External radiation source radar range migration correction method based on star chain communication signal

Abstract

The invention discloses an external radiation source radar range migration correction method based on star chain communication signals, and belongs to the technical field of external radiation source radars. The method comprises the following steps: performing reconstruction and pulse compression processing on a target echo signal; converting the signal to a range frequency-slow time domain; doppler fuzzy number compensation is carried out; dynamically dividing the frequency spectrum of the signal into a first processing area and a second processing area; performing interpolation correction on the signals of the first processing area by adopting a first type of interpolation Keystone transformation algorithm, and performing interpolation correction on the signals of the second processing area by adopting a second type of interpolation Keystone transformation algorithm; the corrected signals are recombined in the range frequency-slow time domain. According to the method, the interpolation strategy can be adaptively adjusted according to the energy distribution of the star chain communication signal, the calculated amount is remarkably reduced while high-precision range migration correction is ensured, and the method is suitable for high-speed target detection of the external radiation source radar of the star chain communication signal.

Description

Technical Field

[0001] This invention relates to the field of external radiation source radar technology, and in particular to a method for range migration correction of external radiation source radar based on Starlink communication signals. Background Technology

[0002] External radiation source radar utilizes signals from third-party, non-cooperative radiation sources (such as broadcast, television, and mobile communication base stations) for target detection, offering advantages such as strong concealment, low cost, and anti-stealth capabilities. In recent years, the rapid deployment of large-scale low Earth orbit (LEO) communication satellite constellations, exemplified by Starlink, has brought revolutionary development opportunities to external radiation source radar technology. However, while LEO satellite constellations offer tremendous opportunities, they also introduce unprecedented technological challenges: extremely high launch platform speeds and short overpass times of LEO satellites cause drastic changes in the radar detection geometry within a short period; the large bandwidth characteristics make range migration more pronounced. Therefore, in external radiation source radar based on Starlink signals, range migration is no longer a simple linear problem, but a highly complex, high-order problem involving a strong coupling of the target's own motion and the high-speed, nonlinear apparent motion of the satellite.

[0003] The Keystone transform is a widely recognized and effective method in radar signal processing for correcting range migration. It decouples range from Doppler by variable substitution when the target velocity is unknown. To achieve the highest accuracy, mainstream methods employ interpolation based on the Sine Cardinalis function (Sinc). Sinc interpolation is the theoretical core of the Nyquist-Shannon sampling theorem and can achieve ideal signal reconstruction, but its global convolutional characteristics result in extremely high computational complexity, making it difficult to meet the real-time processing requirements of radar systems. To meet real-time requirements, another approach uses interpolation based on the Fast Fourier Transform (FFT). This method uses frequency-domain phase operations to approximate time-domain resampling, resulting in extremely high computational efficiency. However, it is essentially an approximation and introduces significant phase errors when processing high-frequency components or highly maneuvering targets, leading to target energy defocusing and decreased image quality. Furthermore, although some studies have proposed using techniques such as Chirp Z-Transform (CZT), Discrete Fourier Transform (DFT), or Lagrange polynomial interpolation for optimization, these methods essentially still employ a fixed, non-adaptive processing strategy, that is, applying the same set of processing standards to all signal components, failing to fundamentally resolve the aforementioned contradiction between accuracy and efficiency.

[0004] In summary, due to the high-order, strongly coupled, and complex inherent physical characteristics of range migration problems in Starlink signal external radiation source radar, existing technologies urgently need novel adaptive processing methods that can both ensure high-precision range migration correction and significantly reduce computational complexity, in order to meet the practical needs of Starlink communication signal-based external radiation source radar in high-speed target detection and imaging. Summary of the Invention

[0005] Purpose of the invention: To address the above problems, the purpose of this invention is to provide a radar range migration correction method based on external radiation sources of Starlink communication signals.

[0006] Technical solution: The present invention provides a radar range migration correction method based on external radiation sources of Starlink communication signals, comprising the following steps: Step 1: Receive Starlink satellite downlink communication signals and direct wave signals, and use the direct wave signals to reconstruct and pulse compress the target echo signals to obtain the first communication signal; Step 2: Perform a Fourier transform on the first communication signal along the fast time dimension to convert the signal to the distance frequency-slow time domain, and obtain the second communication signal. Step 3: Perform Doppler ambiguity compensation on the second communication signal to obtain the third communication signal; Step 4: Calculate the energy distribution of each distance frequency unit and the Doppler spectral entropy of each distance frequency unit along the slow time dimension. Based on the energy distribution and motion sensitivity, execute a preset binary decision rule to dynamically divide the signal spectrum into a first processing region and a second processing region. Step 5: The signal in the first processing area is interpolated and corrected using the Keystone transform algorithm of the first type, and the signal in the second processing area is interpolated and corrected using the Keystone transform algorithm of the second type. Step 6: Recombine the corrected signal in the distance-frequency-slow time domain, and obtain the final corrected time domain signal by performing a distance-dimensional inverse Fourier transform.

[0007] Furthermore, the expression for the first communication signal is: , in, Indicates a fast time. Indicates slow time. A rectangular function indicates that the signal only extends within a length of [length missing]. It is valid within the slow time interval, i.e., its value is 1; otherwise, it is 0. Indicates the total observation time. It is a reference signal With echo signal The cross-correlation results For the history of bistatic distance, For the speed of light, wavelength , For carrier frequency, It represents the imaginary unit.

[0008] Furthermore, the expression for the second communication signal is: , in, This represents the spectrum of the transmitted pulse signal. Indicates distance frequency, The initial distance between the two bases. This represents the coefficient of the first-order term after the Taylor expansion from the historical date. This represents the coefficient of the quadratic term after the Taylor expansion of the distance from the history.

[0009] Furthermore, step 3 includes: The estimated fuzzy number is obtained through Radon transform. The pre-filter is constructed, and its expression is: , The third communication signal is obtained by multiplying the pre-filter and the second communication signal, as shown in the expression: , Among them, parameters .

[0010] Furthermore, step 4 includes: The third communication signal is discretized to obtain the discretization matrix, which is expressed as follows: , in, It is the index of the distance frequency unit, corresponding to continuous frequencies. , The frequency sampling interval; It is a slow-time index, corresponding to continuous time. , The time sampling interval; Calculate the total energy of each distance-frequency unit n along the slow-time dimension of the discretized matrix. The expression is: , in, This represents the total number of sampling points along the azimuth direction in the slow time dimension; Calculate the power spectral density of each distance frequency unit. The expression is: , in, The input signal is represented by a discretized matrix. In a fixed distance unit n Upper and lower slow time dimensions l A single row of data was retrieved; Represents the window function. Indicates the Doppler frequency unit index. , Represents the square of the modulus; The power spectral density is normalized to a probability density function. The expression is: , in, Let be the power spectral density function. m For the summation index of the Doppler frequency units, ; Calculate each distance unit n Doppler spectral entropy The formula is: , in, It is a very small positive number designed to avoid the logarithmic value being zero; Using a preset two-dimensional decision threshold, all frequency units are binary-divided, with the first processing region index set denoted as... The second processing area index set is denoted as , where the symbol Represents logical OR, symbol Represents logical AND, Indicates the energy threshold. Indicates the threshold for motion sensitivity; The signal in the first processing area is denoted as... , The signal in the second processing area is denoted as... , .

[0011] Furthermore, the steps for interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type include: slow time axis Perform a distance-frequency test Related resampling yields a new timeline. , is represented as: , Let parameters ,when When the new sampling points are more densely packed than the original sampling points, interpolation is required. This is achieved by padding the signal with zeros in the frequency domain. The process includes: Step 511, for the original slow time series of length L... Perform FFT to obtain ; Step 512: Calculate the length of the new sequence after interpolation. , Indicates rounding up; Step 513, in the spectrum center insertion There are zero values, among which A new length of [value] is constructed. Doppler spectrum When L is even, the Doppler spectrum The expression is: , When L is odd, the Doppler spectrum The expression is: , in, Indicates the index of the Doppler frequency after zero padding; Step 514, zero-padding the spectrum conduct The inverse Fourier transform of the points yields the interpolated slow time series. The expression is: , Where IFFT stands for Inverse Fourier Transform, and i represents the slow-time index of the new sequence.

[0012] Furthermore, the step of interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type also includes: when When the new sampling points are sparser than the original sampling points, interpolation is required before extraction. The process includes: Step 521: Determine a minimum integer upsampling factor. A(n) , making ,in A(n) The expression is: ; Step 522, send the signal conduct A(n) Interpolation by a factor of 1 yields a temporary sequence. , length is ; Step 523, for the temporary sequence Sampling points are extracted from the sample to obtain the final target sequence. The first of the new sequence Each sampling point corresponds to a temporary sequence. The position in is determined by the following formula: , Where i is the slow time index of the new sequence. From temporary sequence The index of the points extracted from the data. This represents the rounding function; The final target sequence is represented as follows: .

[0013] Furthermore, the step of interpolating and correcting the signal in the first processing area using the Keystone transform algorithm of the first type includes: Construct an adaptive Kaiser window for signal features, and the kernel half-width of the Kaiser window. Based on motion sensitivity Dynamic adjustment, the expression is: , in, This represents the final half-width of the kernel at the nth distance frequency unit. This represents a base width, which is the minimum value of the kernel width. It is an adjustment coefficient that controls the maximum range of variation in kernel width; yes The normalized motion sensitivity index has a value between 0 and 1. Shape parameters of Kaiser window Based on local signal-to-noise ratio Dynamic adjustment, the expression is: , in, It is the preset minimum value, It is a preset Adjustment range, ; Signal Feature Adaptive Kaiser Window The final expression is: , Where k is the index of the discrete point within the window function, and its range is... ; It is a zero-order modified Bessel function; The signal in the first processing region is interpolated using the Sinc function of the adaptive Kaiser window, and the formula for the interpolated signal is as follows: , in, It depends on the distance unit n The adaptive Kaiser window function,i For interpolation output signal Slow-time index, L Signals within the first processing area Total number of sampling points in the slow time dimension.

[0014] Furthermore, the final corrected time-domain signal is denoted as a matrix. This can be represented by the following piecewise function: , in, Represents all distance frequency units in the first processing area The set, Represents all distance frequency units in the second processing area A set of.

[0015] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: This invention introduces the physical quantity of Doppler spectral entropy as the core basis for decision-making, opening up a new technical path for resolving the contradiction between accuracy and efficiency in radar signal processing. By combining energy and motion sensitivity as a two-dimensional joint criterion, it can better cope with the strong coupling and high-order complex migration problems brought about by Starlink signals. It not only realizes the intelligent division of the processing area on a macroscopic level, but also achieves dynamic optimization of interpolation kernel parameters point by point in the most critical high-precision area on a microscopic level. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention; Figure 2 A schematic diagram of the geometric model for detecting moving targets using radar with an external radiation source; Figure 3 This is a simulation diagram of the performance of the Sinc interpolation method on the distance profile. Figure 4 This is a simulation diagram of the performance of the FFT interpolation method on the distance profile. Figure 5 This is a performance simulation diagram of the present invention on the distance profile. Detailed Implementation

[0017] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the embodiments of the present invention, and not all structures.

[0018] In the following description, specific details such as target system architecture and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0019] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0020] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0021] Furthermore, in the description of this application and the appended claims, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0022] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include the target features, structures, or characteristics described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0023] Combination Figure 1 As shown in this embodiment, a radar range migration correction method based on external radiation sources of Starlink communication signals includes the following steps: Step 1: Receive Starlink satellite downlink communication signals and direct wave signals, and use the direct wave signals to reconstruct and pulse compress the target echo signals to obtain the first communication signal.

[0024] In one example, the target is an external radiation source radar. The target can be a flying target, such as a drone, or a ship or vehicle. The geometric model of the moving target detection scene is as follows: Figure 2 As shown, in this example, the target is an aircraft, and the radar acts as the receiver. Its location... It is located at the origin of the coordinate system. Initially, the radiation source's location is... The location of the detected target is The distance from the radiation source to the receiving station is The distance from the radiation source to the target is The distance from the detected target to the receiving station is .exist At what time was the location of the radiation source? The location of the detected target is in The location from the radiation source to the receiving station is Distance from radiation source to target The distance from the target to the receiving station is A direct-echo signal refers to a signal transmitted directly from a satellite and received by a ground station, while a target echo signal refers to a signal transmitted from a satellite, reflected by a target, and ultimately received by a ground station. By using the known pilot frequencies in the direct-echo signal, channel distortion is estimated, thus obtaining a clean copy of the transmitted signal. This allows for the reconstruction of the target echo signal. The reconstructed signal undergoes pulse compression processing to obtain a two-dimensional time-domain complex signal matrix, which serves as the first communication signal.

[0025] Ideally, ignoring the influence of Doppler frequency, after range compression, the first communication signal from the integration time can be obtained in a fast time. and slow time The model was obtained from the model.

[0026] Furthermore, the expression for the first communication signal is: , in, Indicates a fast time. Indicates slow time. A rectangular function indicates that the signal only extends within a length of [length missing]. It is valid within the slow time interval, i.e., its value is 1; otherwise, its value is 0. Indicates the total observation time. It is a reference signal With echo signal The cross-correlation results are as follows: the reference signal is the signal directly emitted by the satellite, which is the reconstructed signal; the echo signal is the signal emitted by the satellite, reflected by the target, and finally received by the ground station. For the history of bistatic distance, For the speed of light, wavelength , For carrier frequency, It represents the imaginary unit.

[0027] Bibase distance history The expression is: , in, , and They represent in The distance between the external radiation source and the target at any given time, the distance between the target and the receiving station, and the distance between the external radiation source and the receiving station.

[0028] The second-order Taylor expansion can be written as: , , in, The initial distance between the two bases; The coefficient of the first-order term after the historical Taylor expansion; The coefficient of the quadratic term after the Taylor expansion of the distance from history; , and The initial distances between the external radiation source and the target, the initial distances between the target and the receiving station, and the initial distances between the external radiation source and the receiving station are respectively listed.

[0029] Step 2: Perform a Fourier transform on the first communication signal along the fast time dimension to convert the signal to the distance-frequency-slow time domain, thus obtaining the second communication signal.

[0030] Furthermore, the expression for the second communication signal is: , in, This represents the spectrum of the transmitted pulse signal. Indicates distance frequency, The initial distance between the two bases. This represents the coefficient of the first-order term after the Taylor expansion from the historical date. This represents the coefficient of the quadratic term after the Taylor expansion of the distance from the history.

[0031] Step 3: Perform Doppler ambiguity compensation on the second communication signal to obtain the third communication signal.

[0032] Furthermore, step 3 includes: The estimated fuzzy number is obtained through Radon transform. The pre-filter is constructed, and its expression is: , The third communication signal is obtained by multiplying the pre-filter and the second communication signal, as shown in the expression: , Among them, parameters .

[0033] Step 4: Calculate the energy distribution of each distance frequency unit and the Doppler spectral entropy of each distance frequency unit along the slow time dimension. Based on the energy distribution and motion sensitivity, execute a preset binary decision rule to dynamically divide the signal spectrum into a first processing region and a second processing region.

[0034] The majority of the signal energy is usually concentrated in a few key frequency units, which correspond to strong targets or strong clutter and are the core factors determining the final imaging quality. Step 4 not only introduces an energy criterion but also a direct quantification of the target motion complexity.

[0035] Furthermore, step 4 includes: The third communication signal is discretized to obtain the discretization matrix, which is expressed as follows: , in, It is the index of the distance frequency unit, corresponding to continuous frequencies. , The frequency sampling interval; It is a slow-time index, corresponding to continuous time. , The time sampling interval; Calculate the total energy of each distance-frequency unit n along the slow-time dimension of the discretized matrix. The expression is: , in, This represents the total number of sampling points along the azimuth direction in the slow time dimension; To quantify the motion complexity of the target, Doppler spectral entropy is introduced as a motion sensitivity index. First, the power spectral density of each distance frequency unit is calculated. The expression is: , in, The input signal is represented by a discretized matrix. In a fixed distance unit n Upper and lower slow time dimensions l A single row of data was retrieved; Represents the window function. Indicates the Doppler frequency unit index. , Represents the square of the modulus; The power spectral density is normalized to a probability density function. The expression is: , in, Let be the power spectral density function. mFor the summation index of the Doppler frequency units, ; Then each distance cell is calculated. n Doppler spectral entropy The formula is: , in, It is a very small positive number designed to avoid the logarithmic value being zero; If the target is moving at a constant velocity in a straight line, its energy will be highly concentrated at a single Doppler frequency. In this case, the probability density function... It will be a sharp peak. The distribution is extremely uneven, with one value close to 1 and others close to 0. According to the definition of entropy, the entropy value of such a highly deterministic distribution is... It will be very low. If the target is highly maneuverable motion (such as acceleration or jerk), its energy will be spread over a continuous Doppler frequency range, forming a broadened spectrum. In this case, the probability density function... It will be a broad and flat peak. The distribution is relatively uniform. According to the definition of entropy, this highly uncertain distribution has an entropy value... It will be very high; Using a preset two-dimensional decision threshold, all frequency units are binary-divided, with the first processing region index set denoted as... The first processing area serves as the high-precision processing area; the index set of the second processing area is denoted as... The second processing area serves as a high-efficiency processing area, in which symbols... Represents logical OR, symbol Represents logical AND, Indicates the energy threshold. Indicates the threshold for motion sensitivity; The signal in the first processing area is denoted as... , The signal in the second processing area is denoted as... , .

[0036] Among them, energy threshold With motion sensitivity threshold The baseline values ​​were obtained through offline Monte Carlo simulation optimization. This optimization process was performed on a database containing various typical target motions and signal-to-noise ratio scenarios. The optimization objective was a cost function that combined imaging quality and computational complexity. The optimal threshold combination that minimized this cost function was found through grid search or random traversal. The expression for the cost function can be written as: , in, A quantitative indicator representing image quality, when and When the setting is lower, more frequency units will enter the first processing area, which will improve the final image quality, thereby... The value decreases; A quantitative indicator representing computational complexity. and When set low, the overall computational complexity is It will increase; This is the weighting factor.

[0037] Step 5: Perform interpolation correction on the signal in the first processing area using the Keystone transform algorithm of the first type, and perform interpolation correction on the signal in the second processing area using the Keystone transform algorithm of the second type.

[0038] The signal in the second processing area is subjected to Keystone transform based on frequency-domain zero-padding FFT interpolation. FFT interpolation first converts the slow-time echo to the frequency domain, and then decouples the Keystone transform through frequency-domain zero-padding, IFFT, and time-domain sampling.

[0039] Furthermore, the steps for interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type include: slow time axis Perform a distance-frequency test Related resampling yields a new timeline. , is represented as: , Let parameters ,when When the new sampling points are more densely packed than the original sampling points, interpolation is required. This is achieved by padding the signal with zeros in the frequency domain. The process includes: Step 511, for the original slow time series of length L... Perform FFT to obtain ; Step 512: Calculate the length of the new sequence after interpolation. , Indicates rounding up; Step 513, in the spectrum center insertion There are zero values, among which A new length of [value] is constructed. Doppler spectrum When L is even, the Doppler spectrum The expression is: , When L is odd, the Doppler spectrum The expression is: , in, Indicates the index of the Doppler frequency after zero padding; Step 514, zero-padding the spectrum conduct The inverse Fourier transform of the points yields the interpolated slow time series. The expression is: , Where IFFT stands for Inverse Fourier Transform, and i represents the slow-time index of the new sequence.

[0040] Furthermore, the step of interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type also includes: when When the new sampling points are sparser than the original sampling points, interpolation is required before extraction. The process includes: Step 521: Determine a minimum integer upsampling factor. A(n) , making ,in A(n) The expression is: ; Step 522, send the signal conduct A(n) Interpolation by a factor of 1 yields a temporary sequence. , length is ; Step 523, for the temporary sequence Sampling points are extracted from the sample to obtain the final target sequence. The first of the new sequence Each sampling point corresponds to a temporary sequence. The position in is determined by the following formula: , in, i For the slow time index of the new sequence, From temporary sequence The index of the points extracted from the data. This represents the rounding function; The final target sequence is represented as follows: .

[0041] For the signal in the first processing region, a more accurate windowed Sinc interpolation method is used. To achieve optimal results, an adaptive Kaiser window is employed, whose window function parameters are customized point-by-point according to the local features of the current processing unit.

[0042] Furthermore, the step of interpolating and correcting the signal in the first processing area using the Keystone transform algorithm of the first type includes: Construct an adaptive Kaiser window for signal features, and the kernel half-width of the Kaiser window. Based on motion sensitivity Dynamic adjustment, the expression is: , in, This represents the final half-width of the kernel at the nth distance frequency unit. This represents a base width, which is the minimum value of the kernel width. It is an adjustment coefficient that controls the maximum range of variation in kernel width; yes The normalized motion sensitivity index has a value between 0 and 1. Shape parameters of Kaiser window Based on local signal-to-noise ratio Dynamic adjustment, as The elevation is appropriate to choose high Values ​​to enhance sidelobe suppression; while If the price is reduced, then a lower price should be chosen. The shape parameters of the Kaiser window are set to ensure energy concentration. The expression is: , in, It is the preset minimum value, It is a preset Adjustment range, ; If it can be set , , The dynamic range will be Changes between; Signal Feature Adaptive Kaiser Window The final expression is: , Where k is the index of the discrete point within the window function, and its range is... ; It is a zero-order modified Bessel function; The signal in the first processing region is interpolated using the Sinc function of the adaptive Kaiser window, and the formula for the interpolated signal is as follows: , in, It depends on the distance unit n The adaptive Kaiser window function, i For interpolation output signal Slow-time index, L Signals within the first processing area Total number of sampling points in the slow time dimension.

[0043] Furthermore, the final corrected time-domain signal is denoted as a matrix. This can be represented by the following piecewise function: , in, Represents all distance frequency units in the first processing area The set, Represents all distance frequency units in the second processing area A set of.

[0044] To further verify the effectiveness and superiority of the radar range migration correction method based on external radiation sources of Starlink communication signals described in this invention, simulation comparison experiments were conducted, and the experimental results are as follows: Figures 3 to 5 As shown in the figure, this simulation simulates a scenario of detecting and processing a high-speed moving target under specific signal-to-noise ratio conditions.

[0045] Figures 3 to 5 All figures show the range profile of the target's range cell after processing with different range migration correction methods. The horizontal axis represents the range cell, and the vertical axis represents the normalized signal amplitude in decibels (dB). Figure 3 The results are shown after correction using the Sinc interpolation method, which has high accuracy among existing technologies. Figure 4 The results are shown after correction using the FFT interpolation method, which is among the most efficient existing techniques. Figure 5 The results of correction using the adaptive hybrid interpolation method proposed in this invention are presented. It can be intuitively seen that the target peak obtained using the method described in this invention is the sharpest, and the energy focusing effect is the best. In contrast, the target peaks processed by traditional Sinc interpolation and FFT interpolation methods are relatively low, indicating that their signal energy has some dissipation. Furthermore, the method of this invention also has a better sidelobe suppression level, and the noise floor around the target peak is flatter and cleaner.

Claims

1. A method for correcting radar range migration based on external radiation sources of Starlink communication signals, characterized in that, Includes the following steps: Step 1: Receive Starlink satellite downlink communication signals and direct wave signals, and use the direct wave signals to reconstruct and pulse compress the target echo signals to obtain the first communication signal; Step 2: Perform a Fourier transform on the first communication signal along the fast time dimension to convert the signal to the distance frequency-slow time domain, and obtain the second communication signal. Step 3: Perform Doppler ambiguity compensation on the second communication signal to obtain the third communication signal; Step 4: Calculate the energy distribution of each distance frequency unit and the Doppler spectral entropy of each distance frequency unit along the slow time dimension. Based on the energy distribution and motion sensitivity, execute a preset binary decision rule to dynamically divide the signal spectrum into a first processing region and a second processing region. Step 5: The signal in the first processing area is interpolated and corrected using the Keystone transform algorithm of the first type, and the signal in the second processing area is interpolated and corrected using the Keystone transform algorithm of the second type. Step 6: Recombine the corrected signal in the distance-frequency-slow time domain, and obtain the final corrected time domain signal by performing a distance-dimensional inverse Fourier transform.

2. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 1, characterized in that, The expression for the first communication signal is: ， in, Indicates a fast time. Indicates slow time. A rectangular function indicates that the signal only extends within a length of [length missing]. It is valid within the slow time interval, i.e., its value is 1; otherwise, it is 0. Indicates the total observation time. It is a reference signal With echo signal The cross-correlation results For the history of bistatic distance, For the speed of light, wavelength , For carrier frequency, It represents the imaginary unit.

3. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 2, characterized in that, The expression for the second communication signal is: ， in, This represents the spectrum of the transmitted pulse signal. Indicates distance frequency, The initial distance between the two bases. This represents the coefficient of the first-order term after the Taylor expansion from the historical date. This represents the coefficient of the quadratic term after the Taylor expansion of the distance from the history.

4. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 3, characterized in that, Step 3 includes: The estimated fuzzy number is obtained through Radon transform. The pre-filter is constructed, and its expression is: ， The third communication signal is obtained by multiplying the pre-filter and the second communication signal, as shown in the expression: ， Among them, parameters .

5. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 4, characterized in that, Step 4 includes: The third communication signal is discretized to obtain the discretization matrix, which is expressed as follows: ， in, It is the index of the distance frequency unit, corresponding to continuous frequencies. , The frequency sampling interval; It is a slow-time index, corresponding to continuous time. , The time sampling interval; Calculate the total energy of each distance-frequency unit n along the slow-time dimension of the discretized matrix. The expression is: ， in, This represents the total number of sampling points along the azimuth direction in the slow time dimension; Calculate the power spectral density of each distance frequency unit. The expression is: ， in, The input signal is represented by a discretized matrix. In a fixed distance unit n Upper and lower slow time dimensions l A single row of data was retrieved; Represents the window function. Indicates the Doppler frequency unit index. , Represents the square of the modulus; The power spectral density is normalized to a probability density function. The expression is: ， in, Let be the power spectral density function. m For the summation index of the Doppler frequency units, ; Calculate each distance unit n Doppler spectral entropy The formula is: ， in, It is a very small positive number designed to avoid the logarithmic value being zero; Using a preset two-dimensional decision threshold, all frequency units are binary-divided, with the first processing region index set denoted as... The second processing area index set is denoted as , where the symbol Represents logical OR, symbol Represents logical AND, Indicates the energy threshold. Indicates the threshold for motion sensitivity; The signal in the first processing area is denoted as... , The signal in the second processing area is denoted as... , .

6. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 5, characterized in that, The steps for interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type include: slow time axis Perform a distance-frequency test Related resampling yields a new timeline. , is represented as: ， Let parameters ,when When the new sampling points are more densely packed than the original sampling points, interpolation is required. This is achieved by padding the signal with zeros in the frequency domain. The process includes: Step 511, for the original slow time series of length L... Perform FFT to obtain ; Step 512: Calculate the length of the new sequence after interpolation. , Indicates rounding up; Step 513, in the spectrum center insertion There are zero values, among which A new length of [value] is constructed. Doppler spectrum When L is even, the Doppler spectrum The expression is: ， When L is odd, the Doppler spectrum The expression is: ， in, Indicates the index of the Doppler frequency after zero padding; Step 514, zero-padding the spectrum conduct The inverse Fourier transform of the points yields the interpolated slow time series. The expression is: ， Wherein, IFFT stands for Inverse Fourier Transform. i This represents the slow time index of the new sequence.

7. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 6, characterized in that, The steps for interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type also include: when When the new sampling points are sparser than the original sampling points, interpolation is required before extraction. The process includes: Step 521: Determine a minimum integer upsampling factor. A(n) , making ,in A(n) The expression is: ; Step 522, send the signal conduct A(n) Interpolation by a factor of 1 yields a temporary sequence. , length is ; Step 523, for the temporary sequence Sampling points are extracted from the sample to obtain the final target sequence. The first of the new sequence Each sampling point corresponds to a temporary sequence. The position in is determined by the following formula: ， in, From temporary sequence The index of the points extracted from the data. This represents the rounding function; The final target sequence is represented as follows: 。 8. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 7, characterized in that, The steps for interpolating and correcting the signal in the first processing region using the Keystone transform algorithm of the first type include: Construct an adaptive Kaiser window for signal features, and the kernel half-width of the Kaiser window. Based on motion sensitivity Dynamic adjustment, the expression is: ， in, The final kernel half-width represents the nth distance frequency unit. This represents a base width, which is the minimum value of the kernel width. It is an adjustment coefficient that controls the maximum range of variation in kernel width; yes The normalized motion sensitivity index has a value between 0 and 1. Shape parameters of Kaiser window Based on local signal-to-noise ratio Dynamic adjustment, the expression is: ， in, It is the preset minimum value, It is a preset Adjustment range, ; Signal Feature Adaptive Kaiser Window The final expression is: ， Where k is the index of the discrete point within the window function, and its range is... ; It is a zero-order modified Bessel function; The signal in the first processing region is interpolated using the Sinc function of the adaptive Kaiser window, and the formula for the interpolated signal is as follows: ， in, It depends on the distance unit n The adaptive Kaiser window function, i For interpolation output signal Slow-time index, L Signals within the first processing area Total number of sampling points in the slow time dimension.

9. The radar range migration correction method based on external radiation source of Starlink communication signal according to claim 8, characterized in that, The final corrected time-domain signal is denoted as a matrix. This can be represented by the following piecewise function: ， in, Represents all distance frequency units in the first processing area The set, Represents all distance frequency units in the second processing area A set of.

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