A non-cooperative moving emitter single station passive location method based on synthetic aperture

Abstract

This invention discloses a single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture radar (SAR). The method includes: using a moving observation station to create two non-uniform velocity observation tracks to acquire raw data information of the two segments of non-cooperative moving radiation source signals; constructing a third-order instantaneous slant range model between the observation station and the radiation source based on their relative positions; constructing a localization model for the non-cooperative moving radiation source based on the third-order instantaneous slant range model and the station's moving tracks; estimating the pulse repetition interval and Doppler parameters of the two segments of SAR data in the localization model; obtaining a coarse solution for the localization parameters based on the Doppler parameter estimates, and iteratively optimizing the solution to finally obtain the localization parameters of the moving radiation source, thus completing the localization. This invention solves the problem of uncertainty in the inversion results of localization parameters in non-cooperative moving radiation source localization due to the fact that there are more localization parameters than imaging parameters.

Description

Technical Field

[0001] This invention belongs to the field of passive positioning technology, specifically relating to a single-station passive positioning method for non-cooperative moving radiation sources based on synthetic aperture. Background Technology

[0002] In the field of modern electronic reconnaissance, passive localization technology has become a core technology for target localization and tracking in complex electromagnetic environments due to its strong concealment advantage. Traditional passive localization methods are divided into two-step localization methods and direct localization methods. Two-step localization methods use a single observation parameter, which, while simple and easy to implement, is prone to non-convergence. Combining multiple observation parameters can solve this problem, but it greatly increases the complexity of the system. Direct localization methods do not require estimation of observation parameters; they directly search for the spatial location of the radiation source through a cost function, reducing information loss caused by measuring observation parameters. Their localization performance under low signal-to-noise ratio conditions is generally superior to that of two-step localization methods.

[0003] Compared to traditional passive positioning methods, which suffer from long observation times, low positioning efficiency, and significant errors under low signal-to-noise ratio conditions, passive positioning methods based on synthetic aperture radar (SAR) can achieve higher positioning accuracy. Current literature on SAR passive positioning methods primarily focuses on fixed ground-based radiation sources, lacking in-depth research on the positioning of moving radiation sources. In reality, in passive positioning scenarios for ground / sea surface radiation sources, the sources are not always stationary but are often in motion. Analysis reveals that the aforementioned SAR positioning methods are difficult to apply to the positioning of moving radiation sources. The fundamental reason lies in the high coupling between the position and velocity information of the radiation source in traditional SAR positioning models, making it difficult to simultaneously and accurately estimate both information under non-cooperative radiation source conditions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture, thereby solving the problem that the inversion results of localization parameters are uncertain due to the fact that there are more localization parameters than imaging parameters in the localization of non-cooperative moving radiation sources.

[0005] This invention provides a single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture, comprising the following steps:

[0006] S1. Utilize the mobility of the observation station to create two non-uniform velocity observation tracks and acquire the raw data information of the radiation source signals from the two non-cooperative motions.

[0007] S2. Based on the relative positional relationship between the observation station and the radiation source in step S1, construct a third-order instantaneous slant range model between the observation station and the radiation source;

[0008] S3. Based on the third-order instantaneous slant range model obtained in step S2 and the maneuvering trajectory of the observation station, construct a non-cooperative motion radiation source localization model;

[0009] S4. Based on the acquired data, estimate the pulse repetition interval (PRI) and Doppler parameters of the two synthetic aperture data segments in the non-cooperative motion radiation source localization model obtained in step S3;

[0010] S5. Obtain a rough solution for the positioning parameters based on the Doppler parameter estimates obtained in step S4, and substitute the rough solution for the positioning parameters as the initial guess values ​​into the non-cooperative moving radiation source positioning model for iterative optimization. Finally, obtain the positioning parameters of the moving radiation source and complete the single-station passive positioning of the non-cooperative moving radiation source.

[0011] Step S2 includes the following steps:

[0012] The observation station observes the radiation source in a three-dimensional oblique-view mode and calculates the instantaneous slant distance between the non-cooperative motion radiation source on the ground and the observation station.

[0013] The obtained instantaneous slant range is expanded using a third-order Taylor series to obtain the third-order Taylor series expansion of the instantaneous slant range; finally, a third-order instantaneous slant range model between the observation station and the radiation source is obtained by combining the results.

[0014] In step S2, both the ground-based non-cooperative motion radiation source and the observation station are in uniform motion, and the instantaneous slant distance between them is expressed as: ;in, For location, slow time; The instantaneous coordinates of the radiation source; These are the instantaneous coordinates of the observation station;

[0015] The third-order Taylor series expansion of the instantaneous slant range is: ; For the constant term, its calculation formula is: ; The coefficients of a first-order polynomial are calculated as follows: ; The coefficients of the second-order polynomial are calculated as follows: ; The coefficients of the third-order polynomial are calculated as follows: ; The coordinates of the center of the radiation source at that moment; The coordinates of the observation station's center time; The velocity of the radiation source; The speed of the observation station.

[0016] Step S3 includes the following steps:

[0017] Based on the third-order instantaneous slant range model obtained in step S2, it is assumed that the radiation source target is in The plane moves at a constant velocity The observation station is at an altitude of [missing information]. In the air, first at a constant speed Moving, continuously receiving signals from the radiation source during this period, the synthetic aperture time is Then at another constant speed Moving and continuously receiving signals from the radiation source, the synthetic aperture time is ;

[0018] The azimuth time of the two synthetic aperture segments are respectively set as and In the first segment of the synthetic aperture, the instantaneous coordinates of the observatory and the radiation source are respectively... and At its central position The coordinates of the time observation station and the radiation source are respectively and In the second synthetic aperture section, the instantaneous coordinates of the observation station and the radiation source are respectively... and At its central position The coordinates of the time observation station and the radiation source are respectively and ;

[0019] The instantaneous slant distance between the radiation source and the observation station in the two segments of the synthetic aperture was constructed. and ;

[0020] Instantaneous slant distance between the radiation source and the observatory in the two synthetic aperture sections and The polynomial coefficient expressions of the third-order polynomial slant range model together constitute the non-cooperative motion radiation source localization model.

[0021] In step S3, the instantaneous slant distance between the radiation source and the observation station in the two synthetic aperture segments is... and The expression for the third-order polynomial slant distance model is: ; ;in, This is a constant term representing the instantaneous slant distance of the first trajectory segment; The coefficients of the first-order polynomial for the instantaneous slant distance of the first segment of the trajectory; The coefficients of the second-order polynomial are the instantaneous slant distance of the first segment of the trajectory; The coefficients of the third-order polynomial are the instantaneous slant distance of the first segment of the trajectory; This is a constant term representing the instantaneous slant distance of the second segment of the trajectory; These are the first-order polynomial coefficients of the instantaneous slant distance of the second segment of the trajectory; For the second-order polynomial coefficients of the instantaneous slant distance of the second segment of the trajectory; The coefficients of the third-order polynomial for the instantaneous slant distance of the second segment of the trajectory;

[0022] The ~ Express it using the following formula:

[0023]

[0024]

[0025] Since the observation station moves at a constant linear velocity, the position of the observation station at the azimuth center between the two composite aperture segments is... and It has the following relationship: ;in, The time interval is the time interval between the centers of two adjacent synthetic aperture segments.

[0026] Step S4 includes the following steps:

[0027] The two one-dimensional radiation source signals received by the observation station are rearranged in two dimensions to obtain two sets of two-dimensional synthetic aperture data matrices, and the accurate PRI is estimated during the two-dimensional rearrangement process.

[0028] Estimate the Doppler parameters of the two radiation source signals.

[0029] Suppose that the radiation source signal is represented by the following formula: ;in, For time; For signal amplitude, For signal carrier frequency, For phase modulation; the two-dimensional rearrangement specifically involves: demodulating the radiation source signal to baseband, and then rearranging it in two dimensions according to the principle of synthetic aperture, expressed by the following formula: ;in, For distance and time, For location and time, This refers to the distance envelope information of the radiation source; The center frequency of the Doppler wave. To tune the frequency for Doppler, It is a third-order frequency modulation;

[0030] Accurate estimation of PRI based on optimal focusing quality of the radiation source signal includes the following steps:

[0031] For radiation source signals Imaging focusing mainly includes Linear Range Walk Correction (LRWC) and azimuth-matched filtering, expressed by the following formula: ; ;in, This represents a distance-to-Fourier transform. This represents the inverse Fourier transform of distance. This indicates a Fourier transform of the orientation. Two-dimensional rearrangement signal The focused signal after imaging;

[0032] LRWC factor And azimuth matched filter function The following formulas can be used to express this: ; Among them, the wavelength of the radiation source signal , For distance frequency;

[0033] Based on the criterion of focusing on optimal quality, the estimation problem of PRI is modeled as the following optimization model: ;in, This indicates the focusing quality of the radiation source signal. The evaluation criteria for focusing quality are the minimum image entropy or the maximum focusing energy.

[0034] The four-dimensional optimization problem in the optimization model is transformed into a two-dimensional optimization problem for estimating PRI and Doppler frequency modulation. A blind search is performed on the number of sampling points for PRI, while the classic line search method is used for Doppler frequency modulation.

[0035] The estimation of the Doppler parameters of the two radiation source signals is specifically as follows:

[0036] After accurately estimating the PRI of the emitted signal from the radiation source, the optimization problem is simplified and expressed by the following formula: ;

[0037] The simplified optimization problem is reduced to several one-dimensional optimization problems, which are then solved one by one.

[0038] For radiation source signals Perform azimuth compression imaging focusing, The estimation model is a Doppler frequency modulation estimation optimization model, which is then solved to obtain the Doppler frequency modulation estimate. The Doppler frequency modulation estimation optimization model is expressed by the following formula: ;

[0039] Based on the obtained Doppler frequency modulation estimate, an optimal model for Doppler center frequency estimation is constructed using LRWC operation and azimuth matched filtering to obtain the initial value of the Doppler center frequency estimate. The optimal model for Doppler center frequency estimation is expressed by the following formula: The obtained Doppler center frequency estimate differs from the true value and needs further correction, expressed by the following formula: ;in, This is the corrected Doppler center frequency. This is the estimated Doppler center frequency. For frequency deviation, its expression is: ;in, This represents the azimuth focusing position of the radiation source signal. Where azimuth is the number of sampling points, and PRF is the pulse repetition frequency;

[0040] A non-parametric method, phase gradient self-focusing, is used to estimate the residual phase error of the position-matched filtered signal. The third frequency modulation is then calculated based on the estimated residual phase. Specifically:

[0041] Assuming the residual phase is estimated from the focusing signal using phase gradient self-focusing, then... This indicates that by considering the remaining phase Polynomial fitting can be used to obtain the coefficients of its cubic term. The third frequency modulation is then calculated using the following formula: .

[0042] In step S5, the steps for calculating the coarse solution of the non-cooperative motion radiation source location information are as follows:

[0043] Based on the two sets of estimated Doppler parameters, the following calculations are performed: ~ In the arithmetic expression and And substitute it as a known number into the following formula: ; After simplification, the following system of equations is obtained: When the observation station speed does not meet the requirements and The system of equations typically has two intersection points. By combining prior information or introducing boundary conditions, a unique valid solution is determined, yielding a rough estimate of the radiation source's velocity. and ;

[0044] Then, the obtained rough velocity estimate of the radiation source and Substitute into the following formula: ; The rough estimate of the location of the radiation source was obtained through calculation. and ;

[0045] joint ~ Eliminate parameters from the arithmetic expression. and The following system of positioning equations is obtained: ;

[0046] The obtained rough velocity estimate of the radiation source and and a rough estimate of the location of the radiation source and The initial guesses are substituted into the above positioning equations for iterative optimization. Iterative optimization can be achieved using numerical optimization methods such as Newton's iteration method and trust region method to obtain accurate estimates of the positioning parameters, thus achieving accurate estimation of the radiation source positioning parameters.

[0047] This invention discloses a single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture, which solves the problem of uncertainty in the inversion results of localization parameters in non-cooperative moving radiation source localization due to the fact that there are more localization parameters than imaging parameters. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0049] Figure 2 The figures show the localization results of 100 Monte Carlo experiments before and after iterative optimization in the embodiment of the method of the present invention; wherein, Figure 2 (a) is a comparison of the 100 localization attempts and the actual location before iterative optimization, when the signal-to-noise ratio is 15dB. Figure 2 (b) is a comparison of the 100 localizations after iterative optimization with the actual location when the signal-to-noise ratio is 15dB.

[0050] Figure 3 This is a graph showing the RMSE results of the X-axis position before and after iterative optimization in an embodiment of the method of the present invention; wherein, Figure 3 (a) The RMSE of the X-axis position before iterative optimization. Figure 3 (b) is the RMSE of the X-axis position after iterative optimization.

[0051] Figure 4 This is a graph showing the RMSE results of the Y-axis position before and after iterative optimization in an embodiment of the method of the present invention; wherein, Figure 4 (a) The RMSE of the Y-axis position before iterative optimization. Figure 4 (b) is the RMSE of the Y-axis position after iterative optimization.

[0052] Figure 5 This is a graph showing the RMSE results of the X-axis velocity before and after iterative optimization in an embodiment of the method of the present invention; wherein, Figure 5 (a) The RMSE of the velocity along the X-axis before iterative optimization. Figure 5 (b) is the RMSE of the X-axis velocity after iterative optimization.

[0053] Figure 6 This is a graph showing the RMSE results of the Y-axis velocity before and after iterative optimization in an embodiment of the method of the present invention; wherein, Figure 6 (a) The RMSE of the Y-axis velocity before iterative optimization. Figure 6 (b) is the RMSE of the Y-axis velocity after iterative optimization. Detailed Implementation

[0054] This invention provides a single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture, comprising the following steps:

[0055] S1. Utilize the mobility of the observation station to create two non-uniform velocity observation tracks and acquire the raw data information of the radiation source signals from the two non-cooperative motions.

[0056] S2. Based on the relative positional relationship between the observation station and the radiation source in step S1, construct a third-order instantaneous slant range model between the observation station and the radiation source;

[0057] Step S2 includes the following steps:

[0058] The observation station observes the radiation source in a three-dimensional oblique-view mode and calculates the instantaneous slant distance between the non-cooperative motion radiation source on the ground and the observation station.

[0059] The obtained instantaneous slant range is expanded using a third-order Taylor series to obtain the third-order Taylor series expansion of the instantaneous slant range; finally, a third-order instantaneous slant range model between the observation station and the radiation source is obtained by combining the results.

[0060] In step S2, both the ground-based non-cooperative motion radiation source and the observation station are in uniform motion, and the instantaneous slant distance between them is expressed as: ;in, For location, slow time; The instantaneous coordinates of the radiation source; These are the instantaneous coordinates of the observation station;

[0061] The third-order Taylor series expansion of the instantaneous slant range is: ; For the constant term, its calculation formula is: ; The coefficients of a first-order polynomial are calculated as follows: ; The coefficients of the second-order polynomial are calculated as follows: ; The coefficients of the third-order polynomial are calculated as follows: ; The coordinates of the center of the radiation source at that moment; The coordinates of the observation station's center time; The velocity of the radiation source; The speed of the observation station.

[0062] S3. Based on the third-order instantaneous slant range model obtained in step S2 and the maneuvering trajectory of the observation station, construct a non-cooperative motion radiation source localization model;

[0063] Step S3 includes the following steps:

[0064] Based on the third-order instantaneous slant range model obtained in step S2, it is assumed that the radiation source target is in The plane moves at a constant velocity The observation station is at an altitude of [missing information]. In the air, first at a constant speed Moving, continuously receiving signals from the radiation source during this period, the synthetic aperture time is Then at another constant speed Moving and continuously receiving signals from the radiation source, the synthetic aperture time is ;

[0065] The azimuth time of the two synthetic aperture segments are respectively set as and In the first segment of the synthetic aperture, the instantaneous coordinates of the observatory and the radiation source are respectively... and At its central position The coordinates of the time observation station and the radiation source are respectively and In the second synthetic aperture section, the instantaneous coordinates of the observation station and the radiation source are respectively... and At its central position The coordinates of the time observation station and the radiation source are respectively and ;

[0066] The instantaneous slant distance between the radiation source and the observation station in the two segments of the synthetic aperture was constructed. and ;

[0067] Instantaneous slant distance between the radiation source and the observatory in the two synthetic aperture sections and The polynomial coefficient expressions of the third-order polynomial slant range model together constitute the non-cooperative motion radiation source localization model.

[0068] In step S3, the instantaneous slant distance between the radiation source and the observation station in the two synthetic aperture segments is... and The expression for the third-order polynomial slant distance model is: ; ;in, This is a constant term representing the instantaneous slant distance of the first trajectory segment; The coefficients of the first-order polynomial for the instantaneous slant distance of the first segment of the trajectory; The coefficients of the second-order polynomial are the instantaneous slant distance of the first segment of the trajectory; The coefficients of the third-order polynomial are the instantaneous slant distance of the first segment of the trajectory; This is a constant term representing the instantaneous slant distance of the second segment of the trajectory; These are the first-order polynomial coefficients of the instantaneous slant distance of the second segment of the trajectory; For the second-order polynomial coefficients of the instantaneous slant distance of the second segment of the trajectory; The coefficients of the third-order polynomial for the instantaneous slant distance of the second segment of the trajectory;

[0069] The ~ Express it using the following formula:

[0070]

[0071]

[0072] Since the observation station moves at a constant linear velocity, the position of the observation station at the azimuth center between the two composite aperture segments is... and It has the following relationship: ;in, The time interval is the time interval between the centers of two adjacent synthetic aperture segments.

[0073] S4. Based on the acquired data, estimate the PRI and Doppler parameters of the two segments of synthetic aperture data in the non-cooperative motion radiation source localization model obtained in step S3;

[0074] Step S4 includes the following steps:

[0075] The two one-dimensional radiation source signals received by the observation station are rearranged in two dimensions to obtain two sets of two-dimensional synthetic aperture data matrices, and the accurate PRI is estimated during the two-dimensional rearrangement process.

[0076] Estimate the Doppler parameters of the two radiation source signals.

[0077] Suppose that the radiation source signal is represented by the following formula: ;in, For time; For signal amplitude, For signal carrier frequency, For phase modulation; the two-dimensional rearrangement specifically involves: demodulating the radiation source signal to baseband, and then rearranging it in two dimensions according to the principle of synthetic aperture, expressed by the following formula: ;in, For distance and time, For location and time, This refers to the distance envelope information of the radiation source; The center frequency of the Doppler wave. To tune the frequency for Doppler, It is a third-order frequency modulation;

[0078] Accurate estimation of PRI based on optimal focusing quality of the radiation source signal includes the following steps:

[0079] For radiation source signals Imaging focusing mainly includes Linear Range Walk Correction (LRWC) and azimuth-matched filtering, expressed by the following formula: ; ;in, This represents a distance-to-Fourier transform. This represents the inverse Fourier transform of distance. This indicates a Fourier transform of the orientation. Two-dimensional rearrangement signal The focused signal after imaging;

[0080] LRWC factor And azimuth matched filter function The following formulas can be used to express this: ; Among them, the wavelength of the radiation source signal , For distance frequency;

[0081] Based on the criterion of focusing on optimal quality, the estimation problem of PRI is modeled as the following optimization model: ;in, This indicates the focusing quality of the radiation source signal. The evaluation criteria for focusing quality are the minimum image entropy or the maximum focusing energy.

[0082] The four-dimensional optimization problem in the optimization model is transformed into a two-dimensional optimization problem for estimating PRI and Doppler frequency modulation. A blind search is performed on the number of sampling points for PRI, while the classic line search method is used for Doppler frequency modulation.

[0083] The estimation of the Doppler parameters of the two radiation source signals is specifically as follows:

[0084] After accurately estimating the PRI of the emitted signal from the radiation source, the optimization problem is simplified and expressed by the following formula: ;

[0085] The simplified optimization problem is reduced to several one-dimensional optimization problems, which are then solved one by one.

[0086] For radiation source signals Perform azimuth compression imaging focusing, The estimation model is a Doppler frequency modulation estimation optimization model, which is then solved to obtain the Doppler frequency modulation estimate. The Doppler frequency modulation estimation optimization model is expressed by the following formula: ;

[0087] Based on the obtained Doppler frequency modulation estimate, an optimal model for Doppler center frequency estimation is constructed using LRWC operation and azimuth matched filtering to obtain the initial value of the Doppler center frequency estimate. The optimal model for Doppler center frequency estimation is expressed by the following formula: The obtained Doppler center frequency estimate differs from the true value and needs further correction, expressed by the following formula: ;in, This is the corrected Doppler center frequency. This is the estimated Doppler center frequency. For frequency deviation, its expression is: ;in, This represents the azimuth focusing position of the radiation source signal. Where azimuth is the number of sampling points, and PRF is the pulse repetition frequency;

[0088] A non-parametric method, phase gradient self-focusing, is used to estimate the residual phase error of the position-matched filtered signal. The third frequency modulation is then calculated based on the estimated residual phase. Specifically:

[0089] Assuming the residual phase is estimated from the focusing signal using phase gradient self-focusing, then... This indicates that by considering the remaining phase Polynomial fitting can be used to obtain the coefficients of its cubic term. The third frequency modulation is then calculated using the following formula: .

[0090] S5. Obtain a rough solution for the positioning parameters based on the Doppler parameter estimates obtained in step S4, and substitute the rough solution for the positioning parameters as the initial guess values ​​into the non-cooperative moving radiation source positioning model for iterative optimization. Finally, obtain the positioning parameters of the moving radiation source and complete the single-station passive positioning of the non-cooperative moving radiation source.

[0091] In step S5, the steps for calculating the coarse solution of the non-cooperative motion radiation source location information are as follows:

[0092] Based on the two sets of estimated Doppler parameters, the following calculations are performed: ~ In the arithmetic expression and And substitute it as a known number into the following formula: ; After simplification, the following system of equations is obtained: When the observation station speed does not meet the requirements and The system of equations typically has two intersection points. By combining prior information or introducing boundary conditions, a unique valid solution is determined, yielding a rough estimate of the radiation source's velocity. and ;

[0093] Then, the obtained rough velocity estimate of the radiation source and Substitute into the following formula: ; The rough estimate of the location of the radiation source was obtained through calculation. and ;

[0094] joint ~ Eliminate parameters from the arithmetic expression. and The following system of positioning equations is obtained: ;

[0095] The obtained rough velocity estimate of the radiation source and and a rough estimate of the location of the radiation source and The initial guesses are substituted into the above positioning equations for iterative optimization. Iterative optimization can be achieved using numerical optimization methods such as Newton's iteration method and trust region method to obtain accurate estimates of the positioning parameters, thus achieving accurate estimation of the radiation source positioning parameters.

[0096] The method of the present invention will be further described below with reference to an embodiment:

[0097] like Figure 2 The figure shown is a rough and precise localization estimation result before and after iterative optimization obtained from 100 Monte Carlo experiments in an embodiment of the present invention. Figure 2 (a) is a comparison of the 100 localization attempts and the actual location before iterative optimization, when the signal-to-noise ratio is 15dB. Figure 2(b) is a comparison of the 100 localizations after iterative optimization with the actual location when the signal-to-noise ratio is 15dB.

[0098] like Figure 3 and Figure 4 The figure shows the RMSE results of the position before and after 100 Monte Carlo iterations for optimization in an embodiment of the method of the present invention. Figure 3 (a) The RMSE of the X-axis position before iterative optimization. Figure 3 (b) is the RMSE of the X-axis position after iterative optimization. Figure 4 (a) The RMSE of the Y-axis position before iterative optimization. Figure 4 (b) is the RMSE of the Y-axis position after iterative optimization. For example... Figure 5 and Figure 6 The figure shows the RMSE results of the speed before and after 100 Monte Carlo iterations for optimization in an embodiment of the method of the present invention. Figure 5 (a) The RMSE of the velocity along the X-axis before iterative optimization. Figure 5 (b) is the RMSE of the velocity along the X-axis after iterative optimization. Figure 6 (a) The RMSE of the Y-axis velocity before iterative optimization. Figure 6 (b) is the RMSE of the Y-axis velocity after iterative optimization.

[0099] Simulation results show that using the rough estimation of positioning parameters as the initial guesses for the iterative optimization algorithm can achieve high-precision estimation of the positioning information of moving radiation sources. Compared with the original algorithm, the accuracy of the position and velocity estimation is significantly improved after optimization.

Claims

1. A single-station passive localization method for a non-cooperative moving radiation source based on synthetic aperture, characterized in that, Includes the following steps: S1. Utilize the mobility of the observation station to create two non-uniform velocity observation tracks and acquire the raw data information of the radiation source signals from the two non-cooperative motions. S2. Based on the relative positional relationship between the observation station and the radiation source in step S1, construct a third-order instantaneous slant range model between the observation station and the radiation source; S3. Based on the third-order instantaneous slant range model obtained in step S2 and the maneuvering trajectory of the observation station, construct a non-cooperative motion radiation source localization model; S4. Based on the acquired data, estimate the pulse repetition interval and Doppler parameters of the two synthetic aperture data segments in the non-cooperative motion radiation source localization model obtained in step S3; S5. Obtain a rough solution for the positioning parameters based on the Doppler parameter estimates obtained in step S4, and substitute the rough solution for the positioning parameters as the initial guess values ​​into the non-cooperative moving radiation source positioning model for iterative optimization, and finally obtain the moving radiation source positioning parameters to complete the single-station passive positioning of the non-cooperative moving radiation source.

2. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 1, characterized in that, Step S2 includes the following steps: The observation station observes the radiation source in a three-dimensional oblique-view mode and calculates the instantaneous slant distance between the non-cooperative motion radiation source on the ground and the observation station. The obtained instantaneous slant range is expanded using a third-order Taylor series to obtain the third-order Taylor series expansion of the instantaneous slant range; finally, a third-order instantaneous slant range model between the observation station and the radiation source is obtained by combining the results.

3. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 2, characterized in that, In step S2, both the ground-based non-cooperative motion radiation source and the observation station are in uniform motion, and the instantaneous slant distance between them is expressed as: ;in, For location, slow time; The instantaneous coordinates of the radiation source; These are the instantaneous coordinates of the observation station; The third-order Taylor series expansion of the instantaneous slant range is: ; For the constant term, its calculation formula is: ; The coefficients of a first-order polynomial are calculated as follows: ; The coefficients of the second-order polynomial are calculated as follows: ; The coefficients of the third-order polynomial are calculated as follows: ; The coordinates of the center of the radiation source at that moment; The coordinates of the observation station's center time; The velocity of the radiation source; The speed of the observation station.

4. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 1, characterized in that, Step S3 includes the following steps: Based on the third-order instantaneous slant range model obtained in step S2, it is assumed that the radiation source target is in The plane moves at a constant velocity The observation station is at an altitude of [missing information]. In the air, first at a constant speed Moving, continuously receiving signals from the radiation source during this period, the synthetic aperture time is Then at another constant speed Moving and continuously receiving signals from the radiation source, the synthetic aperture time is ; The azimuth time of the two synthetic aperture segments are respectively set as and In the first synthetic aperture segment, the instantaneous coordinates of the observation station and the radiation source are respectively... and At its central position The coordinates of the time observation station and the radiation source are respectively and In the second synthetic aperture section, the instantaneous coordinates of the observation station and the radiation source are respectively... and At its central position The coordinates of the time observation station and the radiation source are respectively and ; The instantaneous slant distance between the radiation source and the observation station in the two segments of the synthetic aperture was constructed. and ; Instantaneous slant distance between the radiation source and the observatory in the two synthetic aperture sections and The polynomial coefficient expressions of the third-order polynomial slant range model together constitute the non-cooperative motion radiation source localization model.

5. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 4, characterized in that, In step S3, the instantaneous slant distance between the radiation source and the observation station in the two synthetic aperture segments is... and The expression for the third-order polynomial slant distance model is: ; ;in, This is a constant term representing the instantaneous slant distance of the first segment of the trajectory; The coefficients of the first-order polynomial for the instantaneous slant distance of the first segment of the trajectory; The coefficients of the second-order polynomial are the instantaneous slant distance of the first segment of the trajectory; The coefficients of the third-order polynomial are the instantaneous slant distance of the first segment of the trajectory; This is a constant term representing the instantaneous slant distance of the second trajectory segment; These are the first-order polynomial coefficients of the instantaneous slant distance of the second segment of the trajectory; For the second-order polynomial coefficients of the instantaneous slant distance of the second segment of the trajectory; The coefficients of the third-order polynomial for the instantaneous slant distance of the second segment of the trajectory; The ~ Express it using the following formula: Since the observation station moves at a constant linear velocity, the position of the observation station at the azimuth center between the two composite aperture segments is... and It has the following relationship: ;in, The time interval is the time between the centers of two adjacent synthetic aperture segments.

6. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 1, characterized in that, Step S4 includes the following steps: The two one-dimensional radiation source signals received by the observation station are rearranged in two dimensions to obtain two sets of two-dimensional synthetic aperture data matrices, and the accurate pulse repetition interval is estimated during the two-dimensional rearrangement process. Estimate the Doppler parameters of the two radiation source signals.

7. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 6, characterized in that, The radiation source signal is represented by the following formula: ;in, For time; For signal amplitude, For signal carrier frequency, For phase modulation; the two-dimensional rearrangement specifically involves: demodulating the radiation source signal to baseband, and then rearranging it in two dimensions according to the principle of synthetic aperture, expressed by the following formula: ;in, For distance and time, For location and time, This refers to the distance envelope information of the radiation source; The center frequency of the Doppler wave. To tune the frequency for Doppler, It is a third-order frequency modulation; Accurate estimation of the pulse repetition interval based on the criterion of optimal focusing quality of the radiation source signal includes the following steps: For radiation source signals Imaging focusing mainly includes linear distance travel correction and azimuth-matched filtering, expressed by the following formula: ; ;in, This represents a distance-to-Fourier transform. This represents the inverse Fourier transform of distance. This indicates a Fourier transform of the orientation. Two-dimensional rearrangement signal The focused signal after imaging; LRWC factor And azimuth matched filter function The following formulas can be used to express this: ; Among them, the wavelength of the radiation source signal , For distance frequency; The problem of estimating the pulse repetition interval is modeled as an optimization model based on the criterion of optimal focusing quality: ;in, This indicates the focusing quality of the radiation source signal. The evaluation criteria for focusing quality are the minimum image entropy or the maximum focusing energy. The four-dimensional optimization problem in the optimization model is transformed into a two-dimensional optimization problem for estimating the pulse repetition interval and the Doppler modulation frequency. A blind search is performed on the number of sampling points for the pulse repetition interval, while the classic line search method is used for the Doppler modulation frequency.

8. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 6, characterized in that, The estimation of the Doppler parameters of the two radiation source signals is specifically as follows: After accurately estimating the pulse repetition interval of the radiation source's emitted signal, the optimization problem is simplified and expressed by the following formula: ; The simplified optimization problem is reduced to several one-dimensional optimization problems, which are then solved one by one. For radiation source signals Perform azimuth compression imaging focusing, The estimation model is a Doppler frequency modulation estimation optimization model, which is then solved to obtain the Doppler frequency modulation estimate. The Doppler frequency modulation estimation optimization model is expressed by the following formula: ; Based on the obtained Doppler frequency modulation estimate, an optimal model for Doppler center frequency estimation is constructed using LRWC operation and azimuth matched filtering to obtain the initial value of the Doppler center frequency estimate. The optimal model for Doppler center frequency estimation is expressed by the following formula: The obtained Doppler center frequency estimate differs from the true value. The obtained Doppler center frequency estimate is corrected using the following formula: ;in, The corrected Doppler center frequency, This is the estimated Doppler center frequency. For frequency deviation, its expression is: ;in, This represents the azimuth focusing position of the radiation source signal. Where azimuth is the number of sampling points, and PRF is the pulse repetition frequency; A non-parametric method, phase gradient self-focusing, is used to estimate the residual phase error of the position-matched filtered signal. The third frequency modulation is then calculated based on the estimated residual phase. Specifically: Assuming the residual phase is estimated from the focusing signal using phase gradient self-focusing, then... This indicates that by considering the remaining phase The coefficients of the cubic term are obtained by performing polynomial fitting. The third frequency modulation is then calculated using the following formula: .

9. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 1, characterized in that, In step S5, the steps for calculating the coarse solution of the non-cooperative motion radiation source location information are as follows: Based on the two sets of estimated Doppler parameters, the following calculations are performed: ~ In the arithmetic expression and And substitute it as a known number into the following formula: ; ; After rearranging, the following system of equations is obtained: When the observation station speed does not meet the requirements and The system of equations has two intersection points. By combining prior information or introducing boundary conditions, a unique valid solution can be determined, yielding a rough estimate of the radiation source's velocity. and ; Then, the obtained coarse velocity estimate of the radiation source and Substitute into the following formula: ; ; The rough estimate of the location of the radiation source was obtained through calculation. and .

10. The single-station passive localization method for non-cooperative moving radiation sources based on synthetic aperture as described in claim 9, characterized in that, In step S5, the coarse solution of the obtained positioning parameters is used as the initial guess value and substituted into the non-cooperative motion radiation source positioning model for iterative optimization. Specifically, this involves: combining... ~ Eliminate parameters from the arithmetic expression. and The following system of positioning equations is obtained: ; The obtained rough velocity estimate of the radiation source and and a rough estimate of the location of the radiation source and The initial guesses are substituted into the above positioning equations for iterative optimization. The iterative optimization is achieved using Newton's iteration method or the trust region method to obtain accurate estimates of the positioning parameters, thus realizing accurate estimation of the radiation source positioning parameters.

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