Resolution representation method for arbitrary trajectory cooperative detection imaging based on fuzzy function

Abstract

This invention discloses a method for characterizing the imaging resolution of arbitrary trajectory cooperative detection synthetic aperture radar (SAR) based on fuzzy functions. The method includes: constructing an arbitrary trajectory cooperative detection SAR synthetic aperture radar imaging geometric model and a target plane geometric model; acquiring the slant range history of the arbitrary trajectory cooperative detection SAR and the echo signal after range-direction matched filtering in the two-dimensional time domain; constructing a SAR generalized fuzzy function based on the slant range history and the echo signal after range-direction matched filtering in the two-dimensional time domain; acquiring a normalized SAR generalized fuzzy function; acquiring the range resolution based on range resolution information; acquiring the azimuth resolution based on azimuth resolution information; and constructing a complete arbitrary trajectory cooperative detection SAR imaging resolution model based on the range resolution and azimuth resolution. This invention can effectively characterize the resolution performance in any direction.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a method for characterizing the imaging resolution of arbitrary trajectories based on fuzzy functions for collaborative detection. Background Technology

[0002] Multi-platform cooperative detection systems refer to multiple homogeneous or heterogeneous platforms that, with the support of a communication network, share information and cooperate with each other, coordinating and merging independent individuals into a functionally complementary and tactically coordinated detection group. Complex trajectory cooperative detection forward-looking synthetic aperture radar (SAR) systems possess both receiving and transmitting antenna platforms. Through the coordinated transmission and reception between these platforms, they obtain the non-backscattering characteristics of the target area, thereby acquiring richer scene information. Simultaneously, they significantly improve the synthetic aperture length and anti-jamming performance, and overcome the inherent limitation of single-base SAR radar, which can only perform side-looking observations. This allows for the acquisition of high-resolution two-dimensional images of the area in front of a platform, expanding the application of SAR systems in reconnaissance and detection. Therefore, complex trajectory dual-base cooperative detection forward-looking synthetic aperture radar has become a research focus in recent years.

[0003] Compared to traditional synthetic aperture radar (SAR) imaging systems, the complex trajectory cooperative detection forward-looking SAR imaging configuration is more complex. On the one hand, the maneuverability of the transceiver platform causes the radar motion to deviate from the ideal straight track, and the inevitable acceleration will be coupled into the two-way slant range history, thus affecting the Doppler modulation frequency and higher-order Doppler parameters of the echo. On the other hand, the complex cooperative configuration makes the traditional single-base SAR imaging model no longer applicable, and the traditional single-base resolution analysis method will produce large errors. In addition, due to the non-orthogonality between range resolution and azimuth resolution caused by the cooperative detection configuration, the theoretical resolution performance is no longer consistent with the measured results, and the traditional theoretical methods lose their practical significance.

[0004] Therefore, it is urgent to improve the aforementioned problems existing in the current technology. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a method for characterizing the resolution of arbitrary trajectory cooperative detection imaging based on fuzzy functions. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a method for characterizing the resolution of arbitrary trajectory cooperative detection imaging based on fuzzy functions, comprising:

[0007] An arbitrary trajectory cooperative detection synthetic aperture radar imaging geometric model is constructed, as well as a target plane geometric model; the cooperative detection synthetic aperture radar imaging geometric model includes the geometric relationship between the transmitting antenna platform, the receiving antenna platform, and the imaging scene region;

[0008] Based on the imaging geometric model and target plane geometric model of the cooperative detection synthetic aperture radar, the slant range history of the cooperative detection synthetic aperture radar for arbitrary trajectories and the echo signal after range-direction matched filtering in the two-dimensional time domain are obtained.

[0009] Based on the slant range history of synthetic aperture radar (SAR) and the echo signal after range-direction matched filtering in the two-dimensional time domain, a generalized fuzzy function for SAR is constructed.

[0010] Obtain the normalized synthetic aperture radar generalized ambiguity function; wherein, the normalized synthetic aperture radar generalized ambiguity function includes range resolution information and azimuth resolution information;

[0011] Obtain the range resolution based on the range resolution information;

[0012] Obtain the azimuth resolution based on the azimuth resolution information;

[0013] Based on the range resolution and azimuth resolution, a complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection is constructed.

[0014] The beneficial effects of this invention are:

[0015] This invention provides a resolution characterization method for collaborative detection imaging based on fuzzy functions. It considers the influence of acceleration parameters during the motion of a mobile platform and analyzes the dynamic dual-base model. The fuzzy function method is used to analyze the resolution performance of the collaborative detection dual-base model, obtaining a two-dimensional resolution based on the fuzzy function method. Simulations verify that the resolution model has low error and high application value. Based on the obtained two-dimensional resolution, a complete SAR imaging resolution model is further solved, which can effectively characterize the resolution performance in any direction.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart of an arbitrary trajectory collaborative detection imaging resolution characterization method based on fuzzy functions provided in an embodiment of the present invention;

[0018] Figure 2 This is a schematic diagram of a geometric model for arbitrary trajectory cooperative detection synthetic aperture radar imaging provided in an embodiment of the present invention;

[0019] Figure 3This is a schematic diagram of a two-dimensional resolution direction provided in an embodiment of the present invention. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0021] In existing technologies, a low-degree-of-freedom linear trajectory synthetic aperture radar (SAR) imaging model is constructed to obtain the slant range history at any point, and the slant range history gradient vector is solved. The range resolution direction is then determined based on the direction of the slant range history gradient vector, and a range resolution vector is constructed. The slant range history gradient vector is multiplied by the range resolution vector to obtain the inverse range resolution model. Alternatively, a low-degree-of-freedom parallel track bi-base SAR phase model is constructed, and the Doppler frequency and Doppler gradient vector are further solved. The azimuth resolution direction is then determined based on the Doppler gradient vector, and an azimuth resolution vector is constructed. The Doppler gradient vector is multiplied by the azimuth resolution vector to obtain the inverse azimuth resolution model.

[0022] Existing resolution performance models based on the vector gradient method for ideal straight-line trajectories are based on assumptions made about traditional ideal straight-line trajectories. These assumptions are difficult to adapt to dual-base resolution geometric configurations. Compared to traditional parallel-line geometry, complex trajectory cooperative detection forward-looking synthetic aperture radar (FRAR) systems possess higher degrees of freedom and more complex motion trajectories, leading to more complex imaging slant-range history and Doppler models, further increasing the complexity of the imaging resolution model. Simultaneously, the complex motion trajectory results in severe coupling between range and azimuth resolution, causing the two-dimensional resolution characteristics to influence each other, leading to inconsistencies between theoretical and measured resolutions. Furthermore, resolution analysis models based on the vector gradient method can only provide the magnitude of range and azimuth resolution, making it difficult to obtain resolution performance in other directions.

[0023] In view of this, the present invention provides a resolution characterization method for arbitrary trajectory cooperative detection imaging based on fuzzy functions. When modeling the system, the maneuverability of the transceiver platform is considered, and a highly maneuverable antenna platform imaging model is constructed. Based on the complexity of the model, a generalized fuzzy function for synthetic aperture radar is constructed, and the response of an isolated scattering point per unit scattering cross-section in the image domain is solved to obtain the resolution performance of the scene center point. Finally, the generalized fuzzy function is approximated to obtain a complete arbitrary trajectory cooperative detection synthetic aperture radar imaging resolution model.

[0024] Please see Figures 1-2 As shown, Figure 1 This is a flowchart of an arbitrary trajectory cooperative detection imaging resolution characterization method based on fuzzy functions provided in an embodiment of the present invention. Figure 2This is a schematic diagram of a geometric model for arbitrary trajectory cooperative detection synthetic aperture radar imaging provided in an embodiment of the present invention. The present invention provides a method for characterizing the resolution of arbitrary trajectory cooperative detection imaging based on fuzzy functions, comprising:

[0025] S101. Construct a geometric model for synthetic aperture radar imaging with arbitrary trajectory cooperative detection, and construct a geometric model of the target plane; wherein, the geometric model for synthetic aperture radar imaging with cooperative detection includes the geometric relationship between the transmitting antenna platform, the receiving antenna platform and the imaging scene area.

[0026] For details, please continue to see Figure 2 As shown, this embodiment constructs an arbitrary trajectory cooperative detection synthetic aperture radar (SAR) imaging geometric model. The model is built in a Cartesian coordinate system, oriented towards a mobile platform. The mobile platform includes a transmitting antenna platform and a receiving antenna platform. The arbitrary trajectory cooperative detection SAR imaging geometric model includes the geometric relationships between the transmitting antenna platform, the receiving antenna platform, and the imaging scene region. Figure 2 As shown, a spatial rectangular coordinate system XOYZ is constructed with the center point of the imaging scene area as the origin O. Here, A is the receiving antenna platform, B is the transmitting antenna platform, the X and Y directions represent two arbitrary vertical directions in the horizontal plane, and the Z direction represents the skyward direction. To facilitate the description of the geometric model of synthetic aperture radar imaging with arbitrary trajectory cooperative detection, the azimuth angle γ of the platform is preset, where γ is the angle between the ground projection component of the slant range vector and the positive direction of the X-axis, and the ground rubbing angle β is preset, where β is the angle between the beam vector and the ground plane. The transmitting antenna platform operates in slant-looking mode, and the receiving antenna platform operates in forward-looking mode. The two platforms move along curved trajectories respectively. The radar signal reaches the imaging scene area through the transmitting antenna and is scattered back to the receiving antenna, forming a transmit-receive closed loop.

[0027] Please continue reading Figure 2 As shown, in this embodiment, a target plane geometric model is constructed. The center point of the imaging scene area is taken as the origin O of the coordinate system, and the target plane geometric model is constructed in the horizontal plane. The x-direction and y-direction represent two arbitrary perpendicular directions in the horizontal plane.

[0028] S102. Based on the imaging geometric model of the cooperative detection synthetic aperture radar and the target plane geometric model, obtain the slant range history of the cooperative detection synthetic aperture radar for arbitrary trajectories and the echo signal after range-direction matched filtering in the two-dimensional time domain.

[0029] For details, please continue to see Figure 2 As shown, in this embodiment, the slant range history of a synthetic aperture radar for arbitrary trajectory cooperative detection is obtained through the following process.

[0030] In the coordinate system of the synthetic aperture radar imaging geometric model for arbitrary trajectory cooperative detection, the motion velocity and acceleration of the transmitting antenna platform, as well as the motion velocity and acceleration of the receiving antenna platform, are obtained.

[0031] At azimuth zero, obtain the velocity v of the transmitting antenna platform. t =(v tx ,v ty ,v tz ) and acceleration a t =(a tx ,a ty ,a tz ), obtain the distance R from the transmitting antenna platform to the center point of the imaging scene area. st , rubbing corner β t The platform azimuth angle is γ t ; Preset t m Let azimuth be a slow-time variable, and let the spatial position of the transmitting antenna platform at any given moment be obtained. Its expression is:

[0032]

[0033] The spatial position of the transmitting antenna platform is obtained based on its velocity and acceleration; the spatial position of the receiving antenna platform is obtained based on its velocity and acceleration.

[0034] At azimuth zero, obtain the velocity v of the receiving antenna platform. r =(v rx ,v ry ,v rz ) and acceleration a r =(a rx ,a ry ,a rz ), obtain the distance R from the receiving antenna platform to the center point of the imaging scene area. sr , rub the corner β r The platform azimuth angle is γ r γ r =0, to obtain the spatial position of the receiving antenna platform at any time, its expression is:

[0035]

[0036] Obtain the angle φ between the coordinate system of the synthetic aperture radar imaging geometric model with arbitrary trajectory cooperative detection and the coordinate system of the target plane geometric model. Δ Its expression is:

[0037]

[0038] In the coordinate system of the target geometric model, obtain the planar coordinates P(x) of the points adjacent to the center point of the imaging scene region. n ,y n ).

[0039] Based on the included angle, the planar coordinates of adjacent points to the center point of the imaging scene area are converted into spatial coordinates to obtain the spatial position of adjacent points to the center point of the imaging scene area. The expression for this is:

[0040]

[0041] Based on the spatial positions of the transmitting antenna platform, the receiving antenna platform, and the spatial positions of adjacent points to the center point of the imaging scene area, the slant range history of the synthetic aperture radar for arbitrary trajectory cooperative detection is obtained, and its expression is:

[0042]

[0043] Please continue reading Figure 2 As shown, in this embodiment, the echo signal after range-direction matched filtering in the two-dimensional time domain is obtained through the following process.

[0044] Baseband echo signals are obtained by collaboratively detecting the slant range history of synthetic aperture radar based on arbitrary trajectories.

[0045] A pre-installed dual-base synthetic aperture radar transmitting antenna in the cooperative detection system transmits a linear frequency modulated (LFM) signal, and a receiving antenna receives the scattered echo from the imaging scene area. After orthogonal demodulation processing, the baseband echo signal ss0(t) is obtained. r ,t m Its expression is:

[0046]

[0047] Among them, t r w represents the distance to the fast time variable. r (t r ) represents the distance-to-time window function, w a (t m ) represents the azimuth time-domain window function, exp{·} represents the complex exponential function used to characterize the phase information of the echo signal, j represents the imaginary unit, and K r Indicates the range-modulated frequency, f c The center frequency of the transmitted signal is represented by , c represents the speed of light, and π is the mathematical constant pi.

[0048] Perform a range-to-Fourier transform on the baseband echo signal to obtain the range-frequency domain echo signal.

[0049] The baseband echo signal is subjected to range-to-Fourier transform (FT) using the stationary phase principle (POSP) to obtain the range-frequency echo signal Ss1(f) r ,t m Its expression is:

[0050]

[0051] Among them, f r W represents the distance-frequency variable. r (f r ) represents the range-direction frequency domain window function, where the first exponential term represents range modulation and the second exponential term represents azimuth modulation and range migration.

[0052] A matched filter reference function is constructed in the range-frequency domain and the azimuth-time domain. The matched filter reference function constructed in the range-frequency domain and the azimuth-time domain are multiplied with the echo signal in the range-frequency domain to obtain the range-guided matched filter echo signal.

[0053] A matched filter reference function is constructed in the range-frequency domain and the azimuth-time domain, and its expression is:

[0054]

[0055] Multiplying the matched filter reference function with the range-frequency domain echo signal yields the range-direction matched-filtered echo signal Ss2(f). r ,t m Its expression is:

[0056]

[0057] The range-directed matched-filtered echo signal is converted to the two-dimensional time domain to obtain the range-directed matched-filtered echo signal in the two-dimensional time domain.

[0058] Using the stationary phase principle, the range-guided matched-filtered echo signal is converted to the two-dimensional time domain, resulting in the range-guided matched-filtered echo signal in the two-dimensional time domain, expressed as follows:

[0059]

[0060] S103. Based on the slant range history of the synthetic aperture radar and the echo signal after range-direction matched filtering in the two-dimensional time domain, construct the generalized fuzzy function of the synthetic aperture radar.

[0061] Specifically, in this embodiment, the imaging resolution performance of synthetic aperture radar is characterized by solving the response of isolated scattering points per unit scattering cross-section in the image domain of the generalized fuzzy function of synthetic aperture radar; first, the generalized fuzzy function of synthetic aperture radar is constructed.

[0062] The resolution performance of any point in the preset imaging scene area is approximately equal to the resolution performance of the center point of the imaging scene area, so the resolution performance of the center point of the imaging scene area can be used as a reference.

[0063] S1031. Based on the slant range history of the synthetic aperture radar (SAR) for arbitrary trajectory collaborative detection, obtain the slant range history of the center point of the imaging scene region. Its expression is:

[0064]

[0065] S1032. Based on the echo signal of the center point of the imaging scene region in the two-dimensional time domain after range matching filter and the echo signal of the adjacent points of the center point of the imaging scene region in the two-dimensional time domain after range matching filter, construct the cross-correlation function of the echo signal of the center point of the imaging scene region and the echo signal of the adjacent points of the center point of the imaging scene region in the two-dimensional time domain after range matching filter.

[0066] The echo signal after range-matched filtering in the two-dimensional time domain at the center point of the preset imaging scene area is ss 3o (t r ,t m ), Preset imaging scene area center point adjacent point P(x) P ,y P ,z P The echo signal Ss after range-direction matched filtering in the two-dimensional time domain 3p (f r ,t m Construct a cross-correlation function, the expression of which is:

[0067]

[0068] S1033. Based on the echo signals after distance-directed matched filtering between the center point of the imaging scene area and the adjacent points of the center point of the imaging scene area, update the cross-correlation function, that is, obtain the generalized ambiguity function of synthetic aperture radar.

[0069] According to Passevar's theorem, and the echo signal Ss after distance-direction matched filtering at the center point of the imaging scene region... 3o (f r ,t m Point P adjacent to the center point of the imaging scene region o (x o ,y o ,z o The distance-direction matched-filtered echo signal Ss 3p (f r ,t m This yields the updated cross-correlation function, whose expression is:

[0070]

[0071] The preset distance bandwidth is B r The time for synthesizing the pore size is T. a The generalized ambiguity function of synthetic aperture radar is obtained, and its expression is:

[0072]

[0073] S104. Obtain the normalized synthetic aperture radar generalized ambiguity function; wherein, the normalized synthetic aperture radar generalized ambiguity function includes range resolution information and azimuth resolution information.

[0074] Specifically, in this embodiment, the normalized synthetic aperture radar generalized ambiguity function is obtained through the following process.

[0075] S1041. Obtain the difference between the slant range history of the center point of the imaging scene area and the slant range history of the synthetic aperture radar for arbitrary trajectory collaborative detection.

[0076] S1042. Process the difference and update the synthetic aperture radar generalized fuzzy function.

[0077] Obtain the difference u(t) in the slant range history m ) = R bio (t m )-R bi (t m ), and put it in t m The Taylor expansion at the point = 0 gives the following expression:

[0078] u(t m )=u(0)+u (1) (0)t m ;

[0079] The coefficients in the difference from the historical record are represented by the following expression;

[0080] u(0)=R to0 -R tp0 +R ro0 -R rp0 ;

[0081]

[0082] in,

[0083]

[0084]

[0085]

[0086] Based on the above representation, the updated synthetic aperture radar generalized ambiguity function is expressed as follows:

[0087]

[0088] S1043. The updated synthetic aperture radar generalized fuzzy function is simplified, and the phase term change and amplitude coefficient in the updated synthetic aperture radar generalized fuzzy function are ignored to obtain the normalized synthetic aperture radar generalized fuzzy function.

[0089] Simplifying the updated synthetic aperture radar generalized ambiguity function, we get:

[0090]

[0091] Considering the impact of the generalized ambiguity function of synthetic aperture radar on resolution performance, the phase term variation and amplitude coefficient can be ignored, resulting in the normalized generalized ambiguity function of synthetic aperture radar, whose expression is:

[0092]

[0093] S105. Obtain the range resolution based on the range resolution information.

[0094] Specifically, in this embodiment, the range resolution is analyzed based on the range resolution information in the normalized synthetic aperture radar generalized fuzzy function.

[0095] The slant range history in P(x P ,y P ,z P ) = P o (x o ,y o Expanding at (,0), we get:

[0096]

[0097] Through the analysis of the above formula, vector

[0098]

[0099] Equivalent to the slope distance of point P along (x) p ,y p ) in (x o ,y o Find the gradient at point ) vector [x p -x o ,y p -y o [ ] is the vector pointing from the center point of the imaging scene region to point P. The above formula can be updated to:

[0100]

[0101] When the center point of the imaging scene region is distinguishable from its adjacent points... When it reaches its minimum, The modulus value is the range resolution; to ensure The vector reaches its minimum at this point. and Same direction;

[0102] Therefore, the inverse solution The distance resolution can be calculated from a 3dB width, and its expression is:

[0103]

[0104] S106. Obtain the azimuth resolution based on the azimuth resolution information.

[0105] Specifically, in this embodiment, the azimuth resolution is analyzed based on the azimuth resolution information in the normalized synthetic aperture radar generalized fuzzy function.

[0106] will u (1) (0) in (x) P ,y P ,z P )=(x o ,y o Performing a Taylor expansion at (,0), we get:

[0107] u (1) (0)≈[g x ,g y ]·[(x p -x0),(y p -y0)];

[0108] In the above formula,

[0109]

[0110]

[0111] Preset The azimuth sinc function can also be expressed as

[0112] When the center point of the imaging scene region is resolvable with the adjacent points of the center point of the imaging scene region. When it reaches its minimum, The modulus is the azimuth resolution; to ensure The vector is at its minimum. and Same direction;

[0113] Therefore, the inverse solution The azimuth resolution can be obtained by calculating the 3dB width, and its expression is:

[0114]

[0115] S107. Based on the range resolution and azimuth resolution, construct a complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection.

[0116] Specifically, in this embodiment, a complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection is constructed through the following process.

[0117] S1071. Update the normalized synthetic aperture radar generalized ambiguity function based on the range resolution and azimuth resolution.

[0118] Preset Let be the vector from the center point of the imaging scene region to any point P in the imaging scene region. The expression for the updated normalized synthetic aperture radar generalized ambiguity function is:

[0119]

[0120] S1072. Perform Taylor expansion processing on the updated normalized synthetic aperture radar generalized fuzzy function. Based on the coupling relationship between its range squared term and azimuth squared term, use the 3dB width of the main lobe in a certain direction of the updated normalized synthetic aperture radar generalized fuzzy function as the standard for measuring resolution performance.

[0121] when and When the directions are not the same, the coupling relationship between the two makes it difficult to solve. The modulus of the fuzzy function is difficult to determine, making it hard to solve for the resolution performance in that direction. Therefore, a Taylor expansion is performed on the updated normalized synthetic aperture radar generalized fuzzy function, and its expression is:

[0122]

[0123] Based on the expanded formula, the normalized synthetic aperture radar (SAR) generalized ambiguity function can be approximated as the coupling relationship between the range squared term and the azimuth squared term. Since the approximation is a sinc function, the 3dB width of the main lobe in a certain direction of the normalized SAR SAR generalized ambiguity function can be taken as the standard for measuring resolution performance, i.e.:

[0124]

[0125] S1073. Based on the relationship that the higher order of the coupled range squared term and azimuth squared term is much less than 1, obtain a complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection.

[0126] If we approximate the higher-order coupling between the squared distance term and the squared azimuth term to be much less than 1, we can ignore the higher-order coupling terms between the two dimensions and rearrange to obtain:

[0127]

[0128] Preset Vector and The included angles are α1 and α2, and the resolution in this direction can be expressed as:

[0129]

[0130]

[0131] This fully characterizes the imaging resolution performance of the synthetic aperture radar system. However, the model information is redundant at this point. α1 and α2 can be further simplified. Assuming the angle between the azimuth resolution and the range resolution is η, its expression is:

[0132]

[0133] The complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection is further simplified. Specifically, if the range resolution direction is presumably the X-direction, then the two-dimensional resolution direction is as follows: Figure 3 As shown, Figure 3 This is a schematic diagram of a two-dimensional resolution direction provided in an embodiment of the present invention, with any preset direction. A complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection can be simplified to:

[0134]

[0135] Further simplification yields:

[0136]

[0137] Using the above method, the imaging resolution of collaborative detection of arbitrary trajectories can be characterized based on fuzzy functions.

[0138] In an optional embodiment of the present invention, the effectiveness of the arbitrary trajectory cooperative detection imaging resolution characterization method based on fuzzy function provided by the present invention is verified by the following simulation experiments. Please refer to the simulation parameters in Table 1.

[0139] Table 1 Simulation Parameters

[0140] parameter radar system parameter launch platform Receiving platform frequency band X-band Platform speed (285, -76, -52) m / s (256, 147, -52) m / s signal bandwidth 150MHz Platform Acceleration (2, -1, 1.5) m / s² (1.8, 1.2, -1) m / s² Sampling rate 180MHz Central slope distance 22km 18km PRF 2kHz Platform azimuth 90° -60° Pulse width 5μs mop corner 15° 18°

[0141] To verify the effectiveness of the imaging spatial resolution model based on the fuzzy function method, this invention uses a set of airborne SAR imaging parameters to simulate and verify oblique plane and ground plane scenes. Some parameters are shown in Table 1. By comparing the errors of the resolution model in oblique plane imaging and ground plane imaging, the reliability and limitations of the fuzzy function SAR resolution theory are verified. To reflect the complexity of the transceiver platform trajectory in the forward-looking SAR imaging system with complex trajectory collaborative detection, three-dimensional motion acceleration is added to the simulation. The scene center point is selected as a reference for imaging resolution performance measurement. To avoid the influence of the imaging algorithm, this invention selects the traditional BP algorithm as the imaging method to ensure the effectiveness of the simulation. Please refer to Table 2 for the statistical results of performance index parameters.

[0142] Table 2 Statistical Results of Performance Index Parameters

[0143]

[0144] According to the statistical results of the performance index parameters in Table 2, as the accumulation time increases from 0.25s to 1s, the measured two-dimensional resolution performance and the theoretically calculated resolution performance are shown in the table above. It can be seen that the relative error is no greater than 1%. Excluding the measurement error, the measured value is basically consistent with the theoretical value, which verifies the effectiveness of the arbitrary trajectory cooperative detection imaging resolution characterization method based on fuzzy function provided in this embodiment of the invention.

[0145] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0146] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0147] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for characterizing the imaging resolution of arbitrary trajectories based on fuzzy functions, characterized in that, include: An arbitrary trajectory cooperative detection synthetic aperture radar imaging geometric model is constructed, as well as a target plane geometric model; wherein, the cooperative detection synthetic aperture radar imaging geometric model includes the geometric relationship between the transmitting antenna platform, the receiving antenna platform, and the imaging scene region; Based on the cooperative detection synthetic aperture radar imaging geometric model and the target plane geometric model, the slant range history of the cooperative detection synthetic aperture radar for arbitrary trajectories and the echo signal after range-direction matched filtering in the two-dimensional time domain are obtained. Based on the arbitrary trajectory collaborative detection synthetic aperture radar slant range history and the echo signal after range-direction matched filtering in the two-dimensional time domain, a generalized fuzzy function for synthetic aperture radar is constructed. Obtain the normalized synthetic aperture radar generalized ambiguity function; wherein, the normalized synthetic aperture radar generalized ambiguity function includes range resolution information and azimuth resolution information; Based on the distance resolution information, obtain the distance resolution; Based on the azimuth resolution information, the azimuth resolution is obtained; Based on the range resolution and the azimuth resolution, a complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection is constructed.

2. The method for characterizing imaging resolution based on fuzzy functions for arbitrary trajectories according to claim 1, characterized in that, The process of obtaining the slant range history of the synthetic aperture radar for arbitrary trajectory cooperative detection includes: In the coordinate system of the arbitrary trajectory cooperative detection synthetic aperture radar imaging geometric model, the motion velocity and acceleration of the transmitting antenna platform and the motion velocity and acceleration of the receiving antenna platform are obtained. The spatial position of the transmitting antenna platform is obtained based on its speed and acceleration; the spatial position of the receiving antenna platform is obtained based on its speed and acceleration. Obtain the angle between the coordinate system of the arbitrary trajectory cooperative detection synthetic aperture radar imaging geometric model and the coordinate system of the target plane geometric model; In the coordinate system of the target planar geometric model, obtain the planar coordinates of the points adjacent to the center point of the imaging scene area; Based on the included angle, the planar coordinates of the points adjacent to the center point of the imaging scene area are converted into spatial coordinates to obtain the spatial position of the points adjacent to the center point of the imaging scene area. Based on the spatial positions of the transmitting antenna platform, the receiving antenna platform, and the adjacent points of the center point of the imaging scene area, the slant range history of the arbitrary trajectory cooperative detection synthetic aperture radar is obtained.

3. The method for characterizing imaging resolution based on fuzzy functions for arbitrary trajectories according to claim 1, characterized in that, The process of obtaining the echo signal after range-direction matched filtering in the two-dimensional time domain includes: Based on the arbitrary trajectory collaborative detection synthetic aperture radar slant range history, the baseband echo signal is obtained; Perform a range-to-Fourier transform on the baseband echo signal to obtain the range-frequency domain echo signal; A matched filter reference function is constructed in the range frequency domain and the azimuth time domain, and the constructed matched filter reference function in the range frequency domain and the echo signal in the range frequency domain are multiplied to obtain the range matched filter echo signal; The range-directed matched-filtered echo signal is converted to the two-dimensional time domain to obtain the range-directed matched-filtered echo signal in the two-dimensional time domain.

4. The method for characterizing imaging resolution based on fuzzy functions for arbitrary trajectories according to claim 1, characterized in that, The process of constructing the generalized fuzzy function for synthetic aperture radar includes: Based on the arbitrary trajectory collaborative detection synthetic aperture radar slant range history, the slant range history of the center point of the imaging scene area is obtained. Based on the echo signal of the center point of the imaging scene region in the two-dimensional time domain after range matching filter and the echo signal of the adjacent points of the center point of the imaging scene region in the two-dimensional time domain after range matching filter, a cross-correlation function of the echo signal of the center point of the imaging scene region and the echo signal of the adjacent points of the center point of the imaging scene region in the two-dimensional time domain is constructed. Based on the echo signals after distance-direction matched filtering between the center point of the imaging scene region and the adjacent points of the center point of the imaging scene region, the cross-correlation function is updated, that is, the synthetic aperture radar generalized ambiguity function is obtained.

5. The method for characterizing imaging resolution based on fuzzy functions for arbitrary trajectories according to claim 1, characterized in that, The process of obtaining the normalized synthetic aperture radar generalized ambiguity function includes: The difference between the slant range history of the center point of the imaging scene area and the slant range history of the synthetic aperture radar for the arbitrary trajectory collaborative detection is obtained. The difference is processed to update the synthetic aperture radar generalized fuzzy function; The updated synthetic aperture radar generalized fuzzy function is simplified, and the phase term change and amplitude coefficient in the updated synthetic aperture radar generalized fuzzy function are ignored to obtain the normalized synthetic aperture radar generalized fuzzy function.

6. The method for characterizing imaging resolution based on fuzzy functions for arbitrary trajectories according to claim 1, characterized in that, The construction process of the complete arbitrary trajectory cooperative detection synthetic aperture radar imaging resolution model includes: The normalized synthetic aperture radar generalized ambiguity function is updated based on the range resolution and the azimuth resolution. Taylor expansion is performed on the updated normalized synthetic aperture radar generalized fuzzy function. Based on the coupling relationship between its range squared term and azimuth squared term, the 3dB width of the main lobe in a certain direction of the updated normalized synthetic aperture radar generalized fuzzy function is used as the standard for measuring resolution performance. Based on the relationship that the higher order of the coupled range squared term and azimuth squared term is much less than 1, a complete synthetic aperture radar imaging resolution model for arbitrary trajectory cooperative detection is obtained.

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