A method for calculating the transmission path of spaceborne ice-detection synthetic aperture radar

Abstract

The present invention relates to the field of radar detection technology, and in particular to a method for calculating the transmission path of a satellite-borne ice-penetrating synthetic aperture radar, including: obtaining earth model parameters, system parameters of the satellite-borne ice-penetrating synthetic aperture radar, and echo simulation parameters; the echo simulation parameters include an azimuth time sequence, and an antenna position sequence and a target position in the ice under a rotating geocentric coordinate system; in the Antarctic, the Arctic, or other ice-covered areas to be detected, the air medium is above the earth's surface, and the ice medium is below the earth's surface. For each azimuth time, the geocentric angle corresponding to the corresponding transmission path in the ice medium is solved, and then the length of the transmission path in the air medium and the ice medium is determined respectively; the transmission path connects the corresponding antenna position and the target position in the ice, and is located within the range of the transmitting antenna beam. The present invention can more accurately determine the transmission path, and provide technical support for radar imaging, echo simulation, etc.

Description

Technical Field

[0001] The present invention relates to the field of radar detection technology, and in particular to a method for calculating a transmission path of a satellite-borne ice-detection synthetic aperture radar, a computer device, and a computer-readable storage medium. Background Art

[0002] Since the last century, due to factors such as global warming, the melting of the polar ice caps has intensified, directly leading to rising global sea levels and posing a huge threat to human survival. In order to fully understand the relationship between the polar regions and global climate change, countries around the world have begun to conduct scientific expeditions to the polar regions.

[0003] In the 1960s, ice radar systems were used to detect the Antarctic ice sheet. After nearly 60 years of development, ice radar now plays an important role in ice sheet detection research. At present, there are two main types of ice radars: airborne and vehicle-mounted. Spaceborne Synthetic Aperture Radar (SAR) is an active remote sensing system that is carried on a satellite platform and works in the microwave band. Spaceborne SAR is not restricted by factors such as sunlight, weather, and geography, and can achieve all-day and all-weather earth observation. The use of spaceborne downward-looking ice synthetic aperture radar is expected to conduct more in-depth observations and research on scenes such as polar glaciers.

[0004] Different from detecting conventional ground targets, when detecting targets inside ice, the electromagnetic waves emitted by the radar need to penetrate the interior of the ice layer. Due to the different dielectric constants between the ice medium and the air medium, the electromagnetic waves are deflected at the ice surface. Determining the ice radar transmission path by subtracting the conventional satellite spatial position from the target spatial position will affect the accuracy of the measurement results. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] The technical problem to be solved by the present invention is to solve the problem in the prior art that the inaccurate solution of the ice radar transmission path leads to poor accuracy of radar detection results.

[0007] (II) Technical solution

[0008] In order to solve the above technical problems, the present invention provides a method for calculating the transmission path of a spaceborne ice detection synthetic aperture radar, comprising:

[0009] Acquiring earth model parameters, system parameters of a spaceborne ice-penetrating synthetic aperture radar, and echo simulation parameters; the echo simulation parameters include an azimuth time sequence, an antenna position sequence in a rotating geocentric coordinate system, and a target position in the ice;

[0010] In the area to be detected, the medium above the earth's surface is the air medium and the medium below the earth's surface is the ice medium. For each azimuth moment, the geocentric angle corresponding to the corresponding transmission path in the ice medium is solved, and then the length of the transmission path in the air medium and the ice medium is determined respectively; the transmission path connects the corresponding antenna position and the target position in the ice, and is located within the beam range of the transmitting antenna.

[0011] Optionally, for an azimuth moment, solving the geocentric angle α2 corresponding to the corresponding transmission path in the ice medium includes:

[0012] Calculate the distances from the antenna S to the center of the earth O, the distances from the target P2 in the ice to the center of the earth O, and the distances from the antenna S to the target P2 in the ice, and calculate the geocentric angle α corresponding to the antenna S and the target P2 in the ice;

[0013] Based on the earth model parameters and the corresponding antenna position, the local radius R of the sub-satellite point of antenna S is calculated. L ;

[0014] Assume that the transmission path passes through the ice surface incident point P1, and the distance from the ice surface incident point P1 to the center of the earth O is equal to the local radius R of the sub-satellite point of the antenna S. L Equal, calculate the ice surface incident angle θ at the ice surface incident point P1 respectively i1 Sine of sinθ i1 and the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 Expression of

[0015] According to the refraction theorem, based on sine sinθ i1 and sine θ i2 The expression of the ratio of the dielectric constants of the ice medium to the air medium, n1, is obtained;

[0016] Based on the distance from the antenna S to the center of the earth O, the distance from the target P2 in the ice to the center of the earth O, the distance from the ice surface incident point P1 to the center of the earth O and the geocentric angle α, the geocentric angle α2 corresponding to the transmission path in the ice medium is calculated according to the expression of the ratio n1 of the dielectric constants of the ice medium and the air medium.

[0017] Optionally, the distance between the antenna S and the center of the earth O is calculated as follows:

[0018]

[0019] Among them, R s (t i )=[R sxi ,R syi ,R szi ] represents the i-th (i=1,2,…,N a ) position time t iThe position coordinates of the corresponding antenna S, N a Indicates the number of sampling points in azimuth;

[0020] The distance between the target P2 in the ice and the center of the earth O is calculated as follows:

[0021]

[0022] Among them, [P 2x ,P 2y ,P 2z ] represents the position coordinates of the target P2 in the ice;

[0023] The distance between the computing antenna S and the target P2 in the ice is expressed as:

[0024]

[0025] The calculation of the geocentric angle α between the antenna S and the target P2 in the ice is expressed as:

[0026]

[0027] Optionally, the local radius R of the sub-satellite point of the computing antenna S is L ,include:

[0028] Calculate the latitude Φ of the subsatellite point of antenna S s , the expression is:

[0029]

[0030] Calculate the longitude Ψ of the subsatellite point of antenna S s , the expression is:

[0031]

[0032] Get the local radius R of the subsatellite point L :

[0033]

[0034] Among them, R e is the Earth's equatorial radius, R p is the polar radius of the Earth ellipsoid.

[0035] Optionally, calculate the ice surface incident angle θ at the ice surface incident point P1 i1 Sine of sinθ i1 Expressions include:

[0036]

[0037] α1 represents the geocentric angle corresponding to the transmission path in the air medium, α=α1+α2;

[0038] Calculate the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 Expressions include:

[0039]

[0040] The expression for obtaining the ratio n1 of the dielectric constants of the ice medium and the air medium includes:

[0041] Ice internal refraction angle θ t1 and the incident angle θ of the target P2 in the ice i2 The relationship between t1 =θ i2 -α2, we get the internal refraction angle θ of ice t1 Sine of sinθ t1 The expression is:

[0042]

[0043] According to the refraction theorem, the expression of the ratio of the dielectric constants n1 of the ice medium to the air medium is:

[0044]

[0045] Optionally, calculating the geocentric angle α2 corresponding to the transmission path in the ice medium includes:

[0046] Assume that the geocentric angle α2 is small enough, θ t1 =θ i2 -α2≈θ i2 , then the expression of the ratio of the dielectric constants of the ice medium to the air medium n1 is:

[0047]

[0048] Take the square of both sides of the above expression and set x = sinα2, then:

[0049]

[0050] Assume x is small enough, then When the ice thickness d2 = R L -R tg is not equal to zero, the distance from the ice target P2 to the center of the earth O is less than the local radius R of the sub-satellite point L , then:

[0051]

[0052] Solve sinα2 and then obtain the geocentric angle α2 corresponding to the transmission path in the ice medium.

[0053] Optionally, the length R of the transmission path in the air medium is determined respectively Tair and the length R in the ice medium Tice ,include:

[0054]

[0055]

[0056] Optionally, if the spaceborne down-line ice-penetrating synthetic aperture radar is a dual-station radar including a transmitting antenna and a receiving antenna, then for each azimuth time, the corresponding transmission paths of the transmitting antenna and the receiving antenna are solved respectively, and the final transmission path is obtained by adding them;

[0057] If the satellite-borne down-line ice-penetrating synthetic aperture radar is a single-station radar with a common transmit and receive antenna, then for each azimuth moment, the final transmission path is twice the one-way transmission path.

[0058] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the above-mentioned method for calculating the transmission path of a satellite-borne ice-detection synthetic aperture radar are implemented.

[0059] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned method for calculating the transmission path of a satellite-borne ice-detection synthetic aperture radar are implemented.

[0060] (III) Beneficial effects

[0061] The above technical scheme of the present invention has the following advantages: the present invention provides a method for calculating the transmission path of a satellite-borne ice-penetrating synthetic aperture radar, a computer device and a computer-readable storage medium. The present invention takes into account the problem that the ice radar needs to pass through two different media, air and ice, when detecting targets in ice. The area above the earth's surface is regarded as an air medium area, and the area below the earth's surface is regarded as an ice medium area. Based on the geometric relationship and the law of refraction, the length of the transmission path in the air medium and the ice medium is determined respectively, and the one-way transmission path of the satellite-borne ice-penetrating synthetic aperture radar is obtained. The present invention can determine the transmission path more accurately and provide technical support for radar imaging, echo simulation, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a geometrical diagram of a target observed by a spaceborne ice-penetrating synthetic aperture radar;

[0063] Figure 2 It is a schematic diagram of the transmission path from the launch satellite to the target inside the ice in a space-borne down-line ice-penetrating synthetic aperture radar;

[0064] Figure 3 It is a schematic diagram of the steps of a method for calculating a transmission path of a space-borne ice-detection synthetic aperture radar in an embodiment of the present invention;

[0065] Figure 4 This is a flow chart of another method for calculating a transmission path of a spaceborne down-line ice detection synthetic aperture radar in an embodiment of the present invention;

[0066] Figure 5 A method for calculating the transmission path of a satellite-borne ice-detection synthetic aperture radar in an embodiment of the present invention is shown to solve the slant range error from the transmitting satellite to the target;

[0067] Figure 6 A satellite-borne ice-detection synthetic aperture radar transmission path calculation method for solving the slant range error from the receiving satellite to the target in an embodiment of the present invention is shown.

[0068] Figure 7 A method for calculating the transmission path of a satellite-borne ice-detection synthetic aperture radar in an embodiment of the present invention is shown for solving the slant range error from a transmitting and receiving satellite to a target. DETAILED DESCRIPTION

[0069] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] Figure 1 This is a geometric diagram of a target observed by a satellite-borne ice-penetrating synthetic aperture radar. In order to obtain a more accurate ice radar transmission path, combined with the earth model, the present invention assumes that the earth's surface is an air medium area with a dielectric constant of ε1, and the area below the earth's surface is an ice medium area with a dielectric constant of ε2. Figure 1 As shown, for a dual-station radar, two satellites are respectively equipped with a transmitting antenna and a receiving antenna (respectively marked with S and Q). The transmitting antenna preferably uses a reflector antenna, and the receiving antenna preferably uses a half-wavelength dipole antenna, which can ensure that the echo signals within the beam range of the transmitting antenna can be received by the receiving antenna, that is, the transmitting antenna beam is contained in the receiving antenna beam.

[0071] Figure 2 Taking the transmitting satellite (i.e., the satellite equipped with the transmitting antenna) as an example, the geometric transmission path from the transmitting satellite to the target P2 in the ice in the air medium and the ice medium is given. In fact, the transmission relationship between the receiving satellite (i.e., the satellite equipped with the receiving antenna) and the target is the same, but the transmission direction is opposite. Figure 2 As shown in the figure, O represents the center of the earth. The low-frequency microwave signal emitted by the transmitting antenna S carried by the transmitting satellite passes through point P1 on the interface between air and ice. The incident angle of the ice surface in the air medium is θ i1 , the internal refraction angle of ice in the ice medium is θ t1 , the microwave signal propagates in the ice medium and irradiates the target P2 in the ice. The incident angle at the target point is θ i2 The geocentric angle formed by the antenna S, the boundary point P1 and the center of the earth O is α1, which is the geocentric angle corresponding to the transmission path in the air medium. The geocentric angle formed by the points P1, P2 and the center of the earth O is α2, which is the geocentric angle corresponding to the transmission path in the ice medium.

[0072] like Figure 3 As shown, an embodiment of the present invention provides a method for calculating a transmission path of a spaceborne ice detection synthetic aperture radar, including:

[0073] Step 300, obtain the earth model parameters, the system parameters of the spaceborne ice-penetrating synthetic aperture radar, and the echo simulation parameters. The echo simulation parameters include the azimuth time sequence, the antenna position sequence in the rotating geocentric coordinate system, and the target position in the ice. The system parameters include the operating wavelength λ, the transmitting antenna diameter (or the transmitting antenna azimuth length) L Ta , which can be used to determine the antenna beam range and perform echo simulation.

[0074] The earth model can be obtained by existing technology [R e ,R p ], where R e is the Earth's equatorial radius, R p is the polar radius of the earth ellipsoid. Assume that the first azimuth time and the last azimuth time of the synthetic aperture radar echo are t1 and N a is the number of sampling points in the azimuth direction. All coordinates are in the rotating geocentric coordinate system, the coordinates of the center of the earth O are [0,0,0], R s (t i )=[R sxi ,R syi ,R szi ] represents the i-th (i=1,2,…,N a ) position time t i The coordinate position of the corresponding antenna S, that is, the position of the satellite carrying the antenna S, {R s (t i )} is the antenna position sequence in the rotating geocentric coordinate system, and the coordinates of the target P2 in the ice are [P 2x ,P 2y ,P 2z ].

[0075] Step 302, in the Antarctic, the Arctic or other ice-covered areas to be detected, with the air medium above the earth's surface and the ice medium below the earth's surface, for each azimuth moment, based on the earth model parameters, the system parameters of the satellite-borne down-line ice-penetrating synthetic aperture radar and the echo simulation parameters, the geocentric angle α2 corresponding to the corresponding transmission path in the ice medium is solved, and then the lengths of the transmission path in the air medium and the ice medium are determined respectively; for an azimuth moment, the transmission path connects the antenna position corresponding to the azimuth moment and the target position in the ice, and is located within the beam range of the transmitting antenna to ensure that the target in the ice can be detected.

[0076] Different from the prior art that directly determines the transmission path (or slant range) by subtracting the satellite spatial position from the target spatial position, the present invention takes into account the particularity of ice radar detection targets, establishes a dual-medium model, and calculates and solves the transmission path in the air medium and the ice medium based on the earth model parameters, the system parameters of the satellite-borne down-line ice-detecting synthetic aperture radar, and the echo simulation parameters, and finally obtains a one-way transmission path that is closer to the actual situation. The present invention can improve the accuracy of calculating the ice radar transmission path and provide technical support for radar imaging, echo simulation, etc.

[0077] Preferably, in the method, for a position time t i , solve the geocentric angle α2 corresponding to the corresponding transmission path in the ice medium, specifically including:

[0078] Calculate the distances from the antenna S to the center of the earth O, the distances from the target P2 in the ice to the center of the earth O, and the distances from the antenna S to the target P2 in the ice, and calculate the geocentric angle α corresponding to the antenna S and the target P2 in the ice; the geocentric angle α is the geocentric angle ∠SOP2 formed by the antenna S, the target P2 in the ice, and the center of the earth O;

[0079] Based on the earth model parameters and the corresponding antenna position, the local radius R of the sub-satellite point of antenna S at this azimuth is calculated. L ;

[0080] Assume that the transmission path passes through the ice surface incident point P1, and the distance from the ice surface incident point P1 to the center of the earth O is equal to the local radius R of the sub-satellite point of the antenna S. L Equal, calculate the ice surface incident angle θ at the ice surface incident point P1 respectively i1 Sine of sinθ i1 The expression of and the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 The two expressions are related to the parameter α2 to be solved;

[0081] According to the refraction theorem, based on sine sinθ i1 and sine θ i2The expression of the ratio of the dielectric constants of the ice medium and the air medium, n1, is obtained; the parameter α2 still needs to be solved in this expression;

[0082] Based on the distance from the antenna S to the center of the earth O, the distance from the target P2 in the ice to the center of the earth O, the distance from the ice surface incident point P1 to the center of the earth O and the geocentric angle α, the geocentric angle α2 corresponding to the transmission path in the ice medium is calculated according to the expression of the ratio n1 of the dielectric constants of the ice medium and the air medium.

[0083] Furthermore, at the i-th azimuth time t i , calculate the distance from antenna S to the center of the earth O (or the distance between antenna S and the center of the earth O), the expression is:

[0084]

[0085] Calculate the distance from the target P2 in the ice to the center of the earth O (or the distance between the target P2 in the ice and the center of the earth O), the expression is:

[0086]

[0087] R L is the local radius of the sub-satellite point of antenna S, d2 is the thickness of the ice layer (i.e., the depth of the target in the ice), and d1 represents the distance from antenna S to the earth's surface.

[0088] Calculate the distance from antenna S to target P2 in the ice (or the distance between antenna S and target P2 in the ice), the expression is:

[0089]

[0090] Based on the above three distances and the triangular cosine theorem, the geocentric angle α formed by the transmitting antenna S, the target P2 in the ice and the center of the earth O is calculated. The expression is:

[0091]

[0092] Further, calculate the local radius R of the sub-satellite point of antenna S L ,include:

[0093] Calculate the latitude Φ of the sub-satellite point of antenna S s , the formula is:

[0094]

[0095] Calculate the longitude Ψ of the sub-satellite point of antenna S s , the formula is:

[0096]

[0097] Then we can get the local radius R of the sub-satellite point of antenna S:L for:

[0098]

[0099] like Figure 2 As shown, according to the earth ellipsoid model, it can be considered that the distance from the point near the subsatellite point to the center of the earth is equal to the local radius R of the subsatellite point. L Therefore, the distance between the ice surface incident point P1 and the center of the earth O can be approximately expressed as:

[0100]

[0101] Further, calculate the ice surface incident angle θ at the ice surface incident point P1 i1 Sine of sinθ i1 The expression of can be obtained according to the geometric relationship:

[0102]

[0103] Represents the distance between the ice surface incident point P1 and the antenna S.

[0104] Calculate the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 An expression such as Figure 2 As shown, according to the geometric relationship:

[0105]

[0106] It represents the distance between the incident point P1 on the ice surface and the target P2 inside the ice.

[0107] The relationship between the geocentric angle α1, geocentric angle α2 and geocentric angle α is:

[0108] α=α1+α2 (11)

[0109] The geocentric angle α is known, and the ice surface incident angle θ i1 Sine of sinθ i1 The expression of the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 The expressions of are all related to the parameter θ2 to be solved.

[0110] The expression of the ratio of the dielectric constants of the ice medium to the air medium, n1, is obtained, including:

[0111] Ice internal refraction angle θ t1 and the incident angle θ of the target P2 in the ice i2 The relationship between them is:

[0112] θt1 =θ i2 -α2 (12)

[0113] According to formula (10) and formula (12), the internal refraction angle θ of ice is obtained t1 Sine of sinθ t1 The expression is:

[0114]

[0115] According to the refraction theorem, the incident angle θ on the ice surface i1 and the internal refraction angle θ t1 The ratio is equal to the quadratic root of the ratio of the dielectric constants of the two media, that is:

[0116]

[0117] Substituting formulas (9), (11) and (13) into formula (14), we can obtain the expression of the ratio of the dielectric constants n1 of the ice medium to the air medium:

[0118]

[0119] It can be seen from formula (15) that the expression has only one unknown variable α2. In one embodiment, the parameter α2 can be solved using the solve function in Matlab software, which is an accurate solution.

[0120] Preferably, the present invention further proposes an implementation method for quickly solving the geocentric angle α2 (approximate solution). In the implementation method of the approximate solution, solving the geocentric angle α2 corresponding to the transmission path in the ice medium includes:

[0121] When the local central angle α2 is small enough, we can get:

[0122] θ t1 =θ i2 -α2≈θ i2 (16)Therefore, formula (15) can be rewritten as:

[0123]

[0124] In order to obtain a single variable equation, square both sides of the above formula (17) and set x = sinα2, then:

[0125]

[0126] Since x is a very small value, we have When the ice thickness d2 = R L -R tg When it is not equal to zero, the distance from the ice target P2 to the center of the earth O is less than the local radius R of the sub-satellite pointL , rearranging formula (18) yields a quintic equation about x:

[0127]

[0128] With the expression of the quintic equation in formula (19), we can directly solve sinα2 and then obtain the geocentric angle α2 corresponding to the transmission path in the ice medium.

[0129] By adopting the above implementation, the roots function of Matlab software can be used to solve sinα2. Comparing the two implementations of exact solution and approximate solution, the operation speed has a difference of nearly 1000 times due to the different selection of Matlab software functions. The implementation method of quickly solving the geocentric angle α2 (approximate solution) provided by the present invention is more efficient and can effectively save calculation time.

[0130] Furthermore, the length of the transmission path in the air medium (i.e., the air transmission length) R is determined by the geocentric angle α1, the geocentric angle α2, and the triangular cosine theorem. Tair ,include:

[0131]

[0132] Determine the length of the transmission path in the ice medium (i.e., the transmission length in ice) R Tice ,include:

[0133]

[0134] Optionally, if the spaceborne down-line ice-penetrating synthetic aperture radar is a dual-station radar including a transmitting antenna and a receiving antenna, then for each azimuth time, the corresponding transmission paths of the transmitting antenna and the receiving antenna are solved respectively, and the final transmission path is obtained by adding them;

[0135] If the satellite-borne down-line ice-penetrating synthetic aperture radar is a single-station radar with a common transmit and receive antenna, then for each azimuth moment, the final transmission path is twice the one-way transmission path.

[0136] like Figure 4 As shown, the present invention also provides a method for calculating the transmission path of a satellite-borne downward-looking ice-penetrating synthetic aperture radar, which is used to solve the two-way transmission path of the satellite-borne downward-looking dual-station ice-penetrating synthetic aperture radar. The setting of the target P2 in the ice can be directly illuminated by the range beams of the transmitting antenna S and the receiving antenna Q at the same time, and only needs to consider whether it can be illuminated by the azimuth beams of the transmitting antenna S and the receiving antenna Q at the same time. The method includes:

[0137] Step S1, obtaining earth model parameters, system parameters of a satellite-borne down-line ice-detection synthetic aperture radar, and echo simulation parameters;

[0138] Step S2: at the i-th position time t i , calculate the geocentric angle α formed by the transmitting antenna S, the target P2 in the ice and the center of the earth O, and the local radius R of the sub-satellite point of the transmitting antenna S L ;

[0139] Step S3: Assume that the transmission path passes through the ice surface incident point P1, the geocentric angle α1 corresponding to the transmission path in the air medium is ∠SOP1, and the geocentric angle α2 corresponding to the transmission path in the ice medium is ∠P1OP2, and the ice surface incident angle θ is derived respectively. i1 Sine of sinθ i1 and the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 ;

[0140] Step S4, according to the refraction theorem, approximately solve sinα2 by a quintic equation, and calculate α1 and α2;

[0141] Step S5: Calculate the length R of the transmission path in the air medium using α1, α2 and the trigonometric cosine theorem. Tair and the length R of the transmission path in the ice medium Tice ;

[0142] Step S6: Referring to Step S1 to Step S5, the length R of the transmission path from the target P2 in the ice to the receiving antenna Q in the air medium is calculated. Tair and the length R in the ice medium Tice .

[0143] Step S7: at the i-th position time t i , determine whether the target P2 in the ice is illuminated by the azimuth beam of the transmitting antenna and the azimuth beam of the receiving antenna at the same time.

[0144] Take the example of whether the target P2 is illuminated by the azimuth beam of the transmitting antenna. The azimuth beam width of the transmitting antenna is the ratio of the wavelength to the diameter of the transmitting antenna:

[0145]

[0146] The longitude and latitude of the subsatellite point of the transmitting antenna S are shown in formula (5) and formula (6). Similarly, the latitude of the target P2 and longitude The formulas are:

[0147]

[0148]

[0149] Latitude of ice entry point P1 and longitude They are:

[0150]

[0151]

[0152] Therefore, the coordinates of the ice surface incident point P1 are:

[0153]

[0154] The vector from the transmitting antenna S to the incident point P1 on the ice surface is Refer to the book "Synthetic Aperture Radar Satellite" by Wei Zhongquan et al., and convert the vector Transformed from the geocentric coordinate system to the antenna coordinate system, the vector in the antenna coordinate system is Then the azimuth ζ a The calculation formula is:

[0155]

[0156] Therefore, at the i-th azimuth time t i , when the transmitting antenna S to the target P2 is within the azimuth beam illumination range of the transmitting antenna, the following conditions are satisfied:

[0157]

[0158] If they can be irradiated at the same time, it means that an echo signal can be generated, otherwise no echo signal is generated.

[0159] Similarly, calculate whether the target P2 in the ice from the receiving antenna Q is within the azimuth beam illumination range of the receiving antenna.

[0160] Then, determine whether i is less than the number of azimuth sampling points N a If the condition is met, then i=i+1 and the loop continues to execute steps S2 to S7; otherwise, the loop is exited and the calculation is terminated.

[0161] The present invention also verifies the effectiveness of the proposed method. In a specific implementation, the orbital parameters of the transmitting satellite equipped with the transmitting antenna S and the receiving satellite equipped with the receiving antenna Q are shown in Table 1. According to the orbital parameters, the transmitting antenna S and the receiving antenna Q can realize the satellite-borne downward-looking dual-station observation near the polar region. The transmitting antenna adopts a reflector antenna, and the receiving antenna adopts a half-wavelength dipole antenna.

[0162] Table 1 Orbital parameters of the transmitting and receiving satellites

[0163] Parameter name Numeric Orbital semi-major axis 6806.137Km Argument of perigee 0° Ascending node right ascension 120° Eccentricity of the satellite orbit 0 Receive satellite orbit eccentricity 20e-6 Launch satellite orbit inclination 90° Receiving satellite orbit inclination 90.028° Simulation start time 1380s

[0164] The relevant parameters for the calculation of the transmission path of the spaceborne ice detection synthetic aperture radar are shown in Table 2:

[0165] Table 2 Parameters related to the calculation of the transmission path of the spaceborne ice detection synthetic aperture radar

[0166] Parameter name Numeric Transmitting antenna diameter 40m Pulse repetition interval 5.56e-04s Azimuth sampling points 6096 Earth's equatorial radius 6378137m Polar radius of the Earth's ellipsoid 6356752.315m

[0167] At the simulation center, three targets in the ice were set 5000m away from the sub-satellite point of the transmitting antenna S (5000m in the heading) and perpendicular to the flight direction of the transmitting satellite. They were located at 3900m, 2000m, and 100m in the ice, respectively. The longitude, latitude, and depth in the ice were:

[0168] (116.8567471479693°,89.011722494825293°,3900m)

[0169] (116.8567471479693°,89.011722494825293°,2000m)

[0170] (116.8567471479693°,89.011722494825293°,100m).

[0171] like Figures 5 to 7 As shown, the present invention uses two calculation methods, namely, approximate solution of a quintic equation and exact solution of the equation, to compare the transmission path error (i.e., slant range error) from the transceiver antenna to the target. Figure 5 The figure shows the one-way slant range error from the satellite to the target obtained by the approximate solution relative to the exact solution. The slant range error is closest to 0 when the target is 3900m inside the ice, followed by the slant range error when the target is 2000m inside the ice. The maximum error occurs when the target is 100m inside the ice. Figure 6 The figure shows the one-way slant range error from the receiving satellite to the target obtained by the approximate solution relative to the exact solution. The slant range error is closest to 0 when the target is 3900m inside the ice, followed by the slant range error when the target is 2000m inside the ice. The maximum error occurs when the target is 100m inside the ice. Figure 7 The two-way slant range errors from the transmitting satellite to the target and from the receiving satellite to the target obtained by the approximate solution relative to the exact solution are shown. The slant range error corresponding to the target being 3900m in the ice is closest to 0, followed by the slant range error corresponding to the target being 2000m in the ice, and the maximum error occurs when the target is 100m in the ice. Figures 5 to 7It can be seen that the maximum slant range error caused by solving the quintic equation is 1.86e-4m (the target is 100m deep in the ice). The phase error caused by the slant range error must be less than π / 4, so ΔR≤πλ / 8=0.125m. It can be seen that the slant range error of 1.86e-4m caused by solving the quintic equation is much smaller than 0.125m, thus ensuring the calculation accuracy of the two-way slant range. At the same time, the establishment of the quintic equation can use the roots function in the MATLAB software, which significantly improves the calculation efficiency compared to the accurate solution using the solve function in the MATLAB software.

[0172] An embodiment of the present invention further provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a method for calculating a transmission path of a satellite-borne downward-looking ice-detection synthetic aperture radar in any embodiment of the present invention is implemented.

[0173] An embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the processor executes a method for calculating a transmission path of a satellite-borne down-line ice-detection synthetic aperture radar in any embodiment of the present invention.

[0174] Specifically, a system or device equipped with a storage medium can be provided, on which software program code that implements the functions of any of the above-mentioned embodiments is stored, and a computer (or CPU or MPU) of the system or device can be enabled to read and execute the program code stored in the storage medium.

[0175] In this case, the program code itself read from the storage medium can realize the function of any one of the above-mentioned embodiments, and thus the program code and the storage medium storing the program code constitute a part of the present invention.

[0176] The storage medium embodiments for providing the program code include a floppy disk, a hard disk, a magneto-optical disk, an optical disk (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), a magnetic tape, a non-volatile memory card, and a ROM. Alternatively, the program code can be downloaded from a server computer by a communication network.

[0177] In addition, it should be clear that the functions of any of the above embodiments can be implemented not only by executing the program code read by the computer, but also by enabling an operating system operating on the computer to complete part or all of the actual operations based on instructions from the program code.

[0178] In addition, it can be understood that the program code read from the storage medium is written to a memory provided in an expansion board inserted into the computer or to a memory provided in an expansion module connected to the computer, and then based on the instructions of the program code, a CPU installed on the expansion board or expansion module is enabled to perform part or all of the actual operations, thereby realizing the functions of any of the above-mentioned embodiments.

[0179] In summary, the present invention provides a method for calculating the transmission path of a satellite-borne downward-looking ice-penetrating synthetic aperture radar, a computer device, and a computer-readable storage medium; the present invention is based on a low-orbit satellite looking downward to observe targets in the ice, taking into account the relationship between parameters such as the actual orbital altitude, the range beam width, and the maximum ice penetration depth, and the refraction angle from air to the ice is approximately the incident angle of the target in the ice, and a single-variable quintic equation is established using the Snell refraction theorem. Finally, the roots of the Matlab function library can be used to directly and quickly solve the problem. By comparison, it can be seen that the approximate solution of the quintic equation is about 1000 times faster than the direct accurate solution using the solve function, and the slant range error is also very small, which ensures the accuracy of the transmission path calculation.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the transmission path of a spaceborne ice detection synthetic aperture radar, characterized in that: include: Obtain earth model parameters, system parameters of satellite-borne ice-detection synthetic aperture radar, and echo simulation parameters; The echo simulation parameters include an azimuth time sequence, an antenna position sequence in a rotating geocentric coordinate system, and a target position in the ice; In the area to be detected, the air medium is above the earth's surface and the ice medium is below the earth's surface. For each azimuth moment, the geocentric angle corresponding to the corresponding transmission path in the ice medium is solved, and then the length of the transmission path in the air medium and the ice medium is determined respectively; the transmission path connects the corresponding antenna position and the target position in the ice, and is located within the beam range of the transmitting antenna; for an azimuth moment, the geocentric angle α2 corresponding to the corresponding transmission path in the ice medium is solved, including: Calculate the distances from the antenna S to the center of the earth O, the distances from the target P2 in the ice to the center of the earth O, and the distances from the antenna S to the target P2 in the ice, and calculate the geocentric angle α corresponding to the antenna S and the target P2 in the ice; Based on the earth model parameters and the corresponding antenna position, the local radius R of the sub-satellite point of antenna S is calculated. L ; Assume that the transmission path passes through the ice surface incident point P1, and the distance from the ice surface incident point P1 to the center of the earth O is equal to the local radius R of the sub-satellite point of the antenna S. L Equal, calculate the ice surface incident angle θ at the ice surface incident point P1 respectively i1 Sine of sinθ i1 and the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 Expression of According to the refraction theorem, based on sine sinθ i1 and sine θ i2 The expression of the ratio of the dielectric constants of the ice medium to the air medium, n1, is obtained; Based on the distance from the antenna S to the center of the earth O, the distance from the target P2 in the ice to the center of the earth O, the distance from the incident point P1 on the ice surface to the center of the earth O and the geocentric angle α, according to the expression of the ratio of the dielectric constants of the ice medium to the air medium n1, the geocentric angle α2 corresponding to the transmission path in the ice medium is solved; The distance from the antenna S to the center of the earth O is expressed as: Among them, [R sxi ,R syi ,R szi ] represents the i-th position at time t i The position coordinates of the corresponding antenna S, i = 1, 2, ..., N a ; N a Indicates the number of sampling points in azimuth; The distance from the ice target P2 to the center of the earth O is expressed as: Among them, [P 2x ,P 2y ,P 2z ] represents the position coordinates of the target P2 in the ice; The distance from the antenna S to the target P2 in the ice is expressed as: The geocentric angle α between the antenna S and the target P2 in the ice is expressed as: The local radius R of the sub-satellite point of the calculation antenna S L ,include: Calculate the latitude Φ of the subsatellite point of antenna S s , the expression is: Calculate the longitude Ψ of the subsatellite point of antenna S s , the expression is: Get the local radius R of the subsatellite point L : Among them, R e is the Earth's equatorial radius, R p is the polar radius of the Earth ellipsoid; Calculate the incident angle θ of the ice surface at the incident point P1 i1 Sine of sinθ i1 Expressions include: α1 represents the geocentric angle corresponding to the transmission path in the air medium, α=α1+α2; Calculate the incident angle θ of the target P2 in the ice i2 Sine of sinθ i2 Expressions include: The expression for obtaining the ratio n1 of the dielectric constants of the ice medium and the air medium includes: Ice internal refraction angle θ t1 and the incident angle θ of the target P2 in the ice i2 The relationship between t1 =θ i2 -α2, we get the internal refraction angle θ of ice t1 Sine of sinθ t1 The expression is: According to the refraction theorem, the expression of the ratio of the dielectric constants n1 of the ice medium to the air medium is: The method of calculating the geocentric angle α2 corresponding to the transmission path in the ice medium includes: Assume that the geocentric angle α2 is small enough, θ t1 =θ i2 -α2≈θ i2 , then the expression of the ratio of the dielectric constants of the ice medium to the air medium n1 is: Take the square of both sides of the above expression and set x = sinα2, then: Assume x is small enough, then When the ice thickness d2 = R L -R tg is not equal to zero, the distance from the ice target P2 to the center of the earth O is less than the local radius R of the sub-satellite point L , then: Solve sinα2 to obtain the geocentric angle α2 corresponding to the transmission path in the ice medium; Determine the length R of the transmission path in the air medium respectively Tair and the length R in the ice medium Tice ,include:

2. The method according to claim 1, characterized in that If the spaceborne ice-penetrating synthetic aperture radar is a dual-station radar, including a transmitting antenna and a receiving antenna, then for each azimuth time, the corresponding transmission paths of the transmitting antenna and the receiving antenna are solved respectively, and the final transmission path is obtained by adding them; If the satellite-borne down-line ice-penetrating synthetic aperture radar is a single-station radar with a common transmit and receive antenna, then for each azimuth moment, the final transmission path is twice the one-way transmission path.

3. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method for calculating the transmission path of a space-borne ice-detection synthetic aperture radar as described in any one of claims 1 to 2 are implemented.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for calculating the transmission path of a space-borne ice-detection synthetic aperture radar as described in any one of claims 1 to 2 are implemented.

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