pixels in the frequency-height map and fits the clustered areas with a Gaussian distribution, classifying pixels into O-waves or X-waves accordingly. This method is highly robust and can effectively overcome the influence of factors such as detection equipment. To further overcome the influence of system equipment errors, some scholars have adopted a self-calibration iterative mechanism, using the time delay difference of the F2 layer trace to infer and compensate for frequency-related phase deviations; others have proposed pixel-by-pixel amplitude compensation and refined grid phase statistics strategies to improve local adaptability. However, these methods are all based on the assumption that the X-wave signal is circularly polarized, and perform amplitude or phase compensation on the actual received signal based on this assumption. But the actual incoming wave signal itself is not a circularly polarized wave, so these methods cannot truly reflect the polarization characteristics of the signal. Summary of the Invention

[0009] To address the problems of inaccurate O / X wave separation and weak anti-interference capability in vertical ionospheric probing of the prior art, the present invention aims to provide a vertical ionograph O / X wave separation method based on polarization matched filtering. This method does not rely on the circular polarization assumption, can directly estimate the actual polarization parameters from the dual-channel received signals, and achieves high-precision separation through polarization matched filtering, thereby improving the robustness and accuracy of separation.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0011] A method for separating O / X waves in a vertical ionization map based on polarization matched filtering includes the following steps:

[0012] Step S1: Obtain the complex signal matrices of the north-south and east-west channels of the orthogonal dual-channel receiving system in ionospheric vertical sounding, and perform incoherent accumulation to obtain the echo intensity matrix; Step S2: Apply an ordered statistical constant false alarm rate detector to the echo intensity matrix to identify potential effective signal points and generate a first mask matrix; Step S3: Perform morphological processing on the first mask matrix to remove isolated noise points and small connected regions, generating a second mask matrix; Step S4: Based on the second mask matrix, calculate the phase difference matrix of the north-south and east-west channels, and perform double Gaussian mixing on the phase difference statistical histogram. Step S5: Based on the characteristic phases, estimate the complex polarization ratios of the ordinary and extraordinary waves respectively. The complex polarization ratios include amplitude ratio and phase difference information. Step S6: Based on the estimated complex polarization ratios of the ordinary and extraordinary waves, construct corresponding polarization matched filter weight vectors respectively, and multiply the weight vectors with the dual-channel signal vector matrix to separate the complex signal matrices of the ordinary and extraordinary waves. Step S7: Perform amplitude calculation and signal detection on the separated complex signal matrices of the ordinary and extraordinary waves to generate an ionization map separating the ordinary and extraordinary waves.

[0013] As a further improvement to the above technical solution:

[0014] In step S2, the ordered statistical constant false alarm rate detector sets up a protection unit and a reference unit before and after each detection unit. The echo intensity samples in the reference unit are arranged in ascending order, and the k-th element is selected as the estimated value of the background noise echo intensity, where the value of k is between 50% and 75% of the total number of reference units.

[0015] In step S3, the morphological processing includes performing connected component analysis on the binary mask image and filtering out fragmented regions based on a preset area threshold.

[0016] In step S4, the expression for nonlinear least-squares fitting of the phase difference histogram using a double Gaussian mixture model is as follows:

[0017]

[0018] in, For phase difference, Let be the probability density fitting function for the phase difference. These represent the mean, standard deviation, and amplitude of the corresponding O-wave component, respectively. These represent the mean, standard deviation, and amplitude of the corresponding X-wave component; among them, the two peak values ​​obtained from the fitting are... and These correspond to the characteristic phases of ordinary waves and extraordinary waves, respectively.

[0019] In step S5, the complex polarization ratio Defined as the ratio of the complex signal in the north-south channel to the complex signal in the east-west channel:

[0020]

[0021] in, and These represent the amplitudes of the north-south channel complex signal and the east-west channel complex signal, respectively. The phase difference between two complex signals. It is the imaginary unit.

[0022] In step S6, based on the complex polarization ratio The constructed normalized Jones vector is:

[0023]

[0024] Polarization matched filter weight vector Take as the normalized Jones vector Conjugate matching.

[0025] In step S6, the ordinary wave complex signal matrix obtained by separation Unusual wave complex signal matrix Each element is:

[0026]

[0027]

[0028] in, For the separated O wave at frequency Inflated echo signal at that location, For the separated X-wave at frequency Inflated echo signal at that location, and , respectively, are the polarization matched filter weight vectors for ordinary and unusual waves, with the superscript H indicating conjugate transpose. It is a vector composed of the corresponding elements of the north-south and east-west channels.

[0029] In step S6, since the polarization states of ordinary waves and extraordinary waves are approximately orthogonal, the constructed ordinary wave filter weight vector and extraordinary wave filter weight vector are also approximately orthogonal, so as to suppress orthogonal mode waves while maximizing the reception of target wave signals.

[0030] In step S6, the polarization matched filter weight vector and After multiplying by the corresponding elements of the dual-channel signal vector matrix, the signal energy of the orthogonal polarization mode in the output signal is suppressed, and the residual signal energy after suppression is less than one ten-thousandth of the original signal energy.

[0031] In step S7, the ionospheric echo traces of the separated ordinary and extraordinary waves are marked with different colors in the same frequency-virtual height coordinate system to generate the final ordinary and extraordinary wave separation ionization map.

[0032] The beneficial effects of this invention are:

[0033] (1) Starting directly from the dual-channel orthogonal received signal, the polarization state of the receiving antenna and the target echo signal is optimally matched through polarization parameter estimation and polarization matching filtering, thereby maximizing the signal-to-noise ratio (SNR) and achieving effective separation of O / X waves at the signal level. This overcomes the limitations of traditional methods, which rely on image morphology, are susceptible to noise interference, and assume circular polarization waves. This method can provide a cleaner data foundation for ionospheric parameter inversion, improve the automated processing capability and accuracy of vertical measurement systems, and also has certain reference value for radar, communication, and other polarization-based information processing.

[0034] (2) Physical separation of O / X waves is achieved through polarization matched filtering, without the need to assume ideal circular polarization, adapting to the actual polarization state of the ionosphere and having clear physical significance. This method has strong anti-interference ability and can maintain high separation accuracy and robustness even in complex scenarios such as noise, multi-hop echoes, and ionospheric tilt. The suppression of orthogonal polarization after separation can reach more than 80dB, which is significantly better than existing methods, providing a reliable data foundation for high-precision ionospheric parameter inversion and space environment monitoring. Attached Figure Description

[0035] Figure 1 This is a frequency-virtual-high amplitude diagram of the first channel of the original data in an embodiment of the present invention.

[0036] Figure 2 This is the second channel frequency-virtual high-amplitude diagram of the original data in an embodiment of the present invention.

[0037] Figure 3 This is a frequency-virtual-high amplitude diagram of the noncoherent accumulation of the original data in an embodiment of the present invention.

[0038] Figure 4 This is a one-dimensional OS-CFAR reference sliding window diagram of an embodiment of the present invention.

[0039] Figure 5 This is a frequency-hysteresis-amplitude diagram after OS-CFAR detection in an embodiment of the present invention.

[0040] Figure 6 This is a frequency-virtual height-amplitude diagram after morphological processing according to an embodiment of the present invention.

[0041] Figure 7 This is a phase difference diagram of the two channels of the original data in an embodiment of the present invention.

[0042] Figure 8 This is a phase difference diagram after purification according to an embodiment of the present invention.

[0043] Figure 9 The images show the phase difference histogram and double Gaussian fitting curves in an embodiment of the present invention.

[0044] Figure 10 This is an O / X polarization ellipse diagram of an embodiment of the present invention.

[0045] Figure 11 This diagram illustrates the suppression effect of polarized waves with different phase differences relative to circularly polarized waves when the amplitude ratio is 1 according to an embodiment of the present invention.

[0046] Figure 12 This is a frequency-virtual height-amplitude diagram of the O-wave after polarization matched filtering in an embodiment of the present invention.

[0047] Figure 13 This is a frequency-virtual height-amplitude diagram of the X-wave after polarization matched filtering in an embodiment of the present invention.

[0048] Figure 14 This is a trace of the separated O / X waves in an embodiment of the present invention. Detailed Implementation

[0049] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0050] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0051] A method for separating O / X waves in a vertically lobe ionization map based on polarization matched filtering is presented in this embodiment. The ionization map data collected by a vertically lobe instrument deployed in Shandong, China (35°N, 116°E) is used for processing and explanation. Specifically, a set of data collected at 15:35:00 on January 27, 2025 is used as an example.

[0052] Step S1: Acquire dual-channel signals and perform non-coherent accumulation.

[0053] For an orthogonal dual-channel receiving system for vertical ionospheric sounding, the complex signals measured by the north-south and east-west channels can be represented as two-dimensional complex matrices with respect to frequency and imaginary height. and ,( ),in Indicates the number of frequency points. Represents the number of imaginary height points. A two-dimensional complex matrix. and The frequency-hysteresis-amplitude graphs are shown below. Figure 1 and Figure 2 As shown in the figure, different colors represent different amplitudes (echo intensity), and the color of each point represents the echo intensity at that frequency point and that virtual height.

[0054] To obtain the echo intensity distribution, the complex matrix is... and Incoherent accumulation yields a real-valued echo intensity matrix. ( ):

[0055] (1)

[0056] echo intensity matrix Frequency-hyperbole-amplitude graph as shown Figure 3 As shown.

[0057] Step S2: Signal detection based on OS-CFAR.

[0058] To effectively identify potential ionospheric echo signals from noise and interference, an ordered statistical constant false alarm rate (OS-CFAR) detector is applied to the echo intensity matrix P. The virtual height profile (i.e., a one-dimensional vector) corresponding to each frequency point is then plotted. , (This represents the frequency index) as an independent detection sequence. Represents the extraction matrix The Middle All column elements of the row. For each fixed frequency point. Each of its corresponding virtual height units Each of them is a single detection unit.

[0059] like Figure 4 As shown, for each detection unit Set each of its m neighboring units before and after it as a protection unit, and a detection unit. The n units before and after all the protection units are reference units. The protection units are used to prevent signal energy from leaking into the reference units, ensuring that the background estimation is not affected by the target signal and that its echo intensity value does not participate in the background estimation; the reference units are used to estimate the background noise echo intensity.

[0060] For the echo intensity of each detection unit Extract all echo intensity samples from the reference cells on both sides to form a reference cell set. ,in This represents the total number of reference units. For The elements in the set are arranged in ascending order. Select the first element. Each element is used as an estimate of the background noise echo intensity of the detection unit, i.e.:

[0061] (2)

[0062] in, This is an estimate of the background noise echo intensity of the detection unit. For the first reference unit in the set The echo intensity of each element.

[0063] Theoretically, in a uniform background noise environment Can be taken Any integer between [values]. However, in practice, the amplitude is greatly affected by randomness, especially in environments with non-uniform background noise. The magnitude of the value directly affects its anti-interference ability, therefore, The value is generally between 50% and 75% of the sample size to enhance anti-interference capability. The echo intensity of the unit under test is... With adaptive threshold Compare the results to generate a mask matrix for the effective signal. ( ), where each element is:

[0064] (3)

[0065] in, For frequency Inflated The mask corresponding to the detection unit, , This is the threshold factor. When... When the signal is received, the echo from the corresponding detection unit is considered a valid signal.

[0066] Masking the effective signal matrix With echo intensity matrix Multiplying corresponding elements, we obtain the frequency-artificial height-amplitude plot after OS-CFAR detection, as shown below. Figure 5 As shown.

[0067] Step S3: Morphological purification treatment.

[0068] While OS-CFAR detection can effectively identify potential signal points, it typically contains two types of interference: isolated spurious signal points formed by residual noise or interference, and fragmented tiny connected regions caused by threshold fluctuations. If these interference points are not filtered out, they will introduce serious biases into subsequent phase difference statistics, leading to inaccurate polarization estimations of the O-wave and X-wave.

[0069] To further refine the detection results, this method introduces a morphological processing procedure. This procedure directly performs logical analysis and filtering on the pixel connectivity in the binary image. The core objective is to preserve the true ionospheric echo region, remove unreasonable noise or interference regions, and generate a mask matrix that eliminates isolated pseudo-signal points. ( ). Mask matrix With echo intensity matrix Multiplying corresponding elements yields a morphologically processed frequency-hyperbole-amplitude plot, as shown below. Figure 6 As shown.

[0070] Step S4: Phase difference statistics and double Gaussian fitting.

[0071] Based on signal detection and purification, the polarization parameters of the signal are estimated using phase difference statistical analysis.

[0072] This process includes the following steps:

[0073] Step S41: Phase difference calculation.

[0074] For complex signals of north-south and east-west channels and Calculate the phase difference between corresponding elements of the two channels to obtain a phase difference matrix. ( ), where the phase difference of each element for:

[0075] (4)

[0076] in, This indicates taking the argument of a complex number, and the result is in between; The frequency in the complex signal matrix of the north-south channel Inflated The corresponding element, Represents the complex matrix Frequency in the complex conjugate matrix Inflated The corresponding elements. Phase difference matrix. Phase difference diagram as follows Figure 7 As shown.

[0077] mask matrix Phase difference matrix of the original signals from the two channels Multiply corresponding elements, and for positions where the mask value is 0, set the phase difference to an invalid value (not considered in the statistics), to obtain the purified phase difference matrix. ( ), where the phase difference of each element for:

[0078] (5)

[0079] Phase difference matrix after purification The phase difference diagram is as follows Figure 8 As shown.

[0080] Step S42: Fitting the dual Gaussian mixture model.

[0081] Phase difference matrix after statistical purification The distribution of phase differences for all non-zero values ​​is shown. The purified phase difference data is divided into intervals from -180° to +180° to obtain a phase difference histogram. Ideally, the phase differences corresponding to the O-wave and X-wave should cluster around two different characteristic values, appearing as a bimodal distribution on the histogram, with a phase difference of 180° between the two peaks.

[0082] Based on this, a double Gaussian mixture model is used to perform nonlinear least squares fitting on the phase difference histogram, and the phase difference... probability density fitting function for:

[0083] (6)

[0084] in, These represent the mean, standard deviation, and amplitude of the corresponding O-wave component, respectively. These represent the mean, standard deviation, and amplitude of the corresponding X-wave component, respectively. These parameters (mean, standard deviation, and amplitude) are obtained by minimizing the sum of squared residuals between the fitted curve and the histogram data, thus providing a more accurate characterization of the statistical distribution of the phase difference. Phase Difference Matrix The phase difference histogram and the double Gaussian fitting curve are as follows: Figure 9 As shown.

[0085] Step S5: O / X wave polarization state estimation.

[0086] The polarization state is determined by the complex polarization ratio. The full description is defined as the ratio of the complex signals of two orthogonally polarized channels, i.e.:

[0087] (7)

[0088] in, and These represent the amplitudes of the complex signals from the two orthogonally polarized channels. Let be the phase difference between the two complex signals.

[0089] Based on the above statistical analysis, the two peaks of the double Gaussian fitting curve correspond to the characteristic phases of the O-wave and X-wave, respectively. and Filter out complex signal matrices and The calculated phase difference is located at and For all complex signal points within the range, calculate the amplitude ratio of each complex signal point. The average of all amplitude ratios is taken as the typical amplitude ratio corresponding to the O wave and X wave. and .

[0090] Based on the characteristic phase and amplitude ratios estimated above, the complex polarization ratios of the O-wave and X-wave are constructed:

[0091] , (8)

[0092] in and It contains all the polarization information needed to separate the two waves.

[0093] In this embodiment, the two peaks of the double Gaussian fitting curve correspond to the characteristic phases of the O-wave and X-wave, respectively. and Filter out those with phase differences located at and The average value of all signal points is taken as the typical amplitude ratio corresponding to the O wave and X wave. and By combining the estimated characteristic phase and amplitude ratios, the polarization ratios of the O-wave and X-wave are constructed. and ,according to and The polarization ellipses of O and X waves are obtained as follows: Figure 10 As shown.

[0094] Step S6: Polarization matched filtering is used to separate the O / X waves.

[0095] The basic idea of ​​polarization matched filtering is to project the two measured signals into the respective polarization subspaces of the O-wave and X-wave, thereby achieving physical separation. Based on signal subspace projection theory, this method can extract the energy of the signal polarization modes to the maximum extent while suppressing interference from orthogonal modes or other polarization states, thus possessing clear physical significance.

[0096] The key to polarization matched filtering is constructing a weight vector that matches the polarization state of the signal. The polarization state is determined by the complex polarization ratio. The monochromatic plane wave described can be represented by its normalized Jones vector on the two positive traffic lanes as follows:

[0097] (9)

[0098] In the formula, the denominator This is the normalization factor.

[0099] To extract the signal of this specific polarization mode, we can design a filter weight vector. , so that it is with Conjugate matching, i.e., satisfying:

[0100] (10)

[0101] superscript This indicates the conjugate transpose. This filter is for the input signal... The output is:

[0102] (11)

[0103] When input signal polarization state and When they are perfectly synchronized, the filter output echo intensity is at its maximum, achieving the desired polarization of the signal. Matching reception.

[0104] like Figure 11 The figure shows a simulation example of polarization matched filtering, where it is assumed that... For a left-hand circularly polarized wave ,right Take different polarization states Perform matched filtering to obtain The output shows that when the two wave polarization states are completely orthogonal, the suppression ratio can reach 325dB (this value is the limit of MATLAB software processing, and is theoretically infinitesimal).

[0105] To extract signals of specific polarization modes of O-wave and X-wave from vertical ionogram data, based on the previously estimated O-wave to X-wave polarization ratio... and Construct their corresponding normalized steering vectors respectively. and :

[0106] (12)

[0107] (13)

[0108] Then, the polarization matched filter weight vectors of the O-wave and X-wave are taken as their conjugate transposes:

[0109] (14)

[0110] (15)

[0111] in, Indicates to Take the conjugate, Indicates to Take the conjugate.

[0112] Since the polarization states of the O-wave and X-wave are approximately orthogonal under the magnetic ion theory, i.e., satisfying Therefore, the constructed filter weight vector and It also possesses the property of being approximately orthogonal. This indicates that... While maximizing the reception of O-wave signals, the X-wave component is minimized, and vice versa, thus laying the theoretical foundation for O-wave and X-wave separation.

[0113] The polarization matched filter weight vectors of O-wave and X-wave , Vectors formed by corresponding elements of the north-south and east-west channels, respectively. Multiplying the normalized matrices yields the complex signal matrices of the separated O-wave and X-wave. , ( ), where each element is:

[0114] (16)

[0115] (17)

[0116] in, For the separated O wave at frequency Inflated echo signal at that location, For the separated X-wave at frequency Inflated The echo signal at that location.

[0117] At the same time, as can be seen from the preceding discussion, , The matrix also suppresses interference to a certain extent. To demonstrate the energy effect of mode separation, interference and noise were retained in the separated ionization plot, resulting in the frequency-virtual height-amplitude plots of the O-wave and X-wave after polarization matched filtering, as shown below. Figure 12 and Figure 13 As shown.

[0118] Step S7: Output of separation results and generation of ionization diagram

[0119] For complex signal matrices respectively , Calculate its amplitude to obtain the corresponding echo intensity matrix, and then use the methods in steps S2 and S3 to... , Each element of the echo intensity matrix is ​​detected to obtain the mask matrices for the O-wave and X-wave. , ( ),Will Non-zero values ​​are indicated in red. Non-zero values ​​are represented in blue, and the final ionization diagram after O and X wave separation is shown below. Figure 14 As shown.

[0120] Through the above steps, this embodiment successfully achieved high-precision separation of O-waves and X-waves in the vertical ionization diagram.

[0121] Finally, it is necessary to state that the above embodiments are only used to further illustrate the technical solution of the present invention in detail, and should not be construed as limiting the scope of protection of the present invention. Any non-essential improvements and adjustments made by those skilled in the art based on the above content of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for separating O / X waves in a vertical ionization map based on polarization matched filtering, characterized in that, Includes the following steps: Step S1: Obtain the complex signal matrix of the north-south channel and the complex signal matrix of the east-west channel in the orthogonal dual-channel receiving system for vertical ionospheric sounding, and perform incoherent accumulation to obtain the echo intensity matrix; Step S2: Apply an ordered statistical constant false alarm rate detector to the echo intensity matrix to identify potential effective signal points and generate a first mask matrix; Step S3: Perform morphological processing on the first mask matrix to remove isolated noise points and small connected regions, and generate the second mask matrix; Step S4: Based on the second mask matrix, calculate the phase difference matrix between the north-south channel and the east-west channel, and fit the phase difference statistical histogram with a double Gaussian mixture model to obtain the characteristic phases of ordinary and unusual waves. Step S5: Based on the characteristic phase, estimate the complex polarization ratio of the ordinary wave and the unusual wave respectively, wherein the complex polarization ratio includes amplitude ratio and phase difference information; Step S6: Based on the estimated complex polarization ratios of the ordinary and unusual waves, construct the corresponding polarization matched filter weight vectors respectively, and multiply the weight vectors with the dual-channel signal vector matrix to separate the complex signal matrices of the ordinary and unusual waves; Step S7: Perform amplitude calculation and signal detection on the complex signal matrices of the separated ordinary and extraordinary waves to generate an ionization diagram showing the separation of the ordinary and extraordinary waves.

2. The separation method according to claim 1, characterized in that: In step S2, the ordered statistical constant false alarm rate detector sets up a protection unit and a reference unit before and after each detection unit. The echo intensity samples in the reference unit are arranged in ascending order, and the k-th element is selected as the estimated value of the background noise echo intensity, where the value of k is between 50% and 75% of the total number of reference units.

3. The separation method according to claim 1, characterized in that: In step S3, the morphological processing includes performing connected component analysis on the binary mask image and filtering out fragmented regions based on a preset area threshold.

4. The separation method according to claim 1, characterized in that: In step S4, the expression for nonlinear least-squares fitting of the phase difference histogram using a double Gaussian mixture model is as follows: ； in, For phase difference, Let be the probability density fitting function for the phase difference. These represent the mean, standard deviation, and amplitude of the corresponding O-wave component, respectively. These represent the mean, standard deviation, and amplitude of the corresponding X-wave component, respectively. Among them, the two peaks obtained from the fitting and These correspond to the characteristic phases of ordinary waves and extraordinary waves, respectively.

5. The separation method according to claim 1, characterized in that: In step S5, the complex polarization ratio Defined as the ratio of the complex signal in the north-south channel to the complex signal in the east-west channel: ； in, and These represent the amplitudes of the north-south channel complex signal and the east-west channel complex signal, respectively. The phase difference between two complex signals. It is the imaginary unit.

6. The separation method according to claim 5, characterized in that: In step S6, based on the complex polarization ratio The constructed normalized Jones vector is: ； Polarization matched filter weight vector Take as the normalized Jones vector Conjugate matching.

7. The separation method according to claim 6, characterized in that: In step S6, the ordinary wave complex signal matrix obtained by separation Unusual wave complex signal matrix Each element is: ； ； in, For the separated O wave at frequency Inflated echo signal at that location, For the separated X-wave at frequency Inflated echo signal at that location, and , respectively, are the polarization matched filter weight vectors for ordinary and unusual waves, with the superscript H indicating conjugate transpose. It is a vector composed of the corresponding elements of the north-south and east-west channels.

8. The separation method according to claim 7, characterized in that: In step S6, since the polarization states of ordinary waves and extraordinary waves are approximately orthogonal, the constructed ordinary wave filter weight vector and extraordinary wave filter weight vector are also approximately orthogonal, so as to suppress orthogonal mode waves while maximizing the reception of target wave signals.

9. The separation method according to claim 7, characterized in that: In step S6, the polarization matched filter weight vector and After multiplying by the corresponding elements of the dual-channel signal vector matrix, the signal energy of the orthogonal polarization mode in the output signal is suppressed, and the residual signal energy after suppression is less than one ten-thousandth of the original signal energy.

10. The separation method according to claim 1, characterized in that: In step S7, the ionospheric echo traces of the separated ordinary and extraordinary waves are marked with different colors in the same frequency-virtual height coordinate system to generate the final ordinary and extraordinary wave separation ionization map.

Images