Medium and high orbit SAR satellite cross ambiguity calculation method based on reflector antenna

Abstract

The invention relates to a middle-high orbit SAR satellite cross ambiguity calculation method based on a reflector antenna, and belongs to the field of satellite overall design. Establishing an expression of the ambiguity ASR; establishing a rotating ellipsoid model of the earth surface; establishing an imaging point and fuzzy point distribution geometric schematic diagram by using a rotating ellipsoid model of the earth surface; establishing an expression of an antenna beam ground projection direction angle theta BFP; establishing an expression of a periodically rotating two-dimensional antenna pattern Gea; calculating the earth radius Rte of the position of the imaging target point; calculating the slope distance Rst of the imaging target point and the slope distance Rstm of the cross fuzzy point according to the Rte; calculating an incident angle theta int of an imaging target point and an incident angle theta imm of a fuzzy point; calculating a pitch angle zeta e (k, m3, n3) and an azimuth angle zeta a (k, m3, n3) of a cross fuzzy point corresponding to the imaging target point at any position; establishing a cross ambiguity expression CASRta of an imaging target point at any position; according to the method, the azimuth ambiguity calculation accuracy is greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of satellite overall design and relates to a method for calculating cross-ambiguity of medium and high orbit SAR satellites based on reflector antennas. Background Technology

[0002] Ambiguity is one of the important indicators for evaluating the quality of spaceborne SAR images. Ambiguity is an inherent characteristic of spaceborne SAR and cannot be completely eliminated. It can only be reduced to below a certain threshold through compromise design of system parameters.

[0003] Medium- and high-orbit SAR satellites, and even geostationary orbit SAR satellites, represent the development trend of microwave remote sensing. For medium- and high-orbit SAR satellites, and even geostationary orbit SAR satellites, equipped with reflector antennas, due to their high orbital altitude, a "pitch + roll" attitude angle control method is typically used to achieve beam-side looking or arbitrary pointing imaging, avoiding the use of large yaw angle adjustments to prevent excessive time consumption and impact on the satellite's rapid response capability.

[0004] Based on these characteristics, the antenna beam's projection direction on the ground rotates periodically with its orbital position; therefore, the energy distribution of the antenna's illumination on the ground also varies with the orbital position. When calculating range ambiguity, the variation in signal energy intensity distribution in each ambiguity region with orbital position needs to be considered. Furthermore, if the satellite is designed for emergency missions and uses oblique imaging, the signal energy intensity distribution in each ambiguity region must further consider the changes in signal energy intensity distribution caused by oblique angle. Currently, only ambiguity calculation methods exist for low-Earth orbit SAR satellites, while methods for calculating ambiguity for medium- and high-Earth orbit SAR satellites are lacking. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a method for calculating cross-ambiguity of medium and high orbit SAR satellites based on reflector antennas, which greatly improves the accuracy of azimuth ambiguity calculation.

[0006] The solution of the present invention is:

[0007] A method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas includes:

[0008] Establish the expression for the ambiguity ASR;

[0009] Establish a rotating ellipsoidal model of the Earth's surface;

[0010] A geometrical diagram of the distribution of imaging points and blurred points is established using a rotating ellipsoid model of the Earth's surface;

[0011] Set the antenna beam ground projection direction angle to θ. BFP Establish θ BFP The expression;

[0012] According to θ BFP The expression shows that θ BFP The true pericentric angle f of the orbit varies periodically; a periodically rotating two-dimensional antenna pattern G is established. ea The expression;

[0013] Calculate the Earth's radius R at the location of the imaging target point. te According to R te Calculate the slant range R of the imaging target point st The slant distance R of the intersection blur point stm ;

[0014] Calculate the incident angle θ of the imaging target point int and the incident angle θ of the blurred point inm ;

[0015] According to the ground projection direction angle θ of the antenna beam BFP Calculate the pitch angle ξ of the intersecting blurred points corresponding to the imaging target point at any location. e (k,m3,n3) and azimuth ζ a (k,m3,n3);

[0016] Based on the expression for ambiguity ASR, and according to the periodically rotating two-dimensional antenna pattern G ea , Slant distance R of the imaging target point st Slope distance R of the fuzzy intersection point stm The incident angle θ of the imaging target point int The incident angle θ of the blurred point inm The pitch angle ξ of the cross-fuzzy point e (k,m3,n3) and azimuth ζ a (k,m3,n3) Establish the cross-ambiguity expression (CASR) for imaging target points at arbitrary locations. ta .

[0017] In the above-described method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the expression for the ambiguity ASR is:

[0018]

[0019] In the formula, B p For azimuth processing bandwidth;

[0020] G 2 (f d ,τ) is the radiation pattern of a two-way far-field antenna;

[0021] σ0(f d ,τ) is the radar backscattering coefficient;

[0022] ρ a This refers to the azimuth resolution.

[0023] ρ gr This refers to the ground distance resolution.

[0024] R st (f d ,τ) is the slant range from the imaging point or blurred point to the radar;

[0025] f d The frequency is the Doppler frequency.

[0026] τ is the echo delay time;

[0027] PRF stands for Pulse Repetition Frequency;

[0028] m1 is the Doppler frequency domain ambiguity number;

[0029] n1 is the time-domain ambiguity number of the echo;

[0030] S(f d ,τ) is the main signal strength;

[0031] θ int The incident angle of the imaging target point.

[0032] In the above-mentioned method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the rotating ellipsoid model of the Earth's surface is as follows:

[0033]

[0034] In the formula, R e It is the semi-axial length of the Earth's equator, which is ellipsoidal.

[0035] R p It is the polar semi-axis of the Earth's ellipsoid;

[0036] X t Y t Z t The coordinates are 3-axis coordinates in the WSG-84 coordinate system model.

[0037] In the above-mentioned method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the specific geometric diagram of the distribution of imaging points and ambiguity points is as follows:

[0038] The target point T is a solid circle; the distance blur point is a hollow circle; the azimuth blur point is a triangle; the intersection blur point is a square; the nadir point is denoted as O; the intersection line MN of the zero Doppler plane and the ground surface is perpendicular to the velocity direction of the trajectory of the nadir point O; the ground oblique angle of the target point is denoted as θ. ds ;θ ds =0 indicates a normal side view, θ ds ≠0 indicates strabismus.

[0039] In the aforementioned method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, θ BFP The expression is:

[0040]

[0041] In the formula, u represents the satellite's side-view direction, +1 represents right-view, and -1 represents left-view;

[0042] θ i It is the track inclination angle;

[0043] f is the true pericentric angle of the orbit;

[0044] ω is the argument of perigee;

[0045] ω s It is the satellite's instantaneous angular velocity;

[0046] ω e It is the Earth's rotational angular velocity;

[0047] e is the orbital eccentricity;

[0048] R0 is the slant distance from the phase center of the SAR antenna to the target point T;

[0049] γ0 is the downward angle of the beam center, which is a known quantity;

[0050] H represents the satellite's altitude.

[0051] In the aforementioned method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the periodically rotating two-dimensional antenna pattern G... ea The expression is:

[0052]

[0053] In the formula, ξ e ζ0 and ζ0 represent the pitch angle and azimuth angle, respectively;

[0054] ξ e0 ζ a0 These represent the elevation and azimuth angles of the beam centerline, respectively.

[0055] D r This refers to the antenna size in the range direction of the SAR antenna;

[0056] D a The antenna dimensions are in the azimuth direction of the SAR antenna;

[0057] λ is the signal wavelength.

[0058] In the aforementioned method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the Earth's radius R at the location of the imaging target point is...te , Slant distance R of the imaging target point st The slant distance R of the intersection blur point stm They are respectively:

[0059]

[0060] In the formula, R e It is the semi-axial length of the Earth's equator, which is ellipsoidal.

[0061] R p It is the polar semi-axis of the Earth's ellipsoid;

[0062] δ t Indicates the latitude of the location of the imaging target point;

[0063] R s Indicates the distance from the satellite to the Earth's center;

[0064] α t Indicates the geocentric angle of the imaging target point;

[0065] n2 represents the number of fuzzy regions;

[0066] α m The geocentric angle representing a point of ambiguity;

[0067] c represents the speed of light;

[0068] PRF stands for Pulse Repetition Frequency, which indicates the frequency at which a satellite operates.

[0069] In the aforementioned method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the incident angle θ of the imaging target point... int and the incident angle θ of the blurred point inm They are respectively:

[0070]

[0071] In the aforementioned method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the elevation angle ξ... e (k,m3,n3) and azimuth ζ a (k,m3,n3) are respectively:

[0072]

[0073] In the formula, k represents the number of pulses within the synthesized aperture time;

[0074] m3 represents the number of azimuth ambiguities; m3∈(-M,M), where M is a positive integer; M is the maximum number of azimuth ambiguities.

[0075] n3 is a fuzzy point; n3∈(-N,N), where N is a positive integer; N is the maximum value of the fuzzy point;

[0076] γ t (n3) represents the downward viewpoint obtained by the imaging target point or the corresponding cross-blur point of the target point;

[0077] θ ds This indicates the oblique angle of view from the ground at the target point;

[0078] θ amb (m3) represents the angle by which the target deviates from the ground projection of the beam center within the imaging or blurring area.

[0079] In the aforementioned method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, the cross-ambiguity expression CASR for imaging target points at arbitrary locations is... ta for:

[0080]

[0081] In the formula, k p The total number of pulses transmitted;

[0082] G ea This is a two-dimensional orientation pattern.

[0083] The advantages of this invention compared to the prior art are:

[0084] (1) The high-precision azimuth ambiguity calculation method of the present invention can greatly improve the accuracy of azimuth ambiguity calculation. The technology involved is also applicable to medium and high orbit SAR satellites;

[0085] (2) This invention is based on the "pitch + roll" attitude control method, which combines the orbit position to accurately calculate the intensity distribution of the antenna's two-dimensional radiation pattern on the ground and the changes with the orbit position. Based on this, the signal energy intensity distribution of each cross ambiguity zone is calculated as a function of the orbit position, thereby improving the calculation accuracy of satellite cross ambiguity.

[0086] (3) This invention takes into account the influence of strabismus and adopts a more accurate rotating ellipsoid model to improve calculation accuracy. Attached Figure Description

[0087] Figure 1 This is a flowchart of the cross-ambiguity calculation for high-orbit SAR satellites in this invention;

[0088] Figure 2 This is a geometrical diagram illustrating the distribution of imaging points and blurred points in this invention;

[0089] Figure 3 This is a graph showing the cross ambiguity of a geostationary SAR satellite in a side-view configuration at a latitude angle of 18°, as a function of PRF.

[0090] Figure 4 This is a curve showing the cross-ambiguity of a geosynchronous orbit SAR satellite with a latitude of 18° and a geodetic inclination of 60°, as a function of PRF.

[0091] Figure 5 This is a graph showing the cross ambiguity of a geostationary SAR satellite in a side-view configuration at a latitude angle of 42°, as described in an embodiment of the present invention, as a function of PRF.

[0092] Figure 6 This is a curve showing the cross-ambiguity of a geosynchronous orbit SAR satellite with a latitude of 42° and a geodetic inclination of 60°, as a function of PRF.

[0093] Figure 7 This is a graph showing the cross ambiguity of a geostationary SAR satellite in a side-view configuration at a latitude angle of 82°, as described in an embodiment of the present invention, as a function of PRF.

[0094] Figure 8 This is a curve showing the cross-ambiguity of a geosynchronous orbit SAR satellite with a latitude angle of 82° and a geodetic inclination angle of 60°, as described in an embodiment of the present invention, as a function of PRF. Detailed Implementation

[0095] The present invention will be further described below with reference to the embodiments.

[0096] This invention provides a method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, which can greatly improve the accuracy of azimuth ambiguity calculation. The technology involved is also applicable to medium- and high-orbit SAR satellites.

[0097] A method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, such as Figure 1 As shown, the specific steps include the following:

[0098] Establish the expression for the ambiguity ASR.

[0099] Ambiguity score (ASR) is a fundamental parameter characterizing the performance of a spaceborne SAR system and an important indicator for evaluating radar image quality. According to the classic and well-known theory of SAR satellite ambiguity calculation, it is defined as the ratio of the intensity of the ambiguous signal to the intensity of the main imaging signal within a SAR image resolution cell. The expression for ambiguity score ASR is:

[0100]

[0101] In the formula, B p For azimuth processing bandwidth;

[0102] G2 (f d ,τ) is the radiation pattern of a two-way far-field antenna;

[0103] σ0(f d ,τ) is the radar backscattering coefficient;

[0104] ρ a This refers to the azimuth resolution.

[0105] ρ gr This refers to the ground distance resolution.

[0106] R st (f d ,τ) is the slant range from the imaging point or blurred point to the radar;

[0107] f d The frequency is the Doppler frequency.

[0108] τ is the echo delay time;

[0109] PRF stands for Pulse Repetition Frequency;

[0110] m1 is the Doppler frequency domain ambiguity number;

[0111] n1 is the time-domain ambiguity number of the echo;

[0112] S(f d ,τ) is the main signal strength;

[0113] θ int The incident angle of the imaging target point.

[0114] Establish a rotating ellipsoid model of the Earth's surface.

[0115] The Earth is essentially an irregular, non-smooth ellipsoid with a highly complex shape. Even using high-order models for approximation, it is difficult to describe the Earth's true geometry, especially given the approximately 8800m elevation difference on its surface. Therefore, in the signal modeling and processing of spaceborne SAR, in addition to selecting an appropriate Earth model, corrections should be made for the surface elevation difference. In this patent, when establishing the space-ground geometric model and deriving various formulas, the ellipsoidal curvature of the Earth's surface was not ignored; that is, a more accurate rotating ellipsoidal model was adopted for the surface. The rotating ellipsoidal model of the Earth's surface is as follows:

[0116]

[0117] In the formula, R e It is the semi-axial length of the Earth's equator, which is ellipsoidal.

[0118] R p It is the polar semi-axis of the Earth's ellipsoid;

[0119] X t Y tZ t The coordinates are 3-axis coordinates in the WSG-84 coordinate system model.

[0120] Among them, R e =6378.137km and R p = 6356.752 km, which, in the WSG-84 coordinate system model, represents the equatorial semi-axis and polar semi-axis of the ellipsoidal Earth, respectively. The Earth rotates on its axis from west to east at an angular velocity ωe (ω... e =7.292115×10 -5 (rad / s).

[0121] A geometrical diagram illustrating the distribution of imaging points and blurred points is established using a rotating ellipsoidal model of the Earth's surface. The specific geometrical diagram illustrating the distribution of imaging points and blurred points is as follows:

[0122] like Figure 2 As shown, the imaging target point T is a solid circle; the distance blur point is a hollow circle; the azimuth blur point is a triangular point; the intersection blur point is a square point; the nadir point is denoted as O; the intersection line MN of the zero Doppler plane and the ground surface is perpendicular to the velocity direction of the trajectory of the nadir point O; the ground oblique angle of the target point is denoted as θ. ds ;θ ds =0 indicates a normal side view, θ ds ≠0 indicates strabismus.

[0123] The accuracy of calculating the cross-ambiguity point location and the antenna pattern gain at that location determines the accuracy of the cross-ambiguity calculation. The angle between the range-direction one-dimensional pattern profile and the zero Doppler plane is set as θ, representing the antenna beam's ground projection direction angle. BFP Establish θ BFP The expression.

[0124] θ BFP The expression is:

[0125]

[0126] In the formula, u represents the satellite's side-view direction, +1 represents right-view, and -1 represents left-view;

[0127] θ i It is the track inclination angle;

[0128] f is the true pericentric angle of the orbit;

[0129] ω is the argument of perigee;

[0130] ω s It is the satellite's instantaneous angular velocity;

[0131] ω e It is the Earth's rotational angular velocity;

[0132] e is the orbital eccentricity;

[0133] R0 is the slant distance from the phase center of the SAR antenna to the target point T;

[0134] γ0 is the downward angle of the beam center, which is a known quantity;

[0135] H represents the satellite's altitude.

[0136] According to θ BFP The expression shows that θ BFP The true pericentric angle f of the orbit varies periodically; a periodically rotating two-dimensional antenna pattern G is established. ea The expression.

[0137] Periodically rotating two-dimensional antenna pattern G ea The expression is:

[0138]

[0139] In the formula, ξ e ζ0 and ζ0 represent the pitch angle and azimuth angle, respectively;

[0140] ξ e0 ζ a0 These represent the elevation and azimuth angles of the beam centerline, respectively.

[0141] D r This refers to the antenna size in the range direction of the SAR antenna;

[0142] D a The antenna dimensions are in the azimuth direction of the SAR antenna;

[0143] λ is the signal wavelength.

[0144] Calculate the Earth's radius R at the location of the imaging target point. te According to R te Calculate the slant range R of the imaging target point st The slant distance R of the intersection blur point stm .

[0145] Earth's radius R at the location of the imaging target point te , Slant distance R of the imaging target point st The slant distance R of the intersection blur point stm They are respectively:

[0146]

[0147] In the formula, R e It is the semi-axial length of the Earth's equator, which is ellipsoidal.

[0148] R p It is the polar semi-axis of the Earth's ellipsoid;

[0149] δ t Indicates the latitude of the location of the imaging target point;

[0150] R s Indicates the distance from the satellite to the Earth's center;

[0151] α t Indicates the geocentric angle of the imaging target point;

[0152] n2 represents the number of fuzzy regions;

[0153] α m The geocentric angle representing a point of ambiguity;

[0154] c represents the speed of light;

[0155] PRF stands for Pulse Repetition Frequency, which indicates the frequency at which a satellite operates.

[0156] Calculate the incident angle θ of the imaging target point int and the incident angle θ of the blurred point inm .

[0157] The incident angle θ of the imaging target point int and the incident angle θ of the blurred point inm They are respectively:

[0158]

[0159] According to the ground projection direction angle θ of the antenna beam BFP Calculate the pitch angle ξ of the intersecting blurred points corresponding to the imaging target point at any location. e (k,m3,n3) and azimuth ζ a (k,m3,n3).

[0160] Pitch angle ξ e (k,m3,n3) and azimuth ζ a (k,m3,n3) are respectively:

[0161]

[0162] In the formula, k represents the number of pulses within the synthesized aperture time;

[0163] m3 represents the number of azimuth ambiguities; m3∈(-M,M), where M is a positive integer; M is the maximum number of azimuth ambiguities.

[0164] n3 is a fuzzy point; n3∈(-N,N), where N is a positive integer; N is the maximum value of the fuzzy point;

[0165] γ t (n3) represents the downward viewpoint obtained by the imaging target point or the corresponding cross-blur point of the target point;

[0166] θ ds This indicates the oblique angle of view from the ground at the target point;

[0167] θ amb (m3) represents the angle by which the target deviates from the ground projection of the beam center within the imaging or blurring area.

[0168] Based on the expression for ambiguity ASR, and according to the periodically rotating two-dimensional antenna pattern G ea , Slant distance R of the imaging target point st Slope distance R of the fuzzy intersection point stm The incident angle θ of the imaging target point int The incident angle θ of the blurred point inm The pitch angle ξ of the cross-fuzzy point e (k,m3,n3) and azimuth ζ a (k,m3,n3) Establish the cross-ambiguity expression (CASR) for imaging target points at arbitrary locations. ta .

[0169] The cross-ambiguity expression for imaging target points at arbitrary locations (CASR) ta for:

[0170]

[0171] In the formula, k p The total number of pulses transmitted;

[0172] G ea This is a two-dimensional orientation pattern.

[0173] Example

[0174] Taking a geostationary SAR satellite as an example, the results of the method described in this patent are demonstrated through simulation calculations. The simulation parameters are shown in Table 1. To illustrate the differences between different orbital positions, considering that the Geo-SAR orbit is symmetrical in both north-south and east-west directions, it is sufficient to analyze the 0-90° latitude argument range. Therefore, three typical latitude arguments of 18°, 42°, and 82° are selected for simulation calculations. To illustrate the differences between different oblique angles, a frontal side view (with an oblique angle of 0°) and an oblique angle of 60° are selected for simulation.

[0175] Table 1

[0176] name parameter Semi-major axis of the track (km) 42163.5 Track inclination angle (°) 28 Orbital eccentricity 0.001 Argument of perigee (°) 90 Earth Model WSG84 Incident angle range (°) (18,60) Antenna diameter (m) 25 System wavelength (m) 0.24 Imaging swath width (km) 350

[0177] like Figures 3-8 The curves show the cross-ambiguity of geostationary orbit SAR satellites as a function of PRF under different satellite states.

[0178] This invention uses a geostationary orbit SAR satellite as an example to illustrate a high-precision method for calculating azimuth ambiguity, which can greatly improve the accuracy of azimuth ambiguity calculation. The technology involved is also applicable to medium and high orbit SAR satellites.

[0179] Three main aspects were considered to improve the calculation accuracy: First, based on the adoption of the "pitch + roll" attitude control method, the intensity distribution of the antenna's two-dimensional radiation pattern on the ground surface and its change with the orbit position were accurately calculated in combination with the orbit position. Based on this, the signal energy intensity distribution of each intersection ambiguity zone was calculated as a function of the orbit position. Second, the effect of squinting was considered. Third, a more accurate rotating ellipsoid model was adopted to improve the calculation accuracy.

[0180] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas, characterized in that: include: Establish the expression for the ambiguity ASR; Establish a rotating ellipsoidal model of the Earth's surface; A geometrical diagram of the distribution of imaging points and blurred points is established using a rotating ellipsoid model of the Earth's surface; Set the antenna beam ground projection direction angle to θ. BFP Establish θ BFP The expression; According to θ BFP The expression shows that θ BFP The true pericentric angle f of the orbit varies periodically; a periodically rotating two-dimensional antenna pattern G is established. ea The expression; Calculate the Earth's radius R at the location of the imaging target point. te According to R te Calculate the slant range R of the imaging target point st The slant distance R of the intersection blur point stm ; Calculate the incident angle θ of the imaging target point int and the incident angle θ of the blurred point inm ; According to the ground projection direction angle θ of the antenna beam BFP Calculate the pitch angle ξ of the intersecting blurred points corresponding to the imaging target point at any location. e (k,m3,n3) and azimuth ζ a (k,m3,n3); Based on the expression for ambiguity ASR, and according to the periodically rotating two-dimensional antenna pattern G ea , Slant distance R of the imaging target point st Slope distance R of the fuzzy intersection point stm The incident angle θ of the imaging target point int The incident angle θ of the blurred point inm The pitch angle ξ of the cross-fuzzy point e (k,m3,n3) and azimuth ζ a (k,m3,n3) Establish the cross-ambiguity expression (CASR) for imaging target points at arbitrary locations. ta .

2. The method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 1, characterized in that: The expression for Ambiguity Scale (ASR) is: In the formula, B p For azimuth processing bandwidth; G 2 (f d ,τ) is the radiation pattern of a two-way far-field antenna; σ0(f d ,τ) is the radar backscattering coefficient; ρ a This refers to the azimuth resolution. ρ gr This refers to the ground distance resolution. R st (f d ,τ) is the slant range from the imaging point or blurred point to the radar; f d The frequency is the Doppler frequency. τ is the echo delay time; PRF stands for Pulse Repetition Frequency; m1 is the Doppler frequency domain ambiguity number; n1 is the time-domain ambiguity number of the echo; S(f d ,τ) is the main signal strength; θ int The incident angle of the imaging target point.

3. The method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 1, characterized in that: The rotating ellipsoid model of the Earth's surface is as follows: In the formula, R e It is the semi-axial length of the Earth's equator, which is ellipsoidal. R p It is the polar semi-axis of the Earth's ellipsoid; X t Y t Z t The coordinates are 3-axis coordinates in the WSG-84 coordinate system model.

4. The method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 3, characterized in that: The specific geometric diagram illustrating the distribution of imaging points and blurred points is as follows: The target point T is a solid circle; the distance blur point is a hollow circle; the azimuth blur point is a triangle; the intersection blur point is a square; the nadir point is denoted as O; the intersection line MN of the zero Doppler plane and the ground surface is perpendicular to the velocity direction of the trajectory of the nadir point O; the ground oblique angle of the target point is denoted as θ. ds ;θ ds =0 indicates a normal side view, θ ds ≠0 indicates strabismus.

5. The method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 1, characterized in that: θ BFP The expression is: In the formula, u represents the satellite's side-view direction, +1 represents right-view, and -1 represents left-view; θ i It is the track inclination angle; f is the true pericentric angle of the orbit; ω is the argument of perigee; ω s It is the satellite's instantaneous angular velocity; ω e It is the Earth's rotational angular velocity; e is the orbital eccentricity; R0 is the slant distance from the phase center of the SAR antenna to the target point T; γ0 is the downward angle of the beam center, which is a known quantity; H represents the satellite's altitude.

6. The method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 1, characterized in that: Periodically rotating two-dimensional antenna pattern G ea The expression is: In the formula, ξ e ζ0 and ζ0 represent the pitch angle and azimuth angle, respectively; ξ e0 ζ a0 These represent the elevation and azimuth angles of the beam centerline, respectively. D r This refers to the antenna size in the range direction of the SAR antenna; D a The antenna dimensions are in the azimuth direction of the SAR antenna; λ is the signal wavelength.

7. The method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 6, characterized in that: Earth's radius R at the location of the imaging target point te , Slant distance R of the imaging target point st The slant distance R of the intersection blur point stm They are respectively: In the formula, R e It is the semi-axial length of the Earth's equator, which is ellipsoidal. R p It is the polar semi-axis of the Earth's ellipsoid; δ t Indicates the latitude of the location of the imaging target point; R s Indicates the distance from the satellite to the Earth's center; α t Indicates the geocentric angle of the imaging target point; n2 represents the number of fuzzy regions; α m The geocentric angle representing a point of ambiguity; c represents the speed of light; PRF stands for Pulse Repetition Frequency, which indicates the frequency at which a satellite operates.

8. The method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 7, characterized in that: The incident angle θ of the imaging target point int and the incident angle θ of the blurred point inm They are respectively:

9. The method for calculating cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 8, characterized in that: Pitch angle ξ e (k,m3,n3) and azimuth ζ a (k,m3,n3) are respectively: In the formula, k represents the number of pulses within the synthesized aperture time; m3 represents the number of azimuth ambiguities; m3∈(-M,M), where M is a positive integer; M is the maximum number of azimuth ambiguities. n3 is a fuzzy point; n3∈(-N,N), where N is a positive integer; N is the maximum value of the fuzzy point; γ t (n3) represents the downward viewpoint obtained by the imaging target point or the corresponding cross-blur point of the target point; θ ds This indicates the oblique angle of view from the ground at the target point; θ amb (m3) represents the angle by which the target deviates from the ground projection of the beam center within the imaging or blurring area.

10. The method for calculating the cross-ambiguity of medium- and high-orbit SAR satellites based on reflector antennas according to claim 9, characterized in that: The cross-ambiguity expression for imaging target points at arbitrary locations (CASR) ta for: In the formula, k p The total number of pulses transmitted; G ea This is a two-dimensional orientation pattern.

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