Starlink communication signal based range migration correction method for passive radar

Abstract

The application discloses a star chain communication signal-based external radiation source radar range migration correction method and belongs to the technical field of external radiation source radars. The method comprises the following steps: reconstructing and pulse compressing a target echo signal; converting the signal to a range frequency-slow time domain; compensating for Doppler ambiguity; dynamically dividing the spectrum of the signal into a first processing area and a second processing area; correcting the signal in the first processing area by using a first interpolation Keystone transformation algorithm and correcting the signal in the second processing area by using a second interpolation Keystone transformation algorithm; and recombining the corrected signals in the range frequency-slow time domain. The application can adaptively adjust an interpolation strategy according to the energy distribution of a star chain communication signal, significantly reduces the calculation amount while ensuring high-precision range migration correction, and is suitable for high-speed target detection of a star chain communication signal-based external radiation source radar.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of external radiation source radar, and particularly relates to a method for correcting range migration of external radiation source radar based on Starlink communication signals. BACKGROUND

[0002] External radiation source radar utilizes third-party non-cooperative radiation sources (such as broadcast, television, mobile communication base stations, etc.) for target detection, and has the advantages of strong concealment, low cost, and anti-stealth. In recent years, the rapid deployment of low earth orbit (LEO) giant communication satellite constellations represented by Starlink has brought revolutionary development opportunities for external radiation source radar technology. However, the LEO satellite constellation, while bringing great opportunities, also introduces unprecedented technical challenges: extremely high launch platform speed, short LEO satellite overpass time, resulting in dramatic changes in radar detection geometry in a short period of time, and large bandwidth characteristics, making the range migration phenomenon more obvious. Therefore, in external radiation source radar based on Starlink signals, range migration is no longer a simple linear problem, but a highly coupled, high-order complex problem that mixes target motion and high-speed, non-linear apparent motion of satellites.

[0003] Keystone transformation is a recognized effective method for correcting range migration in the field of radar signal processing, which can realize the decoupling of range and Doppler through variable substitution without knowing the target speed. To pursue the highest precision, the mainstream method uses 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 convolution property leads to extremely high computational complexity, making it difficult to meet the real-time processing requirements of radar systems. To meet the real-time requirements, another method uses interpolation based on Fast Fourier Transform (FFT), which uses frequency domain phase operations to approximate time domain resampling, and has extremely high computational efficiency, but it is essentially an approximate implementation that introduces significant phase errors when processing high-frequency components or highly maneuverable targets, resulting in target energy defocusing and degraded imaging quality. In addition, although some studies have proposed using Chirp Z-Transform (CZT), Discrete Fourier Transform (DFT), or Lagrange polynomial interpolation to optimize, these methods still essentially use a fixed, non-adaptive processing strategy, i.e., the same processing standard is used for all signal components, and the contradiction between precision and efficiency cannot be fundamentally solved.

[0004] In summary, due to the high-order, strong coupling and complex internal physical characteristics of the range migration problem in the star chain signal external radiation source radar, the existing technology urgently needs a new adaptive processing method that can ensure high-precision range migration correction and significantly reduce the computational complexity to meet the actual needs of the star chain communication signal-based external radiation source radar in high-speed target detection and imaging. SUMMARY

[0005] The purpose of the application is to provide a range migration correction method for a star chain communication signal-based external radiation source radar.

[0006] Technical scheme: A range migration correction method for a star chain communication signal-based external radiation source radar according to the application comprises the following steps:

[0007] Step 1: receiving a star chain satellite downlink communication signal and a direct wave signal, reconstructing and pulse compression processing the target echo signal using the direct wave signal to obtain a first communication signal;

[0008] Step 2: performing Fourier transform on the first communication signal along the fast time dimension to convert the signal to the range frequency-slow time domain to obtain a second communication signal;

[0009] Step 3: compensating the Doppler ambiguity number of the second communication signal to obtain a third communication signal;

[0010] Step 4: calculating the energy distribution of each range frequency unit and the Doppler spectrum entropy of each range frequency unit along the slow time dimension, and based on the energy distribution and the motion sensitivity, performing a preset binary decision rule to dynamically divide the spectrum of the signal into a first processing area and a second processing area;

[0011] Step 5: performing interpolation correction on the signal in the first processing area using a first type of interpolation Keystone transform algorithm and performing interpolation correction on the signal in the second processing area using a second type of interpolation Keystone transform algorithm;

[0012] Step 6: recombining the corrected signals in the range frequency-slow time domain and performing inverse Fourier transform on the range dimension to obtain a time-domain signal that is finally corrected.

[0013] Further, the expression of the first communication signal is:

[0014] ,

[0015] wherein, represents the fast time, represents the slow time, is a rectangular function, and represents that the signal is only in the length is valid in the slow time interval, i.e. value 1, and 0 otherwise, denotes the whole observation time, is the reference signal and the echo signal , is the bistatic range history, is the light speed, wavelength , is the carrier frequency, denotes the imaginary unit.

[0016] Further, the expression of the second communication signal is:

[0017] ,

[0018] where, denotes the spectrum of the transmitted pulse signal, denotes the range frequency, is the bistatic initial range, denotes the first order coefficient of the Taylor expansion of the range history, denotes the second order coefficient of the Taylor expansion of the range history.

[0019] Further, step 3 comprises:

[0020] obtaining the estimated ambiguity number by Radon transform , the pre-filter is constructed, the expression is:

[0021] ,

[0022] multiplying the pre-filter and the second communication signal to obtain the third communication signal, the expression is:

[0023] ,

[0024] where, the parameter .

[0025] Further, step 4 comprises:

[0026] discretizing the third communication signal to obtain a discrete matrix, the expression is:

[0027] ,

[0028] where, is the index of the range frequency unit, corresponding to the continuous frequency , is the frequency sampling interval; is the index of the slow time, corresponding to the continuous time , The time sampling interval;

[0029] Calculate the total energy of each distance-frequency unit n along the slow-time dimension of the discretized matrix. The expression is:

[0030] ,

[0031] in, This represents the total number of sampling points along the azimuth direction in the slow time dimension;

[0032] Calculate the power spectral density of each distance frequency unit. The expression is:

[0033] ,

[0034] 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;

[0035] The power spectral density is normalized to a probability density function. The expression is:

[0036] ,

[0037] in, Let be the power spectral density function. m For the summation index of the Doppler frequency units, ;

[0038] Calculate each distance unit n Doppler spectral entropy The formula is:

[0039] ,

[0040] in, It is a very small positive number designed to avoid the logarithmic value being zero;

[0041] 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;

[0042] The signal in the first processing area is denoted as... , The signal in the second processing area is denoted as... , .

[0043] Furthermore, the steps for interpolating and correcting the signal in the second processing area using the Keystone transform algorithm of the second type include:

[0044] slow time axis Perform a distance-frequency test Related resampling yields a new timeline. , represented as:

[0045] ,

[0046] 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:

[0047] Step 511, for the original slow time series of length L... Perform FFT to obtain ;

[0048] Step 512: Calculate the length of the new sequence after interpolation. , Indicates rounding up;

[0049] 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:

[0050] ,

[0051] When L is odd, the Doppler spectrum The expression is:

[0052] ,

[0053] in, Indicates the index of the Doppler frequency after zero padding;

[0054] Step 514, zero-padding the spectrum conduct The inverse Fourier transform of the points yields the interpolated slow time series. The expression is:

[0055] ,

[0056] Where IFFT stands for Inverse Fourier Transform, and i represents the slow-time index of the new sequence.

[0057] 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:

[0058] when When the new sampling points are sparser than the original sampling points, interpolation is required before extraction. The process includes:

[0059] Step 521: Determine a minimum integer upsampling factor. A(n) , making ,in A(n) The expression is: ;

[0060] Step 522, send the signal conduct A(n) Interpolation by a factor of 1 yields a temporary sequence. , length is ;

[0061] 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:

[0062] ,

[0063] 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;

[0064] The final target sequence is represented as follows:

[0065] .

[0066] Furthermore, the step of interpolating and correcting the signal in the first processing area using the Keystone transform algorithm of the first type includes:

[0067] 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:

[0068] ,

[0069] 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.

[0070] Shape parameters of Kaiser window Based on local signal-to-noise ratio Dynamic adjustment, the expression is:

[0071] ,

[0072] in, It is the preset minimum value, It is a preset Adjustment range, ;

[0073] Signal Feature Adaptive Kaiser Window The final expression is:

[0074] ,

[0075] 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;

[0076] 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:

[0077] ,

[0078] 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.

[0079] Furthermore, the final corrected time-domain signal is denoted as a matrix. This can be represented by the following piecewise function:

[0080] ,

[0081] wherein, represents a set of all distance-frequency units in the first processing area, represents a set of all distance-frequency units in the second processing area.

[0082] Advantages: Compared with the prior art, the present application has the following advantages:

[0083] The present application introduces Doppler spectrum entropy as a core basis for decision-making, opening up a new technical path for solving the contradiction between precision 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 by star chain signals; Not only does it achieve intelligent division of the processing area on a macro level, but also on a micro level, in the most critical high-precision area, it achieves dynamic optimization of point-by-point customization of interpolation kernel parameters. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 is a flowchart of the present application;

[0085] Figure 2 is a geometric model diagram of the external radiation source radar moving target detection scene;

[0086] Figure 3 is a performance simulation diagram of the Sinc interpolation method on the distance profile;

[0087] Figure 4 is a performance simulation diagram of the FFT interpolation method on the distance profile;

[0088] Figure 5 is a performance simulation diagram of the present application on the distance profile. DETAILED DESCRIPTION

[0089] The embodiments of the present application will be further described below in conjunction with the drawings and examples. It can be understood that the specific embodiments described herein are only used to explain the embodiments of the present application, and not to limit the embodiments of the present application. In addition, it should be noted that, in order to facilitate description, only parts related to the embodiments of the present application are shown in the drawings, not all structures.

[0090] ​​In the following description, for purposes of explanation and not limitation, specific details are set forth such as target system architectures, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application can be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.

[0091] It is to be understood that the terminology "includes", "has", "holds", "contains" and / or "comprising", when used in this specification and in the following claims, indicates the presence of the described features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0092] It is also to be understood that the terminology "and / or" when used in this specification and in the following claims, refers to at least one of the items, or any combination of the items, and includes all possible combinations when used in the description of the items.

[0093] In addition, in the description of the specification and the appended claims of this application, the terms "first", "second", and the like are used only to distinguish different descriptions, and cannot be understood as indicating or implying relative importance.

[0094] In this specification, the phrase "one embodiment" or "some embodiments" etc. means that a feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present application. Thus, the occurrence of the phrase "in one embodiment", "in some embodiments", "in other embodiments", "in additional embodiments", etc. in various places in the specification is not necessarily all referring to the same embodiment, unless otherwise specifically noted. Rather, it is meant that one or more embodiments of the present application include the feature, structure, or characteristic.

[0095] In conjunction with Figure 1 As shown, the method for correcting range migration of a satellite communication signal based on an external radiation source radar according to the present embodiment includes the following steps:

[0096] Step 1, receiving satellite downlink communication signals and direct wave signals, reconstructing and pulse compression processing the target echo signal using the direct wave signal to obtain a first communication signal.

[0097] In one example, the object is an external radiation source radar, and the target to be detected can be a flying target such as a drone, or a ship or a vehicle, etc. The geometric model of the motion target detection scene is as shown in Figure 2 As shown, in this example, the target to be detected is an airplane, and the radar is the receiver, whose position is at the coordinate origin. At the initial moment, the position of the radiation source is The position of the probe target is The distance from the radiation source to the receiving station is The distance from the radiation source to the probe target is The distance from the probe target to the receiving station is At , the position of the radiation source is The position of the probe target is The position of the radiation source to the receiving station is The distance from the radiation source to the target is The distance from the target to the receiving station is The direct wave signal refers to a signal directly emitted from the satellite and received by the ground station, and the target echo signal refers to a signal emitted from the satellite, reflected by the target, and finally received by the ground station. By estimating the channel distortion in the known pilot of the direct wave signal, a pure transmission signal copy is obtained, the target echo signal is reconstructed, the reconstructed signal is subjected to pulse compression processing, and a two-dimensional time domain complex signal matrix is obtained as the first communication signal.

[0098] In an ideal case, ignoring the influence of the Doppler frequency, after range compression, the first communication signal from the integration time can be modeled in fast time and slow time .

[0099] Further, the expression of the first communication signal is:

[0100] ,

[0101] wherein represents the fast time, represents the slow time, is a rectangular function, indicating that the signal is valid only in the slow time interval with a length of , that is, the value is 1, and the value is 0 at other times, represents the entire observation time, is the cross-correlation result of the reference signal and the echo signal , the reference signal is a signal directly emitted from the satellite, that is, the reconstructed signal, and the echo signal refers to a signal emitted from the satellite, reflected by the target, and finally received by the ground station; is the bistatic range history, is the speed of light, and the wavelength , is the carrier frequency, represents the imaginary unit.

[0102] The expression of the bistatic range history is:

[0103] ,

[0104] wherein, , and respectively represent the distance of the external emitter and the target, the distance of the target and the location of the receiving station, the distance of the external emitter and the receiving station at the time.

[0105] The second order Taylor expansion of the distance history can be written as:

[0106] ,

[0107] ,

[0108] wherein, is the bistatic initial range; is the first order coefficient of the Taylor expansion of the distance history; is the second order coefficient of the Taylor expansion of the distance history; , and respectively represent the initial distance of the external emitter and the target, the initial distance of the target and the location of the receiving station, the initial distance of the external emitter and the receiving station.

[0109] Step 2, performing Fourier transform on the first communication signal along the fast time dimension, converting the signal to the range-frequency-slow time domain, obtaining a second communication signal.

[0110] Further, the expression of the second communication signal is:

[0111] ,

[0112] wherein, represents the spectrum of the transmitted pulse signal, represents the range frequency, is the bistatic initial range, represents the first order coefficient of the Taylor expansion of the distance history, represents the second order coefficient of the Taylor expansion of the distance history.

[0113] Step 3, performing Doppler ambiguity number compensation on the second communication signal, obtaining a third communication signal.

[0114] Further, step 3 includes:

[0115] obtaining an estimated ambiguity number by Radon transform , constructing a pre-filter, the expression of which is:

[0116] ,

[0117] The pre-filter is multiplied by the second communication signal to obtain a third communication signal, expressed as:

[0118] ,

[0119] wherein the parameter .

[0120] Step 4, the energy distribution of each distance-frequency unit is calculated, and the Doppler spectrum entropy of each distance-frequency unit along the slow time dimension is calculated, and based on the energy distribution and the motion sensitivity, a preset binary decision rule is executed to dynamically divide the spectrum of the signal into a first processing area and a second processing area.

[0121] Most of the energy of the signal is usually concentrated in a few key frequency units, which correspond to the main body of strong targets or strong clutter, and are the core of determining the final imaging quality. Step 4 not only introduces the energy criterion, but also introduces a direct quantification of the complexity of target motion.

[0122] Further, step 4 includes:

[0123] The third communication signal is discretized to obtain a discretization matrix, expressed as:

[0124] ,

[0125] wherein is the index of the distance-frequency unit, corresponding to the continuous frequency , is the frequency sampling interval; is the index of the slow time, corresponding to the continuous time , is the time sampling interval;

[0126] The total energy of each distance-frequency unit n along the slow time dimension of the discretization matrix is calculated , expressed as:

[0127] ,

[0128] wherein is the total number of sampling points along the slow time dimension in the azimuth direction;

[0129] The motion complexity of the quantified target is introduced, and the Doppler spectrum entropy is introduced as a motion sensitivity index. First, the power spectral density of each distance-frequency unit is calculated , expressed as:

[0130] ,

[0131] wherein represents the input signal, which is the discretization 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;

[0132] The power spectral density is normalized to a probability density function. The expression is:

[0133] ,

[0134] in, Let be the power spectral density function. m For the summation index of the Doppler frequency units, ;

[0135] Then each distance cell is calculated. n Doppler spectral entropy The formula is:

[0136] ,

[0137] in, It is a very small positive number designed to avoid the logarithmic value being zero;

[0138] 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;

[0139] 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, denotes an energy threshold, denotes a motion sensitivity threshold;

[0140] Let the signal in the first processing region be denoted as , Let the signal in the second processing region be denoted as , .

[0141] where the energy threshold and the motion sensitivity threshold are optimized by offline Monte Carlo simulation, which is performed in a database containing multiple typical target motion and SNR scenarios, with a cost function that combines imaging quality and computational complexity as the optimization objective, and the optimal threshold combination that minimizes the cost function is found by grid search or random traversal. The expression of the cost function can be written as:

[0142] ,

[0143] where, represents a quantitative indicator of imaging quality, and when and are set to be lower, more frequency units will enter the first processing region, which will improve the final imaging quality and thus make the value of smaller; represents a quantitative indicator of computational complexity, and are set to be lower, the total computational complexity will increase; is a weighting factor.

[0144] Step 5: The signal in the first processing region is corrected by using a first type of interpolation Keystone transform algorithm, and the signal in the second processing region is corrected by using a second type of interpolation Keystone transform algorithm.

[0145] In the second processing region, the signal is corrected by using a Keystone transform based on FFT interpolation of zero padding in the frequency domain. The FFT interpolation first converts the slow-time echo into the frequency domain, and then completes the Keystone transform decoupling through frequency domain zero padding, IFFT and time domain sampling.

[0146] Further, the step of correcting the signal in the second processing region by using the second type of interpolation Keystone transform algorithm includes:

[0147] performing resampling of the slow-time axis once on the distance frequency to obtain a new time axis , which is represented as:

[0148] ,

[0149] 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:

[0150] Step 511, for the original slow time series of length L... Perform FFT to obtain ;

[0151] Step 512: Calculate the length of the new sequence after interpolation. , Indicates rounding up;

[0152] 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:

[0153] ,

[0154] When L is odd, the Doppler spectrum The expression is:

[0155] ,

[0156] in, Indicates the index of the Doppler frequency after zero padding;

[0157] Step 514, zero-padding the spectrum conduct The inverse Fourier transform of the points yields the interpolated slow time series. The expression is:

[0158] ,

[0159] Where IFFT stands for Inverse Fourier Transform, and i represents the slow time index of the new sequence.

[0160] 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:

[0161] when When the new sampling points are sparser than the original sampling points, interpolation is required before extraction. The process includes:

[0162] Step 521, determine a minimum integer up-sampling rate A(n) such that where A(n) The expression of is: ;

[0163] Step 522, interpolate the signal by times, to obtain a temporary sequence A(n) , length ; ;

[0164] Step 523, decimate the sampling points in the temporary sequence to obtain the final target sequence , the th sampling point of the new sequence corresponds to the position in the temporary sequence by the following formula:

[0165] ,

[0166] where i is the slow time index of the new sequence, is the index of the decimated point from the temporary sequence , and represents the rounding function;

[0167] The final target sequence is represented as:

[0168] .

[0169] For the signal of the first processing area, a higher-precision windowed Sinc interpolation method is used. To achieve optimal results, a signal feature adaptive Kaiser window is used, and the window function parameters are customized point by point according to the local features of the current processing unit.

[0170] Further, the step of interpolating and correcting the signal of the first processing area using the first type of interpolation Keystone transformation algorithm includes:

[0171] Constructing a signal feature adaptive Kaiser window, the core half-width of the Kaiser window is dynamically adjusted according to the motion sensitivity , and the expression is:

[0172] ,

[0173] where represents the final core half-width of the th distance frequency unit, represents a basic width, which is the minimum value of the core 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.

[0174] 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:

[0175] ,

[0176] in, It is the preset minimum value, It is a preset Adjustment range, ;

[0177] If it can be set , , The dynamic range will be Changes between;

[0178] Signal Feature Adaptive Kaiser Window The final expression is:

[0179] ,

[0180] 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;

[0181] 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:

[0182] ,

[0183] 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.

[0184] Further, the time-domain signal finally completed correction is recorded as matrix , which is represented by the following piecewise function:

[0185] ,

[0186] wherein, represents the set of all distance-frequency units in the first processing area, represents the set of all distance-frequency units in the second processing area.

[0187] In order to further verify the effectiveness and superiority of the star chain communication signal external radiation source radar range migration correction method described in the present application, a simulation comparison experiment is carried out, and the experimental results are shown in Figures 3 to 5 . The simulation simulates the scene of detecting and processing a high-speed moving target under certain signal-to-noise ratio conditions.

[0188] Figures 3 to 5 All show the distance profile of the distance unit where the target is located after being processed by different distance migration correction methods. Among them, the horizontal axis represents the distance unit, and the vertical axis represents the normalized signal amplitude, in decibels (dB). Figure 3 shows the result after correction using the Sinc interpolation method with high precision in the prior art, Figure 4 shows the result after correction using the FFT interpolation method with high efficiency in the prior art, Figure 5 shows the result after correction using the adaptive hybrid interpolation method proposed in the present application. It can be directly seen that the target peak obtained by using the method described in the present application is the sharpest, and the energy focusing effect is the best. In contrast, the target peak processed by the traditional Sinc interpolation method and the FFT interpolation method is relatively low, indicating that there is a certain dissipation of signal energy. In addition, the sidelobe suppression level of the method of the present application is also better, and the noise floor around the target peak is more flat and clean.​​

Claims

1. A method for range migration correction of a star chain communication signal based on an external emitter radar, characterized in that, The method comprises the following steps: Step 1, receiving a satellite downlink communication signal and a direct wave signal, reconstructing and pulse compression processing the target echo signal by using the direct wave signal, and obtaining a first communication signal; Step 2, performing Fourier transform on the first communication signal along the fast time dimension, converting the signal to a range frequency-slow time domain, and obtaining a second communication signal; Step 3, performing Doppler ambiguity number compensation on the second communication signal, and obtaining a third communication signal; Step 4, calculating the energy distribution of each range frequency unit, calculating the Doppler spectrum entropy of each range frequency unit along the slow time dimension, and based on the energy distribution and the motion sensitivity, performing a preset binary decision rule to dynamically divide the spectrum of the signal into a first processing area and a second processing area; Step 5, performing interpolation correction on the signal in the first processing area by using a first interpolation Keystone transform algorithm, and performing interpolation correction on the signal in the second processing area by using a second interpolation Keystone transform algorithm; Step 6, recombining the corrected signals in the range frequency-slow time domain, and obtaining a time domain signal which is finally corrected by distance dimension inverse Fourier transform.

2. The method of Starlink communication signal exo-source radar range migration correction based on claim 1, characterized in that, The expression of the first communication signal is: ， wherein represents the fast time, represents the slow time, is a rectangular function, indicating that the signal is only valid in a slow time interval of length , i.e. has the value 1, and is 0 otherwise, represents the total observation time, is the reference signal and the cross-correlation result of the echo signal , is the bi-static range history, is the speed of light, the wavelength , is the carrier frequency, denotes the imaginary unit.

3. The method of Starlink communication signal exo-source radar range migration correction according to claim 2, characterized in that, The expression of the second communication signal is: ， wherein, represents a spectrum of the transmitted pulse signal, represents a range frequency, is a bistatic initial range, represents a first order coefficient of the Taylor expansion of the range history, represents a second order coefficient of the Taylor expansion of the range history.

4. The method of Starlink communication signal exo-source radar range migration correction according to claim 3, characterized in that, Step 3 comprises: Obtaining an estimated blur number by radon transform A pre-filter is constructed and has an expression of ， Multiplying the pre-filter and the second communication signal to obtain the third communication signal, and the expression is: ， wherein the parameters .

5. The method of Starlink communication signal exo-source radar range migration correction based on claim 4, characterized in that, Step 4 comprises: Discretizing the third communication signal to obtain a discrete matrix, and the expression is: ， wherein, is an index of distance frequency unit, corresponding to continuous frequency , is a frequency sampling interval; is an index of slow time, corresponding to continuous time , is a time sampling interval; The total energy of each distance frequency unit n is calculated along the slow time dimension for the discretized matrix The expression is: ， wherein, Ntot is the total number of samples along the azimuthal slow-time dimension; calculating a power spectral density for each distance frequency cell , the expression is: ， wherein represents the input signal, is a discretized matrix In the fixed distance unit n above, along the slow time dimension l the row of data taken out; represents a window function, represents a Doppler frequency unit index, , represents the square of the modulus; Normalizing the power spectral density to a probability density function , the expression is: ， wherein is a power spectral density function, m is a summation index in Doppler frequency units, ; The Doppler spectrum entropy of each distance cell is calculated n The formula is:​ ， wherein is a very small positive number to avoid log of zero; All frequency bins are divided into two by a preset two-dimensional decision threshold, wherein a first processing area index set is denoted as , and a second processing area index set is denoted as , wherein a symbol represents a logical or, a symbol represents a logical and, denotes an energy threshold, denotes a motion sensitivity threshold. Let the signal of the first processing zone be denoted by , ; and the signal of the second processing zone be denoted by , .

6. The method of Starlink communication signal exo-source radar range migration correction based on claim 5, characterized in that, The step of performing interpolation correction on the signal in the second processing area by using the second interpolation Keystone transform algorithm comprises: The slow time axis is A resampling is performed once per distance frequency related to the slow time axis is given by ， Let the parameter When The new sampling points are denser than the original sampling points, and interpolation is needed, which is realized by zero-padding in the center of the frequency domain of the signal, and the implementation process includes: Step 511, performing FFT on the original slow time sequence of length L to obtain ; and ; Step 512, calculate the new length of the interpolated sequence , denotes 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 is given by the expression: ， wherein, denotes the index of the zero-padded Doppler frequency; Step 514, inverse Fourier transform of the zero-padded spectrum to obtain the interpolated slow-time sequence , expressed as​ ， where IFFT denotes an inverse Fourier transform, i denotes the slow time index of the new sequence.

7. The method of Starlink communication signal exo-source radar range migration correction based on claim 6, characterized in that, The step of performing interpolation correction on the signal in the second processing area by using the second interpolation Keystone transform algorithm further comprises: When The new sampling points are sparser than the original sampling points, and need to be interpolated before decimation. The implementation process includes: Step 521, determine a minimum integer up-sampling rate A(n) such that wherein A(n) The expression for ; Step 522, signal is performed A(n) interpolation by a factor of 2 to obtain a temporary sequence of length ; Step 523, the temporary sequence is extracted to obtain the final target sequence The position of the first sample point of the new sequence corresponds to the position in the temporary sequence which is determined by the following formula: ， wherein is an index of a point drawn from a temporary sequence is an index of a point drawn from a temporary sequence denotes a rounding function; The finally obtained target sequence is represented as: 。 8. The method of Starlink communication signal exo-source radar range migration correction according to claim 7, wherein, The step of performing interpolation correction on the signal in the first processing area by using the first interpolation Keystone transform algorithm comprises: The signal feature adaptive Kaiser window is constructed, and the kernel half-width of the Kaiser window is According to the motion sensitivity Dynamic adjustment, the expression is: ， wherein, represents the final kernel half-width of the nth distance-frequency unit, represents a base width, which is the minimum value of the kernel width, is an adjustment factor that controls the maximum variation range of the kernel width; is is the normalized motion sensitivity index, whose value is between 0 and 1. Shape parameters of Kaiser windows According to the local signal-to-noise ratio Dynamic adjustment, the expression is: ， wherein, is a preset minimum value, 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, ranging from ; is the zeroth-order modified Bessel function. Performing interpolation on the signal in the first processing area by using a Sinc function of an adaptive Kaiser window, and the formula of the interpolated signal is: ， 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 method of Starlink communication signal exo-source radar range migration correction according to claim 8, wherein, The time domain signal finally corrected is denoted by the matrix and is represented by the following piecewise function: ， wherein represents a set of all distance-frequency cells in the first processing zone, represents a set of all distance-frequency cells in the second processing zone. represents a set of all distance-frequency cells in the second processing zone.​

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