Space-borne SAR scene matching curve imaging spatio-temporal frequency three-dimensional constraint time-varying heavy frequency design

Abstract

A kind of spaceborne SAR scene matching curve imaging space-time frequency three-dimensional constraint time-varying heavy frequency design method can realize low data loss, high blur performance high-quality data acquisition.This patent first establishes the space-time frequency constraint model of echo time delay in the "azimuth time-central slant range-pulse repetition frequency" three-dimensional space, realizes the constraint representation of echo time delay under the condition of variable space-ground illumination geometry;Then, the fuzzy space-time frequency constraint model is established, and the influence law of space-ground illumination geometry on the ratio of Doppler blur to range and azimuth two-dimensional blur is clarified;Finally, the nonlinear time-varying heavy frequency design method is studied, the three-dimensional constraint of space-time frequency is reduced and projected to the more intuitive "azimuth time-pulse repetition frequency" two-dimensional space, according to the influence law of the constraint model after projection on the heavy frequency, the graphical time-varying heavy frequency design is realized.

Description

Technical Field

[0001] This invention relates to the field of Synthetic Aperture Radar (SAR) technology, specifically to a time-varying repetition frequency design method for spaceborne SAR scene matching curve imaging with three-dimensional constraints. Background Technology

[0002] In conventional spaceborne SAR imaging modes, the imaging band follows the satellite track direction, exhibiting a simple linear distribution. However, many hotspots (such as roads, bridges, rivers, and coastlines) have complex and variable geographical orientations, often displaying complex curved distributions. Using conventional spaceborne SAR imaging modes to observe such areas leads to problems such as resolution degradation, prolonged data acquisition cycles, and increased data redundancy, resulting in limited observation timeliness. To address this, the spaceborne SAR scene-matching curve imaging mode has emerged. Its core lies in adding one degree of freedom to the imaging band, allowing for the flexible generation of imaging bands that highly match the scene's orientation based on prior geographical information, significantly improving observation timeliness.

[0003] On the one hand, the slant range and viewing angle vary greatly in spaceborne SAR scene matching curve imaging, resulting in significant variations in echo delay and blur performance. Using a fixed repetition frequency for data acquisition leads to problems such as high imaging grating lobes and severe blurring, seriously affecting imaging quality. Therefore, it is necessary to adjust the pulse repetition frequency in a time-varying manner to simultaneously meet delay and blur constraints, minimizing echo occlusion loss and blur energy.

[0004] On the other hand, the geometry of satellite-to-ground illumination in spaceborne SAR scene matching curve imaging is complex. Situations may arise where the beam center slant range is the same at different azimuths and times, but the slant angle and downward angle differ significantly, resulting in large differences in Doppler bandwidth and two-dimensional blur ratio. Different satellite-to-ground illumination geometries correspond to the same location in the zebra diagram, leading to design ambiguity. Therefore, the pulse repetition frequency (PRF) design needs to further consider the constraints of the azimuth and time dimensions to achieve a unique correspondence between the PRF and the satellite-to-ground illumination geometry.

[0005] To address the aforementioned issues, this patent first establishes a spatiotemporal frequency constraint model for echo delay in a three-dimensional space of "azimuth-time-center slant distance-pulse repetition frequency" to characterize echo delay constraints under varying satellite-ground illumination geometry. Then, a fuzzy spatiotemporal frequency constraint model is established to clarify the influence of satellite-ground illumination geometry on Doppler ambiguity and the ambiguity ratio in the range and azimuth dimensions. Finally, a nonlinear time-varying repetition frequency design method is studied, projecting the three-dimensional spatiotemporal frequency constraint onto a more intuitive two-dimensional space of "azimuth-time-pulse repetition frequency". Based on the influence of the projected constraint model on the repetition frequency, a graphical time-varying repetition frequency design is achieved. Summary of the Invention

[0006] In view of this, the present invention proposes a time-varying repetition frequency design method with three-dimensional constraints of spacetime and frequency for spaceborne SAR scene matching curve imaging, so as to achieve high-quality data acquisition with low data loss and high ambiguity performance in spaceborne SAR scene matching curve imaging.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] Step 1: In the three-dimensional space of "azimuth-time-spatial distance-pulse repetition rate", for each instantaneous azimuth time t, the maximum slant range R within the beam range can be found. f (t) and minimum slope distance R n (t); The instantaneous repetition frequency selection at this moment is to find a band with a coverage range of [R] within the corresponding two-dimensional space of "spatial distance-pulse repetition frequency" without strip occlusion. n (t), R f The perpendicular segment of [t] is expressed as:

[0009]

[0010] Where PRF(t) is the pulse repetition rate, M and N are the ambiguity numbers of the transmitted pulse and the nadir echo, respectively, and H is the pulse repetition rate. f T represents the maximum slant range of the nadir echo. g and T p The pulse widths are for transmission and protection, respectively. Therefore, time-varying repetition frequency design is to find a similar vertical line segment at each azimuth time, that is, to find a feasible strip-shaped region within the feasible domain represented by the "surface volume" composed of the slant range.

[0011] However, selecting a strip-shaped region within this "curved surface" is not intuitive, primarily because the echo slant range is not unique when the azimuth and time are fixed; considering the scene-matching curve imaging, the center slant range R... c (t) can be uniquely determined by azimuth and time, and the "center slant distance" coordinate axis can be used instead of the "spatial distance" coordinate axis; in this case, the expression can be written as:

[0012]

[0013] Where ΔR n (t) and ΔR f (t) represents the maximum echo slant range R. f (t), minimum slope distance R n (t) and R c The change in (t), i.e., ΔR n (t)=R c (t)-R n (t), ΔR f (t)=R f (t)-Rc (t).

[0014] Step 2: In the three-dimensional space consisting of "azimuth time - center slant distance - pulse repetition frequency", analyze the time-varying law of the Doppler bandwidth within the beam and establish a constrained model of Doppler fuzziness.

[0015] Based on the mapping relationship between azimuth time and center slant distance, a three-dimensional surface can be extracted in three-dimensional space to characterize the changes in the relative position distribution of scene echo, nadir echo, and transmitted pulse with azimuth time throughout the entire data acquisition period; to avoid Doppler blurring caused by the designed pulse repetition frequency sequence, the Doppler bandwidth B is considered. a By analyzing the variation of (t) with azimuth time t, we can obtain the lower limit of the selectable repetition frequency PRF(t) for each azimuth time, which is expressed as:

[0016] PRF(t)≥kB a (t)

[0017] Where k represents the azimuth oversampling coefficient.

[0018] Step 3, let the spaceborne SAR be in azimuth time t a The pulse repetition frequency is PRF a The main and side lobes of the antenna are represented by solid and dashed lines in the elevation direction, respectively; T A (Triangle point) represents the position with the worst distance blur ratio within the beamwidth at time ta, T A1 T A2 (dot) indicates T A The distance blur position of the first sidelobe, which contributes the most to the distance blur ratio, has the following relationship:

[0019]

[0020] Where RASR(t) a PRF a T) represents the position time t a Pulse Repetition Rate (PRF) a At that time, the distance ambiguity ratio at position T, where l represents the set of positions of the antenna main lobe in the illumination area in the elevation direction;

[0021] Due to the center slope distance R c R is a function of azimuth time t c , t a The center slope distance at time can be written as R. c (t a Then the coordinates of data acquisition state A in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition frequency" are A(t); a R c (t a ), PRFa The worst distance blur ratio Ω is ), RASR for:

[0022] Ω RASR (t a R c (t a ), PRF a )=RASR(t a PRF a T A )

[0023] The worst possible distance blur ratio Ω can be found at all times and in all directions. RASR Furthermore, Ω is obtained in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate". RASR The distribution of Ω at this time, where point A corresponds to Ω. RASR The value is -32dB; if we assume that the distance blur ratio threshold that the imaging needs to meet is -26dB, then the infeasible region for time-varying repetition frequency design in the curved surface can be obtained.

[0024] Step four: This patent first found the relationship between the instantaneous azimuth ambiguity ratio and the true azimuth ambiguity ratio, and then found the worst possible value of the instantaneous azimuth ambiguity ratio as a design constraint for the azimuth ambiguity ratio.

[0025] The true azimuth ratio is the ratio of the integrals of the azimuth fuzzy energy to the integrals of the unfuzzy energy; by the sum-partition ratio theorem, there must exist t. * At time T, the true azimuth ambiguity ratio AASR(T) at position T is better than the instantaneous azimuth ambiguity ratio at that time, is:

[0026]

[0027] Where S A S(t) and S0(t) represent the azimuth ambiguity energy and the unambiguity energy at position T at time t, respectively;

[0028] Assume t * At that time, the SAR satellite's data acquisition status was B, and the pulse repetition rate was PRF. b The circled area represents the antenna sidelobe illumination area that causes azimuth ambiguity; T1 and T2 (dots) represent the areas illuminated by the antenna sidelobe at time t. * At time t, the first sidelobe azimuth ambiguity position that contributes the most to the instantaneous azimuth ambiguity ratio at position T; at t * Instantaneous azimuth ambiguity ratio ω AASR The worst possible value of the azimuth ratio at position T is denoted as:

[0029]

[0030] Calculate the instantaneous azimuth ambiguity at all locations within the beam, and the difference will be used as t. * Design constraints on the time-azimuth ambiguity ratio; where the dashed circle represents the beam illumination area, T B (Triangle point) indicates the location with the worst instantaneous azimuth blur ratio within the beam illumination area at that moment, T B1 T B2 (dot) indicates T B The location of the first sidelobe with the largest contribution to the instantaneous azimuth blur ratio at the given location; based on the above description, the following relationship exists:

[0031]

[0032] Where P main This represents the set of locations of the area illuminated by the antenna's main lobe.

[0033] The coordinates of data acquisition state B in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate" are B(t). * R c (t * ), PRF b The worst distance blur ratio Ω is ), AASR for:

[0034] Ω AASR (t * R c (t * ), PRF a )=ω AASR (t * PRF b T B ).

[0035] Step 5: Based on the constraint model of time delay and ambiguity in the two-dimensional space of "azimuth-time-pulse repetition frequency" after projection and superposition, determine the feasible region for time-varying repetition frequency design; the time-varying repetition frequency sequence must be selected from the feasible region, and must correspond to a unique pulse repetition frequency at any azimuth time. Assuming the feasible region set of repetition frequencies is F, the repetition frequency sequence PRF(t) must satisfy the following expression:

[0036]

[0037] Where t s t e These are the start and end times for data acquisition, respectively. In addition, the repetition frequency sequence PRF(t) should ensure that the pulse repetition frequency changes continuously between adjacent time intervals to reduce echo loss caused by changes in the transmit and receive ambiguity.

[0038] Beneficial effects:

[0039] This invention solves the problem of difficult data acquisition in spaceborne SAR scene matching curve imaging, achieving high-quality data acquisition with low data loss and high ambiguity performance. Steps one and two present spatiotemporal frequency constraint models for time delay and Doppler ambiguity in the three-dimensional space of "azimuth-time-center slant range-pulse repetition frequency"; steps three and four present spatiotemporal frequency constraint models for range ambiguity ratio and azimuth ambiguity ratio; based on these, step five projects the three-dimensional spatiotemporal frequency constraints to a more intuitive two-dimensional space of "azimuth-time-pulse repetition frequency," and, according to the influence of the projected constraint models on the repetition frequency, implements time-varying repetition frequency design in a graphical manner. Attached Figure Description

[0040] Figure 1 This is a flowchart of the spaceborne SAR scene matching curve imaging spatiotemporal frequency three-dimensional constraint time-varying repetition frequency design method described in this invention.

[0041] Figure 2 This is a schematic diagram of the time delay constraint modeling of spatiotemporal frequency echo as described in this invention;

[0042] Figure 3 This is a schematic diagram of the spatiotemporal frequency Doppler fuzzy constraint modeling described in this invention;

[0043] Figure 4 This is a schematic diagram of the spatiotemporal-frequency distance ambiguity ratio constraint modeling described in this invention;

[0044] Figure 5 This is a schematic diagram of the spatiotemporal frequency-azimuth ambiguity ratio constraint modeling described in this invention;

[0045] Figure 6 This is a schematic diagram of the dimensionality reduction projection process of the spatiotemporal frequency constraint model described in this invention;

[0046] Figure 7 This is a schematic diagram of the feasible region of repetition frequency in the two-dimensional space of "azimuth time-pulse repetition frequency" as described in this invention;

[0047] Figure 8 These are the wave foot trajectory and satellite attitude history in the embodiment;

[0048] Figure 9 This is the pulse repetition frequency timing design result using the method proposed in this invention in the embodiment;

[0049] Figure 10 These are the distance and orientation ambiguities corresponding to the pulse repetition frequency timing in the embodiment;

[0050] Figure 11 This is the orientation focusing result of the scene center point in the embodiment. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0052] The flowchart of the spaceborne SAR scene matching curve imaging spatiotemporal frequency three-dimensional constrained time-varying repetition frequency design method described in this invention is shown below. Figure 1 The present invention includes the following steps:

[0053] Step 1: Spatiotemporal frequency constraint modeling of time delay;

[0054] Based on the zebra diagram, a "location-time" dimension is added, upgrading the two-dimensional "spatial distance-pulse repetition rate" space to a three-dimensional "location-time-spatial distance-pulse repetition rate" space. (See...) Figure 2 (a).

[0055] In the three-dimensional space of "azimuth-time-spatial distance-pulse repetition rate", for each instantaneous azimuth time t, the maximum slant range R within the beam range can be found. f (t) and minimum slope distance R n (t), see Figure 2 (b) The figure above. The instantaneous repetition frequency selection at this moment is to find a band with a coverage range of [R] within the corresponding two-dimensional space of "spatial distance-pulse repetition frequency" without occlusion of the strip. n (t), R f The perpendicular segment of [(t)] is expressed in equation (1), where PRF(t) is the pulse repetition frequency, M and N are the ambiguity numbers of the transmitted pulse and the nadir echo, respectively, and H is the pulse repetition frequency. f T represents the maximum slant range of the nadir echo. g and T p These are the transmit and protection pulse widths, respectively. Therefore, time-varying repetition rate design involves finding similar vertical segments at each azimuth time, that is, finding a feasible strip-shaped region within the feasible domain represented by the "surface" formed by the slant range. (See...) Figure 2 (b) The following diagram.

[0056]

[0057] However, selecting a strip-shaped region within this "curved surface" is not intuitive, primarily because the echo slant range is not unique when the azimuth and time are fixed. Considering scene-matching curve imaging, the center slant range R... c (t) can be uniquely determined by azimuth and time, and the "center slant distance" coordinate axis is used instead of the "spatial distance" coordinate axis. In this case, equation (1) can be written as:

[0058]

[0059] Where ΔR n (t) and ΔR f (t) represents the maximum echo slant range R. f (t), minimum slope distance R n(t) and R c The change in (t), i.e., ΔR n (t)=R c (t)-R n (t), ΔR f (t)=R f (t)-R c (t).

[0060] Equation (2) means Figure 2 (b) The "perpendicular segment" at each azimuth time will be reduced to a dimensionless value. Figure 2 The "triangle points" in (c) further reduce the dimension of the strip region to a curve. Among them, Figure 2 (c) In the above figure, the curve located in the two-dimensional space of "azimuth-time-center slant distance" represents the change history of the center slant distance with azimuth-time. The time-varying repetition frequency design that satisfies the time delay constraint involves selecting curves composed of triangles at different times on a surface perpendicular to the "azimuth-time-center slant distance" plane, with this curve as the intersection line. (See...) Figure 2 (c) The following figure.

[0061] Step 2: Spatiotemporal frequency constraint modeling of Doppler fuzziness;

[0062] Within the three-dimensional space comprised of "azimuth time - center slant distance - pulse repetition frequency", the time-varying pattern of the Doppler bandwidth within the beam is analyzed, and a constrained model of Doppler fuzziness is established.

[0063] Spatiotemporal frequency echo delay constraint model as follows Figure 3 As shown in the left figure, based on the mapping relationship between azimuth time and center slant distance, a three-dimensional surface can be extracted in three-dimensional space to characterize the changes in the relative position distribution of scene echo, nadir echo, and transmitted pulse with azimuth time throughout the entire data acquisition period. Figure 3 The middle figure shows the feasible region for a pulse repetition frequency (PRF) design without return loss, where the white area represents the region. To avoid Doppler ambiguity in the designed PRF sequence, the Doppler bandwidth B is considered. a The variation of (t) with azimuth time t is used to obtain the lower limit of the selectable repetition frequency PRF(t) for each azimuth time, as shown in equation (3), where k represents the azimuth oversampling coefficient. The selectable repetition frequency range for each time moment is plotted on the graph to avoid Doppler blurring, see [reference needed]. Figure 3 The right image shows the black area corresponding to the frequency repetition selection that produces Doppler blur.

[0064] PRF(t)≥kB a (t) (3)

[0065] Step 3: Spatiotemporal frequency constraint modeling of distance ambiguity ratio;

[0066] Since a single "point" in the three-dimensional space of "azimuth-time-center slant range-pulse repetition rate" corresponds to the data acquisition state at a given instant (i.e., satellite position, beam pointing, and instantaneous pulse repetition rate), and this data acquisition state corresponds to all targets within the beam, this means that when establishing a range ambiguity ratio constraint model in three-dimensional space, a single "point" in space should simultaneously constrain all targets within the beam. In other words, the worst-case range ambiguity ratio for all targets within the beam should satisfy the ambiguity constraint condition. Therefore, the core of range ambiguity ratio constraint modeling is finding the worst-case range ambiguity ratio for that data acquisition state.

[0067] The following uses azimuth time t a Taking data acquisition state A as an example, this section explains how to obtain the worst range ambiguity ratio under this data acquisition state. Let the spaceborne SAR be in azimuth time t... a The pulse repetition frequency is PRFa, see Figure 4 The main and side lobes of the antenna are represented by solid and dashed lines in the elevation direction, respectively; T A (Triangle point) represents the position with the worst distance blur ratio within the beamwidth at time ta, T A1 T A2 (dot) indicates T A The distance blur position of the first sidelobe, which contributes the most to the distance blur ratio, has the following relationship:

[0068]

[0069] Where RASR(t) a PRF a T) represents the position time t a Pulse Repetition Rate (PRF) a At that time, the distance ambiguity ratio at position T, l represents the set of positions of the antenna main lobe in the illumination area in the elevation direction.

[0070] Due to the center slope distance R c R is a function of azimuth time t c , t a The center slope distance at time can be written as R. c (t a Then, the coordinates of data acquisition state A in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate" are A(t). a R c (t a ), PRF a The worst distance blur ratio Ω is ), RASR for:

[0071] Ω RASR (t a R c (t a ), PRFa )=RASR(t a PRF a T A (5)

[0072] According to formulas (4) and (5), the worst possible distance ambiguity ratio Ω can be found at all azimuth times. RASR Furthermore, Ω is obtained in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate". RASR Distribution, see examples Figure 4 (b), at this time, the Ω opposite point A is RASR The value is -32dB. If we assume the required distance blur ratio threshold for imaging is -26dB, then the infeasibility region for time-varying repetition rate design in the curved surface can be obtained, such as... Figure 4 (c) shows the black area.

[0073] Step 4: Spatiotemporal frequency constraint modeling of azimuth ambiguity ratio;

[0074] Similar to the range ambiguity ratio, the constraint analysis of the orientation ambiguity ratio also requires obtaining the worst-case value of the orientation ambiguity ratio based on data at a certain moment. However, compared to the range ambiguity ratio, it is more complex that the target orientation ambiguity ratio is not determined by a single instant, but is obtained by integration over the pulse accumulation time. Therefore, this patent first finds the relationship between the instantaneous orientation ambiguity ratio and the true orientation ambiguity ratio, and then finds the worst possible value of the instantaneous orientation ambiguity ratio as the design constraint for the orientation ambiguity ratio.

[0075] The true azimuth ratio is the ratio of the integrals of the azimuth fuzzy energy to the integrals of the unfuzzy energy. By the sum-partition ratio theorem, there must exist a t. * At time T, the true azimuth ambiguity ratio AASR(T) at position T is better than the instantaneous azimuth ambiguity ratio at that time, is:

[0076]

[0077] Where S A S(t) and S0(t) represent the azimuth ambiguity energy and the non-ambiguity energy at position T at time t, respectively.

[0078] Assume t * At that time, the SAR satellite's data acquisition status was B, and the pulse repetition rate was PRF. b ,See Figure 5 (a). The circled areas represent the antenna sidelobe illumination areas that cause azimuth ambiguity; T1 and T2 (dots) represent the areas illuminated by the antenna sidelobe at time t. * At time t, the first sidelobe azimuth ambiguity position that contributes the most to the instantaneous azimuth ambiguity ratio at position T. * Instantaneous azimuth ambiguity ratio ω AASR The worst possible value of the azimuth ratio at position T is denoted as:

[0079]

[0080] The following example, data acquisition state B, illustrates the method for obtaining the worst instantaneous azimuth ambiguity ratio under this data acquisition state. The instantaneous azimuth ambiguity at all locations within the beam is calculated, and the difference between these values ​​is used as t. * Design constraints for time-azimuth ambiguity ratio, see Figure 5 (b). The dashed circle represents the beam illumination area, T B (Triangle point) indicates the location with the worst instantaneous azimuth blur ratio within the beam illumination area at that moment, T B1 T B2 (dot) indicates T B The location of the first sidelobe azimuth blur that contributes the most to the instantaneous azimuth blur ratio. Based on the above description, the following relationship holds:

[0081]

[0082] Where P main This represents the set of locations of the area illuminated by the main lobe of the antenna.

[0083] The coordinates of data acquisition state B in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate" are B(t). * R c (t * ), PRF b The worst distance blur ratio Ω is ), AASR for:

[0084] Ω AASR (t * R c (t * ), PRF a )=ω AASR (t * PRF b T B (9)

[0085] According to formulas (6) to (9), all targets in the scene can find the possible worst distance ambiguity ratio Ω at a certain position and time during the data acquisition period. AASR Furthermore, Ω is obtained in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate". AASR Distribution, see examples Figure 5 (c), at this time, the Ω opposite point B is... AASR The value is -29dB. If we assume the required distance blur ratio threshold for imaging is -26dB, then the infeasible region for time-varying repetition rate design in the curved surface can be obtained, such as... Figure 5 (d) shows the gray area.

[0086] Step 5: Time-varying repetition frequency design;

[0087] Constraint analysis of time delay and fuzziness in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition frequency" is not intuitive. Therefore, based on the mapping relationship between azimuth and time and center slant distance, the three-dimensional constraints are reduced and projected to the more intuitive two-dimensional space of "azimuth-time-pulse repetition frequency" for analysis. This space is then used as the design criterion for the feasible region of time-varying repetition frequency design, and a nonlinear time-varying repetition frequency sequence is designed using a graphical method.

[0088] The prerequisite for achieving dimensionality reduction projection with 3D spatial time delay and fuzzy constraints is that the 3D surface has a single mapping along the projection direction. Since the central slope distance is a function of azimuth time, the proposed method chooses to project along the central slope distance direction, ensuring a single mapping relationship before and after projection. See the example below. Figure 6 .in, Figure 6 The figures above show the constraint models for time delay and Doppler, range ambiguity ratio, and azimuth ambiguity ratio in three-dimensional space. Projecting these models along the central slant distance axis yields the constraint models in the two-dimensional space of "azimuth-time-pulse repetition rate," as shown in the figure. Figure 6 See the image below.

[0089] Based on the constraint model of time delay and ambiguity in the two-dimensional space of "azimuth-time-pulse repetition frequency" after projection and superposition, the feasible region of time-varying repetition frequency design is determined, corresponding to Figure 7 The white area. The time-varying repetition frequency sequence needs to be selected within the feasible region, and the pulse repetition frequency corresponding to any orientation time must be unique. Assuming the feasible region set of the repetition frequency is F, the repetition frequency sequence PRF(t) must satisfy the relationship shown in equation (10), where t s t e These represent the start and end times of data acquisition, respectively. Furthermore, the repetition frequency sequence PRF(t) should ensure continuous variation of pulse repetition frequencies between adjacent time points to reduce echo loss caused by changes in the transmit / receive ambiguity number.

[0090]

[0091] Simulation Experiment

[0092] The simulation parameters for the time-varying repetition frequency design of spacetime frequency three-dimensional constraint for spaceborne SAR scene matching curve imaging are shown in Table 1.

[0093] Table 1 Simulation Parameter List

[0094]

[0095]

[0096] To verify the design of time-varying repetition frequency with three-dimensional constraints in spacetime-frequency spatiotemporal constraints for spaceborne SAR scene matching curve imaging, high-quality data acquisition with low data loss and high ambiguity performance was achieved. Taking the reflector system as an example, computer simulations were performed using the parameters in Table 1. Figure 8 (a) and (b) respectively show the wave foot trajectory and satellite attitude history of the determined spaceborne SAR scene matching curve imaging mode during data acquisition.

[0097] The design results of the pulse repetition frequency sequence using the method described in this patent are shown below: Figure 9 (a) shows the distribution of the designed pulse repetition frequency sequence in the two-dimensional space of "azimuth-time-pulse repetition frequency" (black solid lines a to c). It can be seen that all black solid lines are located within the white feasible region; the evolution of the pulse repetition frequency sequence with azimuth-time is shown in [reference needed]. Figure 9 (b) Right figure. Figure 10 Figures (a) and (b) show the variation of range and azimuth ambiguities with imaging swathe length using the designed pulse repetition frequency sequence, respectively. The results show that the overall blur performance is better than the set threshold of -29.5 dB, ensuring that the echo data meets the required blur performance. Finally, Figure 11 The azimuth imaging results of the scene center point are presented. Evaluation shows a resolution of 0.496m, a peak sidelobe ratio of -13.28dB, and an integral sidelobe ratio of -9.87dB. The imaging results are well-focused and meet the expected resolution. The simulation results demonstrate that the method described in this patent can achieve high-quality echo data acquisition.

[0098] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-dimensional constrained time-varying repetition frequency design for spaceborne SAR scene matching curve imaging, characterized in that, Includes the following steps: Step S1, Spatiotemporal frequency constraint modeling of time delay; in the three-dimensional space of "azimuth-time-spatial distance-pulse repetition frequency", for each instantaneous azimuth time... t The maximum slant range within the beam range can be found in all cases. R f ( t and minimum slope distance R n ( t The instantaneous repetition frequency selection at this moment is to find a coverage area of ​​[ ] within the corresponding two-dimensional space of "spatial distance-pulse repetition frequency" without strip occlusion. R n ( t ), R f ( t The perpendicular segment of ] is expressed as: ； Among them, PRF( t ) represents the pulse repetition rate. M and N These are the ambiguity numbers of the transmitted pulse and the nadir echo, respectively. c At the speed of light, H The satellite's orbital altitude, H f This represents the maximum slant range corresponding to the nadir echo. T g and T p These are the transmit and protection pulse widths, respectively. Therefore, time-varying repetition frequency design is to find a similar vertical line segment at each azimuth time, that is, to find a feasible strip region within the feasible domain represented by the "surface volume" composed of the slant range; however, selecting a strip region in this "surface volume" is not intuitive, the essential reason being that when the azimuth time is determined, the echo slant range is not unique. Considering the center slant distance in scene matching curve imaging R c ( t The coordinates can be uniquely determined by azimuth and time, and the "center slant distance" can be used instead of the "spatial distance" coordinate axis; in this case, the expression is written as: ； Where Δ R n ( t ) and Δ R f ( t () represent the maximum slant range of the echo. R f ( t ), minimum slope distance R n ( t )and R c ( t The change in ) is Δ R n ( t ) = R c ( t )- R n ( t ), Δ R f ( t ) = R f ( t )- R c ( t ); Step S2: Spatiotemporal frequency constraint modeling of Doppler ambiguity; Within the three-dimensional space comprised of "azimuth time - center slant range - pulse repetition frequency," analyze the time-varying pattern of the Doppler bandwidth within the beam to establish a constraint model for Doppler ambiguity; Based on the mapping relationship between azimuth time and center slant range, extract a three-dimensional surface in the three-dimensional space to characterize the changes in the relative position distribution of scene echo, nadir echo, and transmitted pulse with azimuth time throughout the entire data acquisition period; To avoid Doppler ambiguity generated by the designed pulse repetition frequency sequence, consider the Doppler bandwidth... B a ( t ) with direction and time t The variation pattern was used to obtain the selectable repetition frequency (PRF) for each azimuth time. t The lower bound of ) is expressed as: ； in k Indicates the azimuth oversampling coefficient; Step S3, Spatiotemporal frequency constraint modeling of range ambiguity ratio; assuming the spaceborne SAR in azimuth time... t a The pulse repetition frequency is PRF a The main and side lobes of the antenna are represented by solid and dashed lines in the elevation direction, respectively; T A express t a The position with the worst range blur ratio within the beamwidth at a given time has the following relationship: ； Among them, RASR ( t a , PRF a (T) represents the azimuth time. t a Pulse Repetition Rate (PRF) a At that time, the distance blur ratio at position T, L main This represents the set of positions of the antenna main lobe in the illumination area along the elevation direction; due to the center slant distance... R c Location and time t function R c , t a The center slope distance at time is written as R c ( t a Then the coordinates of data acquisition state A in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition frequency" are A( t a , R c ( t a ), PRF a The distance blur ratio it corresponds to is the worst value. for: ； The worst possible distance blur ratio can be found at all times and in all directions. Furthermore, in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate", the following can be obtained: The distribution of points A and B, where point A is located. The value is -32 dB; if we assume that the distance blur ratio threshold that the imaging needs to meet is -26 dB, then the infeasibility region for time-varying repetition frequency design in the curved surface can be obtained. Step S4: Spatiotemporal frequency constraint modeling of azimuth ambiguity ratio; find the relationship between instantaneous azimuth ambiguity ratio and true azimuth ambiguity ratio, and then find the worst possible value of instantaneous azimuth ambiguity ratio as the design constraint of azimuth ambiguity ratio. The true azimuth ratio is the ratio of the integrals of the azimuth fuzzy energy to the integrals of the unfuzzy energy. By the theorem of composition and division, it must exist t * At time T, the true azimuth ambiguity ratio AASR(T) at position T is better than the instantaneous azimuth ambiguity ratio at that time, is: ； in S A ( t )and S 0( t ) respectively represent t The ambiguity energy and non-ambiguity energy at time and location T; Assumption t * At that time, the SAR satellite's data acquisition status was B, and the pulse repetition rate was PRF. b； The circled area represents the antenna sidelobe illumination area that causes azimuth ambiguity; in t * instantaneous azimuth ratio ω AASR The worst possible value of the azimuth ratio at position T is denoted as: ； Calculate the instantaneous azimuth ambiguity at all locations within the beam, and the difference will be used as... t * Design constraints on the time-azimuth ambiguity ratio; where the dashed circle represents the beam illumination area, T B The location with the worst instantaneous azimuth blur ratio within the beam illumination area at that moment is represented as: ； in P main This represents the set of locations of the area illuminated by the antenna's main lobe. The coordinates of data acquisition state B in the three-dimensional space of "azimuth-time-center slant distance-pulse repetition rate" are B( t * , R c ( t * ),PRF b The distance blur ratio it corresponds to is the worst value. for: ； Step S5: Selection of time-varying repetition frequency sequence based on time delay and fuzzy constraints; Based on the constraint model of time delay and fuzziness in the two-dimensional space of "azimuth-time-pulse repetition frequency" after projection and superposition, determine the feasible region of the time-varying repetition frequency design; the time-varying repetition frequency sequence must be selected from the feasible region, and a unique pulse repetition frequency must correspond to any azimuth time. Assume the set of feasible repetition frequency regions is... F Then the repetition frequency sequence PRF ( t The expression to be satisfied is: ; in t s , t e These represent the start and end times of data acquisition, respectively; additionally, the repetition frequency sequence PRF ( t It is necessary to ensure that the pulse repetition frequency changes continuously between adjacent time intervals to reduce echo loss caused by changes in the transmit and receive ambiguity number.

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