Non-cooperative motion radiation source single-station passive positioning method based on synthetic aperture

Abstract

The invention discloses a non-cooperative motion radiation source single-station passive positioning method based on synthetic aperture, and the method comprises the steps: making two sections of non-constant-speed observation tracks through a moving observation station, and obtaining the original data information of two sections of non-cooperative motion radiation source signals; according to the relative position relationship between the observation station and the radiation source, constructing a three-order instantaneous slope distance model between the observation station and the radiation source; constructing a non-cooperative motion radiation source positioning model based on the three-order instantaneous slope distance model and the maneuvering orbit of the observation station; estimating a pulse repetition interval and a Doppler parameter of two segments of synthetic aperture data in the non-cooperative motion radiation source positioning model; and obtaining a rough solution of the positioning parameter according to the Doppler parameter estimation value, and performing iterative optimization to finally obtain the positioning parameter of the moving radiation source to complete positioning. According to the method, the problem that the inversion result of the positioning parameters has uncertainty due to the fact that the positioning parameters are more than the imaging parameters in the positioning of the non-cooperative motion radiation source is solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of passive location technology, and particularly relates to a non-cooperative moving radiation source single-station passive location method based on synthetic aperture. BACKGROUND

[0002] In the field of modern electronic reconnaissance, passive location technology has become the core technology for target location and tracking in complex electromagnetic environment due to its strong concealment. The traditional passive location method is divided into two-step location method and direct location method. The two-step location method uses a single observation parameter for location, which is simple and easy to implement, but it is easy to lead to non-convergence of the result. Combining multiple observation parameters can solve this problem, but it greatly increases the complexity of the system. The direct location method does not need to estimate the observation parameter, and it directly searches the spatial position of the radiation source through the cost function, which can reduce the information loss caused by measuring the observation parameter, and the location performance under low signal-to-noise ratio conditions is usually better than that of the two-step location method.

[0003] Compared with the traditional passive location method with long observation time, low positioning efficiency, and large error under low signal-to-noise ratio, the passive location method based on synthetic aperture system can achieve higher positioning accuracy. In the current literature on synthetic aperture passive location method, the positioning objects involved mainly focus on ground fixed radiation sources, and the positioning of moving radiation sources still lacks in-depth research. In fact, in the passive location scene of ground / sea surface radiation sources, the radiation source is not always stationary, but often in motion. Through analysis, it is found that the above synthetic aperture location method is difficult to apply to the location of moving radiation sources, and the fundamental reason lies in that the position information and velocity information of the radiation source in the traditional synthetic aperture location model are highly coupled, which leads to the difficulty in accurately estimating the position information and velocity information of the radiation source under the condition of non-cooperative radiation source. SUMMARY

[0004] In view of the deficiencies of the prior art, the purpose of the present application is to provide a non-cooperative moving radiation source single-station passive location method based on synthetic aperture, which solves the problem that the inversion result of the location parameter has uncertainty due to the fact that the number of location parameters is greater than that of imaging parameters in the location of non-cooperative moving radiation sources.

[0005] The present application provides a non-cooperative moving radiation source single-station passive location method based on synthetic aperture, comprising the following steps:

[0006] S1. Two non-uniform velocity observation orbits are made by using the maneuverability of the observation station, and the original data information of the two non-cooperative moving radiation source signals is obtained;

[0007] S2. According to the relative position relationship between the observation station and the radiation source in step S1, a third-order instantaneous slant range model between the observation station and the radiation source is constructed;

[0008] S3. Constructing a non-cooperative moving emitter positioning model based on the third-order instantaneous slant range model obtained in step S2 and the maneuvering orbit of the observation station;

[0009] S4. Estimating the pulse repetition interval (PRI) and Doppler parameter of the two segments of synthetic aperture data in the non-cooperative moving emitter positioning model obtained in step S3 according to the acquired data information;

[0010] S5. Obtaining a coarse solution of the positioning parameter according to the Doppler parameter estimation value obtained in step S4, and substituting the obtained coarse solution of the positioning parameter as an initial guess into the non-cooperative moving emitter positioning model for iterative optimization, finally obtaining the positioning parameter of the moving emitter, and completing the non-cooperative moving emitter single-station passive positioning.

[0011] Step S2 includes the following steps:

[0012] The observation station observes the emitter in a three-dimensional space in a slant mode, and calculates the instantaneous slant range between the ground non-cooperative moving emitter and the observation station;

[0013] The obtained instantaneous slant range is expanded by a third-order Taylor series to obtain an instantaneous slant range third-order Taylor series expansion formula; and finally a third-order instantaneous slant range model between the observation station and the emitter is obtained.

[0014] In step S2, the ground non-cooperative moving emitter and the observation station are both in a uniform motion state, and the instantaneous slant range expression between the two is: ; wherein, is the azimuth slow time; is the instantaneous coordinate of the emitter; is the instantaneous coordinate of the observation station;

[0015] The instantaneous slant range third-order Taylor series expansion formula is: ; is a constant term, and its calculation formula is ; is a first-order polynomial coefficient, and its calculation formula is ; is a second-order polynomial coefficient, and its calculation formula is ; is a third-order polynomial coefficient, and its calculation formula is ; is the coordinate of the center time of the emitter; is the coordinate of the center time of the observation station; is the velocity of the emitter; is the velocity 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 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; is the first order polynomial coefficient of the instantaneous slant range of the second segment trajectory; is the second order polynomial coefficient of the instantaneous slant range of the second segment trajectory; is the third order polynomial coefficient of the instantaneous slant range of the second segment trajectory;

[0022] The is expressed by using the following formula:

[0023] Based on the observation station moving as a uniform straight line motion, therefore the observation station position at the azimuth center time moment in two segments of synthetic aperture and have the following relationship: ; wherein, is the time interval of the adjacent two segments of synthetic aperture center.

[0024] The step S4 comprises the following steps:

[0025] The two segments of one-dimensional radiation source signals received by the observation station are two-dimensionally rearranged to obtain two groups of two-dimensional synthetic aperture data matrices, and the accurate PRI is estimated in the two-dimensional rearrangement process;

[0026] The Doppler parameters of the two segments of radiation source signals are estimated.

[0027] Supposing that the radiation source signal is expressed by using the following formula: ; wherein, is the time; is the signal amplitude, is the signal carrier frequency, is the modulation phase; the two-dimensional rearrangement is specifically as follows: after the radiation source signal is demodulated to the baseband, it is two-dimensionally rearranged according to the synthetic aperture principle, and is expressed by using the following formula: ; wherein, is the range time, is the azimuth time, is the radiation source range envelope information; is the Doppler center frequency, is the Doppler frequency modulation, is the third frequency modulation;

[0028] The accurate estimation of the PRI is performed according to the criterion of the optimal radiation source signal focusing quality, comprising the following steps:

[0029] The radiation source signal ​The imaging focusing mainly includes linear range walk correction (LRWC) and azimuth matched filtering, which are expressed by the following formulas: ; ; wherein, represents a distance direction Fourier transform, represents a distance direction inverse Fourier transform, represents an azimuth direction Fourier transform; is a two-dimensional rearranged signal after imaging;

[0030] LRWC factor and azimuth matched filtering function are respectively expressed by the following formulas: ; ; wherein, the wavelength of the radiation source signal , is a distance frequency;

[0031] The estimation of the PRI is modeled as an optimization model with the optimal focusing quality as a criterion, as follows: ; wherein, represents the focusing quality of the radiation source signal, and the evaluation criterion of the focusing quality adopts image minimum entropy or maximum focusing energy;

[0032] The four-dimensional optimization problem in the optimization model is converted into a two-dimensional optimization problem for PRI and Doppler frequency estimation, and the blind search of the sampling points of the PRI is performed, and the classic line search method is used for the Doppler frequency estimation.

[0033] The Doppler parameters of the two radiation source signals are estimated, and specifically,

[0034] After the PRI of the radiation source transmitted signal is accurately estimated, the optimization problem is simplified, and is expressed by the following formula: ;

[0035] The simplified optimization problem is reduced to a plurality of one-dimensional optimization problems, which are solved one by one;

[0036] The azimuth direction compressed imaging focusing is performed on the radiation source signal , and the estimation of is modeled as a Doppler frequency estimation optimization model, and the Doppler frequency estimation value is obtained by solving, and the Doppler frequency estimation optimization model is expressed by the following formula: ;

[0037] Combining the obtained Doppler frequency estimation value, the Doppler center frequency estimation optimization model is constructed by means of the LRWC operation and the azimuth matched filtering, and the initial value of the Doppler center frequency estimation is obtained, and the Doppler center frequency estimation optimization model is expressed by the following formula: The obtained Doppler center frequency estimation value has a gap with the true value, and needs to be further corrected, and the following formula is used: ; wherein, is the corrected Doppler center frequency, is the Doppler center frequency estimation value, is the frequency deviation, and the expression is: ; wherein, is the azimuth focusing position of the radiation source signal, is the number of azimuth sampling points, and PRF is the pulse repetition frequency;

[0038] The non-parametric method phase gradient autofocus is used to estimate the residual phase error of the azimuth matched filtered signal, and the third order frequency is calculated according to the estimated residual phase inversion, and the specific method is as follows:

[0039] Suppose that the residual phase estimated from the focused signal by the phase gradient autofocus is represented by , and the third order coefficient of the residual phase is obtained by polynomial fitting, then the third order frequency is calculated by the following formula: .

[0040] In step S5, the steps of calculating the rough solution of the non-cooperative moving radiation source positioning information are as follows:

[0041] According to the estimated two groups of Doppler parameters, the ~ in the algorithm expression of the formula is calculated, and , and is substituted into the following formula as a known number: ; ; After arrangement, the following equation group is obtained: ; When the observation station speed does not satisfy and , the equation group usually has two intersection points, and the unique effective solution is determined by combining the prior information or introducing the boundary condition, and the rough speed estimation value of the radiation source and is obtained;

[0042] The obtained rough speed estimation value of the radiation source and is substituted into the following formula: ; ​; the coarse position estimate of the radiation source is calculated and ;

[0043] the joint ~ expression of the formula is eliminated from the parameters and , the following positioning equation group is obtained: ;

[0044] the coarse velocity estimate of the radiation source obtained and and the coarse position estimate of the radiation source and are substituted into the above positioning equation group as initial guess values for iterative optimization, the iterative optimization can be realized by using numerical optimization methods such as Newton iteration method, trust region method, etc., to obtain accurate estimation values of the positioning parameters, and realize accurate estimation of the positioning parameters of the radiation source.

[0045] The application discloses a non-cooperative moving radiation source single-station passive positioning method based on synthetic aperture, and solves the problem that the inversion result of the positioning parameters has uncertainty due to more positioning parameters than imaging parameters in the positioning of the non-cooperative moving radiation source. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 It is a method flowchart of the method of the application.

[0047] Figure 2 It is a positioning result graph of 100 times of Monte Carlo experiments before and after iterative optimization of the method embodiment of the application; wherein, Figure 2 (a) is a comparison graph of 100 times of positioning and the real position before iterative optimization when the signal-to-noise ratio is 15dB, Figure 2 (b) is a comparison graph of 100 times of positioning and the real position after iterative optimization when the signal-to-noise ratio is 15dB.

[0048] Figure 3 It is an X-axis direction position RMSE result graph before and after iterative optimization of the method embodiment of the application; wherein, Figure 3 (a) is the X-axis direction position RMSE before iterative optimization, Figure 3 (b) is the X-axis direction position RMSE after iterative optimization.

[0049] Figure 4 It is a Y-axis direction position RMSE result graph before and after iterative optimization of the method embodiment of the application; wherein, Figure 4 (a) is the Y-axis direction position RMSE before iterative optimization, Figure 4 (b) is the Y-axis direction position RMSE after iterative optimization.

[0050] Figure 5 Figure 1 is a diagram of X-axis direction velocity RMSE results before and after iterative optimization of an embodiment of the method of the present application; wherein, Figure 5 (a) is X-axis direction velocity RMSE before iterative optimization, Figure 5 (b) is X-axis direction velocity RMSE after iterative optimization.

[0051] Figure 6 Figure 2 is a diagram of Y-axis direction velocity RMSE results before and after iterative optimization of an embodiment of the method of the present application; wherein, Figure 6 (a) is Y-axis direction velocity RMSE before iterative optimization, Figure 6 (b) is Y-axis direction velocity RMSE after iterative optimization. DETAILED DESCRIPTION

[0052] The present application provides a non-cooperative moving radiation source single station passive positioning method based on synthetic aperture, comprising the following steps:

[0053] S1. Two non-constant speed observation orbits are made by using the maneuverability of the observation station, and original data information of the two non-cooperative moving radiation sources is obtained;

[0054] S2. According to the relative position relationship between the observation station and the radiation source in step S1, a third-order instantaneous slant range model between the observation station and the radiation source is constructed;

[0055] Step S2 comprises the following steps:

[0056] The observation station observes the radiation source in a three-dimensional space oblique mode, and calculates the instantaneous slant range between the ground non-cooperative moving radiation source and the observation station;

[0057] The obtained instantaneous slant range is expanded by a third-order Taylor series to obtain a third-order Taylor series expansion of the instantaneous slant range; and finally a third-order instantaneous slant range model between the observation station and the radiation source is obtained.

[0058] In step S2, the ground non-cooperative moving radiation source and the observation station are both in a uniform motion state, and the instantaneous slant range expression between the two is: ; wherein, is the azimuth slow time; is the instantaneous coordinate of the radiation source; is the instantaneous coordinate of the observation station;

[0059] The third-order Taylor series expansion of the instantaneous slant range is: ; is a constant term, and its calculation formula is ; is a first-order polynomial coefficient, and its calculation formula is ; is a second-order polynomial coefficient, and its calculation formula is ; is the third-order polynomial coefficient, and its calculation formula is is the coordinate of the radiation source at the center time; is the coordinate of the observation station at the center time; is the velocity of the radiation source; is the velocity of the observation station.

[0060] S3. Constructing a non-cooperative moving radiation source positioning model based on the third-order instantaneous slant range model obtained in step S2 and the maneuvering orbit of the observation station;

[0061] Step S3 includes the following steps:

[0062] Based on the third-order instantaneous slant range model obtained in step S2, it is assumed that the radiation source target moves at a constant velocity in the plane, and the observation station moves at a constant velocity in the air at an altitude of , during which the signal of the radiation source is continuously received, and the synthetic aperture time is , and then moves at another constant velocity and continuously receives the signal of the radiation source, and the synthetic aperture time is .

[0063] The azimuth time of the two synthetic apertures is respectively set as and . In the first synthetic aperture, the instantaneous coordinates of the observation station and the radiation source are respectively and , and at the azimuth center time , the coordinates of the observation station and the radiation source are respectively and ; in the second synthetic aperture, the instantaneous coordinates of the observation station and the radiation source are respectively and , and at the azimuth center time , the coordinates of the observation station and the radiation source are respectively and .

[0064] The instantaneous slant ranges between the radiation source and the observation station in the two synthetic apertures are respectively and .

[0065] The instantaneous slant ranges between the radiation source and the observation station in the two synthetic apertures are respectively and .

[0066] ​​The instantaneous slant range between the radiation source and the observation station in the two segments of synthetic aperture in step S3 and The third-order polynomial slant range model expression is: ; ; wherein, is a constant term of the instantaneous slant range of the first segment of trajectory; is a first-order polynomial coefficient of the instantaneous slant range of the first segment of trajectory; is a second-order polynomial coefficient of the instantaneous slant range of the first segment of trajectory; is a third-order polynomial coefficient of the instantaneous slant range of the first segment of trajectory; is a constant term of the instantaneous slant range of the second segment of trajectory; is a first-order polynomial coefficient of the instantaneous slant range of the second segment of trajectory; is a second-order polynomial coefficient of the instantaneous slant range of the second segment of trajectory; is a third-order polynomial coefficient of the instantaneous slant range of the second segment of trajectory;

[0067] The ~ is expressed using the following formula:

[0068] Based on the uniform linear motion of the observation station, the position of the observation station at the center time of the azimuth in the two segments of synthetic aperture and have the following relationship: ; wherein, is the time interval of the center of the adjacent two segments of synthetic aperture.

[0069] S4. According to the obtained data information, estimate the PRI and Doppler parameters of the two segments of synthetic aperture data in the non-cooperative motion radiation source positioning model obtained in step S3;

[0070] Step S4 includes the following steps:

[0071] The two-dimensional rearrangement of the two segments of one-dimensional radiation source signals received by the observation station is performed to obtain two groups of two-dimensional synthetic aperture data matrices, and the accurate PRI is estimated in the two-dimensional rearrangement process;

[0072] The Doppler parameters of the two segments of radiation source signals are estimated.

[0073] Suppose that the radiation source signal is expressed using the following formula: ; wherein, is time; is the signal amplitude, is the signal carrier frequency, for modulating the phase; the two-dimensional rearrangement is specifically: after demodulating the radiation source signal to the baseband, and according to the synthetic aperture principle, the two-dimensional rearrangement is performed, and the following formula is used to represent: ; wherein, is the distance time, is the azimuth time, is the radiation source distance envelope information; is the Doppler center frequency, is the Doppler frequency modulation, is the third frequency modulation;

[0074] The PRI is accurately estimated according to the criterion of optimal radiation source signal focusing quality, including the following steps:

[0075] The radiation source signal is imaged and focused, mainly including linear range walk correction (LRWC) and azimuth matched filtering, and the following formula is used to represent: ; ; wherein, represents a distance Fourier transform, represents a distance inverse Fourier transform, represents an azimuth Fourier transform; is a two-dimensional rearranged signal after imaging;

[0076] The LRWC factor and the azimuth matched filtering function are respectively represented by the following formula: ; ; wherein, the wavelength of the radiation source signal , is a distance frequency;

[0077] The estimation problem of the PRI is modeled as an optimization model as follows according to the criterion of optimal focusing quality: ; wherein, represents the focusing quality of the radiation source signal, and the evaluation criterion of the focusing quality adopts image minimum entropy or maximum focusing energy;

[0078] The four-dimensional optimization problem in the optimization model is converted into a two-dimensional optimization problem for estimating the PRI and the Doppler frequency modulation, the blind search of the sampling point number of the PRI is performed, and the classical line search method is used for the Doppler frequency modulation.

[0079] The Doppler parameters of the two radiation source signals are estimated, specifically:

[0080] After the PRI of the radiation source emission signal is accurately estimated, the optimization problem is simplified, and the following formula is used to represent the optimization problem: ;

[0081] The simplified optimization problem is reduced to several one-dimensional optimization problems, which are then solved one by one;

[0082] The radiation source signal is compressed and imaged in the azimuth direction, and the estimation of is modeled as a Doppler frequency estimation optimization model, which is solved to obtain the Doppler frequency estimation value, and the Doppler frequency estimation optimization model is represented by the following formula: ;

[0083] Combined with the obtained Doppler frequency estimation value, the LRWC operation and the azimuth matched filter are used to construct a Doppler center frequency estimation optimization model to obtain the initial value of the Doppler center frequency estimation, and the Doppler center frequency estimation optimization model is represented by the following formula: The obtained Doppler center frequency estimation value has a gap from the true value, which needs to be further corrected, and the following formula is used to represent the correction: ; wherein is the corrected Doppler center frequency, is the Doppler center frequency estimation value, is the frequency deviation, and its expression is: ; wherein is the azimuth focusing position of the radiation source signal, is the number of azimuth sampling points, and PRF is the pulse repetition frequency;

[0084] The non-parametric method phase gradient autofocus is used to estimate the residual phase error of the azimuth matched filter signal, and the cubic frequency is calculated according to the estimated residual phase, specifically:

[0085] Assuming that the residual phase estimated from the focused signal by the phase gradient autofocus is represented by , the cubic term coefficient of the residual phase can be obtained by polynomial fitting, and the cubic frequency is calculated by the following formula: .

[0086] S5. Obtain a rough solution of the positioning parameter according to the Doppler parameter estimation value obtained in step S4, and substitute the obtained rough solution of the positioning parameter as an initial guess value into the non-cooperative moving radiation source positioning model for iterative optimization, and finally obtain the positioning parameter of the moving radiation source, completing the single-station passive positioning of the non-cooperative moving radiation source.

[0087] In step S5, the calculation of the non-cooperative moving radiation source positioning information rough solution is as follows:

[0088] According to the estimated two groups of Doppler parameters, the ~ in the formula expression of the formula and are calculated and taken as known numbers in the following formula: ; ; After arrangement, the following equation group is obtained: ; When the observation station velocity does not satisfy and , the equation group usually has two intersection points, and in combination with prior information or introduction of boundary conditions, a unique effective solution is determined to obtain the rough velocity estimation value of the radiation source and ;

[0089] The rough velocity estimation value of the radiation source and obtained is taken in the following formula: ; ; The rough position estimation value of the radiation source and is calculated;

[0090] The formula expressions of ~ are combined to eliminate the parameters and in them, and the following positioning equation group is obtained: ;

[0091] The rough velocity estimation value of the radiation source and and the rough position estimation value of the radiation source and are taken as initial guess values and are substituted into the above positioning equation group for iterative optimization, and the iterative optimization can be realized by using numerical optimization methods such as Newton iteration method, trust region method, etc. to obtain accurate estimation values of the positioning parameters, and accurate estimation of the radiation source positioning parameters is realized.

[0092] The method of the application is further described below in combination with an embodiment:

[0093] As shown in Figure 2 , the rough and accurate positioning estimation results before and after iterative optimization obtained by 100 times of Monte Carlo experiments of the embodiment of the method of the application are shown in the figure, wherein Figure 2 (a) is a comparison diagram of 100 times of positioning before iterative optimization and the true position when the signal-to-noise ratio is 15 dB, Figure 2(b) is the position RMSE of the 100th positioning after the iterative optimization when the signal-to-noise ratio is 15 dB.

[0094] As shown in Figure 3 and Figure 4 RMSE results of the position before and after the iterative optimization in the 100 Monte Carlo experiments of the embodiment of the method of the application, wherein Figure 3 (a) is the X-axis direction position RMSE before the iterative optimization, Figure 3 (b) is the X-axis direction position RMSE after the iterative optimization, Figure 4 (a) is the Y-axis direction position RMSE before the iterative optimization, Figure 4 (b) is the Y-axis direction position RMSE after the iterative optimization. As shown in Figure 5 and Figure 6 RMSE results of the velocity before and after the iterative optimization in the 100 Monte Carlo experiments of the embodiment of the method of the application, wherein Figure 5 (a) is the X-axis direction velocity RMSE before the iterative optimization, Figure 5 (b) is the X-axis direction velocity RMSE after the iterative optimization, Figure 6 (a) is the Y-axis direction velocity RMSE before the iterative optimization, Figure 6 (b) is the Y-axis direction velocity RMSE after the iterative optimization.

[0095] According to the simulation results, it can be obtained that the high-precision estimation of the positioning information of the moving radiation source can be realized by taking the rough positioning parameter estimation result as the initial guess value of the iterative optimization algorithm. Compared with before the iterative optimization, the estimation precision of the position and the velocity after the optimization is greatly improved.

Claims

1. A method for non-cooperative moving emitter mono-static passive location based on synthetic aperture, characterized in that, The method comprises the following steps: S1. Two non-constant speed observation orbits are made by using the maneuverability of the observation station, and original data information of two non-cooperative moving radiation source signals is obtained; S2. A third-order instantaneous slant range model between the observation station and the radiation source is constructed according to the relative position relationship between the observation station and the radiation source in step S1; S3. A non-cooperative moving radiation source positioning model is constructed based on the third-order instantaneous slant range model obtained in step S2 and the maneuvering orbit of the observation station; S4. The pulse repetition interval and the Doppler parameter of the two synthesized aperture data in the non-cooperative moving radiation source positioning model obtained in step S3 are estimated according to the obtained data information; S5. A rough solution of the positioning parameter is obtained according to the estimated value of the Doppler parameter in step S4, and the rough solution of the positioning parameter is taken as an initial guess value and substituted into the non-cooperative moving radiation source positioning model for iterative optimization, so that the positioning parameter of the moving radiation source is finally obtained, and the single-station passive positioning of the non-cooperative moving radiation source is completed.

2. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 1, characterized in that, Step S2 comprises the following steps: The observation station observes the radiation source in a three-dimensional space in a squint mode, and calculates the instantaneous slant range between the ground non-cooperative moving radiation source and the observation station; The obtained instantaneous slant range is expanded by a third-order Taylor series to obtain a third-order Taylor series expansion of the instantaneous slant range; and finally, a third-order instantaneous slant range model between the observation station and the radiation source is obtained.

3. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 2, characterized in that, In step S2, the ground non-cooperative radiation source and the observation station are both in uniform motion state, and the expression of the instantaneous slant range between the two is: ; wherein, is the azimuthal slow time; is the instantaneous coordinate of the radiation source; is the instantaneous coordinate of the observation station; The instantaneous slant range third-order Taylor series expansion is: ; is a constant term, and the calculation formula is ; is a first-order polynomial coefficient, and the calculation formula is ; is a second-order polynomial coefficient, and the calculation formula is ; is a third-order polynomial coefficient, and the calculation formula is ; is the coordinate of the radiation source center moment; is the coordinate of the observation station center moment; is the velocity of the radiation source; is the velocity of the observation station.

4. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 1, characterized in that, Step S3 comprises 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 segments of synthetic aperture is respectively set as and ; in the first segment of synthetic aperture, the instantaneous coordinates of the observation station and the radiation source are respectively and , and the coordinates of the observation station and the radiation source at the azimuth center moment are respectively and ; in the second segment of synthetic aperture, the instantaneous coordinates of the observation station and the radiation source are respectively and , and the coordinates of the observation station and the radiation source at the azimuth center moment are respectively and ; Constructing the instantaneous slant range between a radiating source and an observation station in a two-pass synthetic aperture and ; Instantaneous slant range between a radiating source and an observation station in two-pass synthetic aperture and The polynomial coefficient expressions of the third order polynomial slant range model together constitute the non-cooperative moving emitter location model.

5. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 4, characterized in that, In step S3, the instantaneous slant range between the radiation source and the observation station in the two segments of synthetic aperture and The third-order polynomial slant range model expression is: ; ; wherein, is a constant term of the instantaneous slant range of the first segment of trajectory; is a first-order polynomial coefficient of the instantaneous slant range of the first segment of trajectory; is a second-order polynomial coefficient of the instantaneous slant range of the first segment of trajectory; is a third-order polynomial coefficient of the instantaneous slant range of the first segment of trajectory; is a constant term of the instantaneous slant range of the second segment of trajectory; is a first-order polynomial coefficient of the instantaneous slant range of the second segment of trajectory; is a second-order polynomial coefficient of the instantaneous slant range of the second segment of trajectory; is a third-order polynomial coefficient of the instantaneous slant range of the second segment of trajectory; The is expressed using the following equation:​ Based on the observation station moving as a uniform linear motion, therefore the observation station position at the azimuth center time moment in two synthetic apertures and has the following relationship: ; wherein, is the time interval of the center of two adjacent synthetic apertures.

6. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 1, wherein, Step S4 comprises the following steps: The two one-dimensional radiation source signals received by the observation station are two-dimensionally rearranged to obtain two groups of two-dimensional synthesized aperture data matrices, and the accurate pulse repetition interval is estimated during the two-dimensional rearrangement; The Doppler parameters of the two radiation source signals are estimated.

7. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 6, characterized in that, The radiation source signal is expressed by the following formula: ; wherein, is time; is signal amplitude, is signal carrier frequency, is modulation phase; the two-dimensional rearrangement is specifically: after the radiation source signal is demodulated to the baseband, it is two-dimensionally rearranged according to the synthetic aperture principle, and is expressed by the following formula: ; wherein, is range time, is azimuth time, is radiation source range envelope information; is Doppler center frequency, is Doppler frequency modulation, is third frequency modulation; The pulse repetition interval is accurately estimated by taking the optimal signal focusing quality of the radiation source as a criterion, comprising the following steps: Radiation source signal Imaging focusing, which mainly includes linear distance walk correction and azimuth matched filtering, is expressed using the following equations: ; ; where, represents a distance Fourier transform, represents a distance inverse Fourier transform, represents an azimuth Fourier transform; is a two-dimensional rearranged signal is an imaged focused signal; LRWC factor and azimuth matched filter function are expressed respectively using the following equations: ; ; where the wavelength of the radiation source signal , is the range frequency; The estimation of the pulse repetition interval is modeled as an optimization model with the criterion of optimal focusing quality as follows: ; wherein, denotes the focusing quality of the radiation source signal, and the evaluation criterion of the focusing quality adopts the minimum entropy or maximum focusing energy of the image. The four-dimensional optimization problem in the optimization model is converted into a two-dimensional optimization problem for estimating the pulse repetition interval and the Doppler frequency modulation, the pulse repetition interval is blindly searched for the number of sampling points, and the classical line search method is used for the Doppler frequency modulation.

8. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 6, characterized in that, The Doppler parameters of the two radiation source signals are estimated, specifically as follows: After accurate estimation of the pulse repetition interval of the emitter signal, the optimization problem is simplified and expressed using the following equation: ; The reduced dimension of the simplified optimization problem is one-dimensional optimization problem, which is solved one by one; Radiation source signal Azimuthal compression imaging focusing is performed The estimation of the Doppler frequency is modeled as an optimization model, which is solved to obtain the Doppler frequency estimate, using the following equation: ; Combining the obtained Doppler frequency estimation value, with the help of LRWC operation and azimuth matched filtering, a Doppler center frequency estimation optimization model is constructed to obtain an initial value of the Doppler center frequency estimation, and the Doppler center frequency estimation optimization model is expressed by using the following formula: The obtained Doppler center frequency estimation value has a gap from the true value, and the obtained Doppler center frequency estimation value is corrected, and the following formula is used: ; wherein, is the corrected Doppler center frequency, is the Doppler center frequency estimation value, is a frequency deviation, and the expression is: ; wherein, is the azimuth focusing position of the radiation source signal, is the number of azimuth sampling points, and PRF is the pulse repetition frequency; The non-parametric method of phase gradient autofocus is used to estimate the residual phase error of the azimuth matched filter signal, and the three frequency modulations are calculated according to the estimated residual phase, specifically as follows: Assume that the residual phase estimated from the focus signal using phase gradient autofocusing is denoted by and the third order coefficient of the polynomial fit of the residual phase is denoted by , then the third order frequency is calculated by the following equation: .

9. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 1, characterized in that, In step S5, the steps of calculating the rough solution of the non-cooperative moving radiation source positioning information are as follows: According to the estimated Doppler parameters of the two groups, the values of in the formulaic expressions of the equations are calculated and substituted as known quantities into the following equations:​​​​ The following equation set is obtained after arrangement: ; when the observation station velocity does not satisfy and , the equation set has two intersection points, and in combination with prior information or introduction of boundary conditions, a unique effective solution is determined to obtain a rough velocity estimation value of the radiation source and ; The rough velocity estimate of the radiation source is then obtained and Substituted into the following equation: ; ; calculating a coarse position estimate of the radiation source and .

10. The synthetic aperture based non-cooperative moving emitter mono-static passive localization method according to claim 9, wherein, In step S5, the obtained rough solution of the positioning parameters is substituted as an initial guess value into the non-cooperative moving radiation source positioning model for iterative optimization, specifically: the formula expression of The parameters and in the formula expression are eliminated to obtain the following positioning equation group: ;​ a coarse velocity estimate of the radiation source and a coarse position estimate of the radiation source and as initial guess values into the positioning equation set, and iteratively optimize the initial guess values to obtain accurate estimates of the positioning parameters, thereby achieving accurate estimation of the positioning parameters of the radiation source.

Images