Method for the computer-assisted processing of SAR raw data

Abstract

The invention relates to a method for the computer-assisted processing of SAR raw data (RD) from a radar device (100) which flies over the earth's surface (GR) in an azimuth direction (x), wherein the SAR raw data (RD) represent radar echos of radar pulses (RP) during a one-time flight over an area of the earth's surface (GR), wherein the radar pulses (RP) are or have been emitted by the radar device (100) and the radar echos are or have been received by the radar device (100) as radar pulses reflected by the earth's surface (GR), wherein a) a first frequency range (FB1) of the Doppler spectrum (DS) having a first Doppler center frequency (ƒDC1) and a second frequency range (FB2) of the Doppler spectrum (DS) having a second Doppler center frequency (ƒDC2) are extracted from the SAR raw data (RD); b) a first SAR image (IM1) is ascertained from the first frequency range (FB1) and a second SAR image (IM2) is ascertained from the second frequency range (FB2); c) for a relevant image area (IA) of a number of image areas (IA) in the first SAR image (IM1), a shift value (∆χ) is determined which indicates by what magnitude the image content in the relevant image area (IA) from the first SAR image (IM1) is shifted in the azimuth direction (x) in relation to the same image content in a corresponding image area (IA) from the second SAR image (IM2), with the relevant image area (IA) and the corresponding image area (IA) representing the same surface area in relation to the azimuth direction (x) and the range direction (R); and d) a depth of snow (Zs) in the relevant image area (IA) is determined from the shift value (∆χ).

Description

[0001] Methods for computer-aided processing of SAR raw data

[0002] Description

[0003] The invention relates to a method for computer-aided processing of SAR raw data.

[0004] To determine water resources on the Earth's surface and analyze the effects of climate change, the snow depth and snow density on the Earth's surface, as well as the associated snow-water equivalent, are important parameters. The snow-water equivalent is defined as the height of the water column that would be obtained if all the ice in a corresponding layer of snow were to melt. Specifically, the snow-water equivalent is given by the following equation:

[0005] SWE denotes the snow-water equivalent, Z s is the snow depth, z is the vertical coordinate (coordinate in height direction) and p wis the volumetric mass density of water. s (z) the snow density (i.e. the volumetric mass density of the snow), which depends on the vertical coordinate z.

[0006] To determine the snow-water equivalent locally, pressure sensors, acoustic sensors, or gamma radiation sensors can be used. These sensors are positioned at the location where the snow-water equivalent is to be measured. However, these sensors only allow the snow-water equivalent to be determined at specific locations on the Earth's surface.

[0007] In addition, there are state-of-the-art methods that use remote sensing via passive microwave sensors on satellites to determine snow depths on the Earth's surface. However, these methods have poor spatial resolution in the kilometer range and low accuracy.

[0008] Furthermore, there are state-of-the-art experimental methods that use SAR systems to determine snow depths or corresponding snow-water equivalents on the Earth's surface. SAR systems (Synthetic Aperture Radar) enable remote sensing of the Earth's surface by detecting radar pulses reflected from the Earth's surface. These pulses are emitted by a radar device moving at a constant speed over the Earth's surface in a so-called azimuth direction. With appropriate processing, images of the Earth's surface can be obtained from the raw SAR data acquired by a SAR system.

[0009] To determine snow depths with SAR systems, differential SAR interferometry is currently used, as described, for example, in document [1]. Changes in snow depth or snow-water equivalent are determined by measuring a differential signal delay between two temporally separated SAR acquisitions from the same area of ​​the Earth's surface. The signal delay is caused by refraction at the snow surface and the reduced propagation speed of the radar beams in the snow and depends on the snow depth and snow density. Snow accumulation between two SAR acquisitions leads to a differential signal delay, from which the change in snow depth in the period between the two acquisitions can be determined.

[0010] Known SAR methods for determining snow depth have the disadvantage that they can only detect differences in snow depth, requiring multiple overflights over the same area of ​​the Earth's surface. This can lead to temporal decorrelation effects due to changes in the distribution of backscatterers in the detected area of ​​the Earth's surface. Furthermore, differential SAR interferometry uses phase measurements, which lead to a so-called 27t phase ambiguity, thus complicating the conversion of phase measurements into snow depth or the snow-water equivalent.

[0011] The object of the invention is to provide a method for computer-aided processing of SAR raw data, with which the snow depth of the area of ​​the earth's surface covered by the raw data can be determined in a simple manner from the SAR raw data.

[0012] This object is achieved by the method according to claim 1 and the device according to claim 8. Further developments of the invention are defined in the dependent claims.

[0013] The method according to the invention is used to process SAR raw data originating from a radar device that flies over the Earth's surface in an azimuth direction. The SAR raw data represent radar echoes from radar pulses during a single flyover of an area of ​​the Earth's surface. The radar pulses are or were emitted by the radar device, and the radar echoes are or were received by the radar device as radar pulses reflected from the Earth's surface. The emission and reception of the radar pulses, and in this sense the acquisition of the SAR raw data, can be a component of the method according to the invention. Likewise, the acquisition of the SAR raw data can be outside the scope of the method according to the invention, i.e., the method accesses already acquired SAR raw data. In one embodiment, the SAR raw data is already processed in the radar device or at the location of the radar device using the method according to the invention.Typically, however, the SAR raw data are transmitted to a ground station on the Earth's surface, where the inventive processing of the SAR raw data is then carried out.

[0014] In a manner known per se, the SAR raw data processed according to the invention comprises a plurality of data samples containing a Doppler spectrum. The Doppler spectrum results from the fact that the radar device moves during the acquisition of the SAR raw data, resulting in a phase variation of the acquired radar echoes. Each data sample in the SAR raw data corresponds to an azimuth position along the azimuth direction and a range position along a range direction, with the range direction running perpendicular to the azimuth direction.

[0015] In the method according to the invention, in step a), a first frequency range of the Doppler spectrum with a first Doppler center frequency and a second frequency range of the Doppler spectrum with a second Doppler center frequency are extracted from the SAR raw data. The first frequency range and the second frequency range of the Doppler spectrum are disjoint, i.e., the frequencies of the two frequency ranges do not overlap and their Doppler center frequencies differ. Step a) can be performed using known methods by applying appropriate frequency filters in the frequency range of the SAR raw data.

[0016] In step b) of the method according to the invention, a first SAR image is determined from the first frequency range using a conventional SAR processing technique. Similarly, in step b), a second SAR image is determined from the second frequency range using a conventional SAR processing technique. During SAR processing, the correspondingly focused SAR images are generated using range compression and azimuth compression.

[0017] In a step c) of the method according to the invention, a shift value is determined for a respective image region of a number of image regions in the first SAR image, which shift value indicates by how much the image content in the respective image region from the first SAR image is shifted in the azimuth direction compared to the same image content in a corresponding image region from the second SAR image. The respective image region in the first SAR image and the corresponding image region in the second SAR image represent the same area with respect to the azimuth direction and the range direction, i.e. the image regions have the same coordinates in the azimuth and range directions and also the same extent along these coordinates. Preferably, the first SAR image and correspondingly also the second SAR image are divided into a plurality of image regions, for each of which a shift value is determined.Nevertheless, the first SAR image and the second SAR image can each represent an image area together.

[0018] Finally, the snow depth in the respective image area is determined from the displacement value determined in step c). The term "displacement value" is to be understood broadly. It is a quantity that represents an offset in the azimuth direction in corresponding SAR images. This quantity can be specified by a distance on the Earth's surface, but possibly also by a time offset (azimuth time) corresponding to the movement of the radar system, or by a phase value.

[0019] The method according to the invention is based on the finding that an azimuth shift of the image content in SAR images recorded for different frequency ranges in the Doppler spectrum has a direct relationship to the snow depth. The relationship between this azimuth shift and the snow depth, identified by the inventors, is explained in more detail in the detailed description. The method according to the invention has the great advantage that the absolute snow depth can be determined within the scope of a single overflight over the Earth's surface. Consequently, temporal decorrelation effects play no role. The method thus avoids the disadvantages of differential SAR interferometry, which can only determine changes in snow depth and requires the corresponding area on the Earth's surface to be overflown several times.Furthermore, the method according to the invention can achieve a good spatial resolution in the range of 100 m or less for the determination of corresponding snow depths.

[0020] The snow depth determined using the method according to the invention can be saved for later evaluation and, if necessary, output via a user interface. Furthermore, the snow depth can also be used to determine a value dependent on the snow depth, which in turn can be saved for later evaluation and, if necessary, output via a user interface. In a preferred embodiment, the snow-water equivalent is determined as the value dependent on the snow depth. The snow-water equivalent is a frequently used parameter to determine water resources on the Earth's surface or to analyze the effects of climate change. As already explained above, the snow-water equivalent is defined as the water depth that would exist if all the ice within a snow cover were to melt.

[0021] In a particularly preferred embodiment, the snow depth in step d) is determined as follows: where Z s is the snow depth; where s s is the real part of the relative dielectric permittivity of snow; where h is the flight altitude of the radar device above the snow surface; where 0i is the angle of incidence of the radar pulses in the respective image area; where 0 r is the angle of refraction of the radar pulses in the respective image area at the snow surface; where where Ax is the displacement value in meters in the azimuth direction; where v e is the azimuth velocity of the radar device; where f DC1 is the first Doppler center frequency; where f DC2 is the second Doppler center frequency; where f R a the Doppler rate without snow in the respective image area.

[0022] A derivation of the above equations can be found in the detailed description. As can be seen from the above equations, the snow depth Z s about the size depending on the displacement value Ax.

[0023] In addition to the shift value determined in step c) of the method according to the invention, all other quantities contained in the above formulas are known in advance or can be determined appropriately. For example, the angle of refraction can be determined using Snell's law from the angle of incidence of the radar radiation in the corresponding image area (see equation (2) in the detailed description). Likewise, the Doppler rate can be determined from known quantities (see equation (5) in the detailed description).

[0024] The method according to the invention can be applied to SAR raw data from current space missions. However, a special radar device is preferably used to acquire the SAR raw data, which enables efficient separation of the SAR raw data into two separate Doppler frequency ranges and generates a large separation between the two Doppler frequency ranges.The SAR raw data originates from a radar device comprising an antenna device that generates an antenna beam for transmitting and receiving radar radiation in a first beam direction and an antenna beam for transmitting and receiving radar radiation in a second beam direction (simultaneously). The first beam direction is inclined at a first angle of inclination relative to the plane perpendicular to the azimuth direction, and the second beam direction is inclined at a second angle of inclination relative to the plane perpendicular to the azimuth direction, with the first beam direction and the second beam direction differing from one another. With this setup, dedicated SAR raw data is acquired in two separate Doppler frequency ranges across different inclination angles. These inclination angles are also referred to as squint angles.The above-described first beam direction and the above-described second beam direction preferably each represent a main beam direction of the antenna device, wherein the main beam direction is the direction in which the greatest power is emitted within the corresponding antenna beam.

[0025] In a particularly preferred embodiment, the first inclination angle is a backward angle, so that the first beam direction lies behind the radar device in relation to the movement of the radar device in the azimuth direction. In contrast, the second inclination angle is a forward angle, so that the second beam direction lies in front of the radar device in relation to the movement of the radar device in the azimuth direction. In other words, the antenna beam in the first beam direction illuminates an area on the earth's surface that lies behind the radar device in the direction of flight, whereas the antenna beam in the second beam direction illuminates an area on the earth's surface that lies in front of the radar device in the direction of flight.

[0026] In a further preferred embodiment, the forward angle is between 2° and 40°, preferably between 5° and 25°, and particularly preferably between 15° and 25°. Likewise, the backward angle can be between 2° and 40°, preferably between 5° and 25°, and particularly preferably between 15° and 25°. The mentioned angle degrees refer to the smallest included angle between the first or second beam direction and the plane perpendicular to the azimuth direction. The mentioned angle ranges enable efficient separation of the SAR raw data into two frequency ranges with different Doppler center frequencies and a large distance between the two frequency ranges, thus enabling precise determination of the above shift value or the snow depth determined therefrom.

[0027] In a further preferred embodiment, the forward angle is the same as the backward angle, thereby simplifying the processing of the raw SAR data.

[0028] In addition to the method described above, the invention relates to a device for the computer-aided processing of SAR raw data which originate from a radar device which flies over the earth's surface in an azimuth direction, wherein the SAR raw data represent radar echoes of radar pulses during a single flyover over an area of ​​the earth's surface, wherein the radar pulses are or were emitted by the radar device and the radar echoes are or were received by the radar device as radar pulses reflected at the earth's surface, wherein the SAR raw data comprise a plurality of data samples which contain a Doppler spectrum, wherein a respective data sample belongs to an azimuth position along the azimuth direction and to a range position along a range direction, wherein the range direction is perpendicular to the azimuth direction.

[0029] The device according to the invention is designed to carry out the method according to the invention. In other words, the device includes a signal processing device with which steps a) to d) of the method of claim 1 can be carried out. In a particularly preferred embodiment, the device according to the invention is designed to carry out one or more preferred variants of the method according to the invention. Depending on the configuration, the radar device described above can belong to the device according to the invention, or the device according to the invention can also contain only the signal processing device for carrying out steps a) to d). The signal processing device can be provided on the platform on which the radar device is located. However, the signal processing device is preferably provided on the earth's surface, such asin a ground station where the raw SAR data transmitted to Earth is evaluated.

[0030] The invention further relates to a computer program product having a program code stored on a machine-readable carrier for carrying out the method according to the invention or one or more preferred variants of the method according to the invention when the program code is executed on a computer.

[0031] Furthermore, the invention relates to a computer program with a program code for carrying out the method according to the invention or one or more preferred variants of the method according to the invention when the program code is executed on a computer.

[0032] Embodiments of the invention are described in detail below with reference to the attached figures.

[0033] They show:

[0034] Fig. 1 is a schematic diagram explaining the SAR principle used in the invention;

[0035] Fig. 2 and Fig. 3 are schematic representations illustrating the effects of a snow layer on the acquisition of SAR raw data; Fig. 4 is a schematic representation illustrating the acquisition of SAR raw data according to an embodiment of the invention;

[0036] Fig. 5 is a diagram illustrating the steps of an embodiment of the method according to the invention; and

[0037] Fig. 6 to Fig. 10 diagrams which illustrate the results of an embodiment of the method according to the invention using a simulation.

[0038] Fig. 1 shows a schematic representation of a SAR radar device 100, which is indicated as a rectangular aperture and, depending on the design, comprises one or more antennas or one or more main antenna radiation directions. In the scenario shown, the radar device is located on a satellite (not shown) that moves at altitude h along the radar trajectory RT above the Earth's surface GR. The direction of the radar trajectory corresponds to the known azimuth direction, which is designated by reference symbol x in Fig. 1. Instead of moving the radar device using a satellite, it may also be possible to use another flying object, such as an aircraft.

[0039] The radar device 100 transmits radar pulses RP at successive pulse repetition intervals with a predetermined pulse repetition frequency in an oblique direction toward the Earth's surface GR. The majority of the energy of each radar pulse is directed toward the elliptical surface FP on the Earth's surface. This surface is typically referred to as the "footprint" of the radar device or the associated radar antenna.

[0040] According to Fig. 1, each radar pulse RP has a predetermined pulse duration T, so that the radar pulse has the spatial extent coT, where co corresponds to the speed of light. During a SAR measurement, radar echoes of the radar pulses RP scattered back from the Earth's surface are received and recorded by the SAR radar device 100 as they move along the path RT. In this way, information about the Earth's surface is detected in the swath SW. The radar device is designed such that it is configured both to emit radar pulses and to receive corresponding radar echoes. The radar echoes recorded by the radar device depend on the shape and nature of the Earth's surface and, with known downstream signal processing, enable the calculation of SAR images of the Earth's surface.

[0041] Prior to downstream signal processing, the acquired radar echoes are available as so-called SAR raw data following analog-to-digital conversion. This raw data is data samples containing the amplitude and phase of the sampled radar echoes. The raw data is arranged in a two-dimensional matrix, with one dimension of the matrix corresponding to the respective transmitted radar pulse (represented by a pulse number) and the other dimension of the matrix representing a time delay, which represents the time required for a sampled radar echo to propagate from the radar device to the Earth's surface and back to the radar device 100. In other words, this time represents the so-called slant range R, which corresponds to the distance between the radar device and the scattering point of the radar echo on the Earth's surface.This distance is therefore equivalent to a direction from which the scanned radar echo from the earth's surface GR reaches radar device 1.

[0042] The scenario in Fig. 1 illustrates the reflection of a radar echo at scattering point P on the Earth's surface. The slant range of this radar echo is denoted by Ro. The slant range is geometrically related to the so-called ground range (ground distance), which is denoted by y in Fig. 1 and represents the distance between the vertical projection of the radar trajectory RT onto the Earth's surface and the corresponding scattering point. The value of a slant range R can thus be unambiguously converted into the value of a corresponding ground range y.

[0043] As already mentioned, the raw SAR data undergoes downstream signal processing, also known as SAR processing. Depending on the design, this signal processing can already take place on the satellite, with the processed information then being sent to a ground station on the Earth's surface. It is also possible for the raw SAR data to be sent to a ground station without any further processing, with the ground station carrying out the post-processing to obtain corresponding SAR images from the raw data. Post-processing comprises two filter operations, which are carried out along the range direction R or y and along the azimuth direction x. The filter operation along the range direction is often referred to as range compression, and the filter operation along the azimuth direction is often referred to as azimuth compression.These operations focus the raw SAR data to calculate SAR images.

[0044] When acquiring SAR raw data, radar device 100 moves along the azimuth direction x, so that the corresponding point P on the Earth's surface is acquired multiple times from different positions relative to radar device 100. Depending on the relative position, the phase of the backscattered radar pulses varies, which corresponds to the well-known Doppler effect. The change in phase as a function of the azimuth position of radar device 100 relative to scattering point P is the well-known Doppler frequency. The SAR raw data thus contains a Doppler spectrum of Doppler frequencies in the frequency domain.

[0045] In the embodiment of the invention described here, the SAR raw data is processed in such a way that the snow depth or the snow-water equivalent for the Earth's surface detected by the SAR radar device can be determined directly in a single overflight. Before discussing an embodiment of the invention in detail, we will first explain, using Fig. 2, how the radar radiation emitted by a SAR radar device is altered by snow on the Earth's surface.

[0046] Fig. 2 shows, in the direction of view of an oncoming flying object (ie, in the direction opposite to the azimuth direction x in Fig. 1), the signal propagation of the radar radiation emitted by a SAR radar device 100 installed in the flying object. On the Earth's surface GR, there is snow with a snow depth Z s, where the surface of the snow is indicated by a dotted line L. The flight altitude of the radar device above the snow surface is denoted by h in Fig. 2.

[0047] The dashed arrow AR1 in Fig. 2 illustrates the propagation path of a radar beam to a point P on the Earth's surface when there is no snow. In contrast, the solid arrow AR2 illustrates the propagation path in the presence of snow with the snow depth Z sThe radar radiation partially penetrates the snow and interacts with it through absorption, scattering, refraction, and a reduced propagation speed. For a snow layer a few meters deep, absorption and scattering effects are negligible compared to the backscattered energy from the underlying earth's surface GR. In contrast, the effect of refraction and reduced propagation speed of the radar radiation is not negligible. The refraction leads to a deflection of the radar radiation falling on the snow at the snow surface L. According to Fig. 2, the angle of incidence of the radar radiation on the snow surface is denoted by 0^, whereas the angle of reflection or refraction of the radar radiation, reduced by refraction, is denoted by 0 rThe refraction of radar radiation is caused by the difference in dielectric permittivity between air and snow. In a well-known manner, the refraction is described by Snell's law of refraction, which is as follows: Here s denotes a or E S the real part of the relative dielectric permittivity of air or snow. The permittivity E a of air is approximately 1. The propagation speed c of radar radiation in snow is reduced compared to the speed of light c0in air and is as follows.

[0048] C = > ( 3 )

[0049] The real part of the relative permittivity E S of snow is a function of snow density p s .

[0050] In the context of the embodiment of the invention described below, the additional phase delay of the backscattered radar radiation caused by the snow layer, which has an effect on the Doppler frequency or the Doppler rate (ie the temporal change or derivative of the Doppler frequency), is used to obtain the snow depth of the snow layer or the snow-water equivalent.

[0051] During conventional SAR processing of raw SAR data, only air is assumed to be the propagation medium, without considering the effects of snow cover. This leads to a phase error along the azimuth direction between the recorded SAR signal and the signal after filtering during SAR processing. This phase error is used to determine the snow depth or snow-water equivalent.

[0052] If there is no snow on the Earth's surface, the phase of the radar signal along the azimuth direction for a point target detected by the SAR radar system is described in a conventional manner as follows: t az denotes the azimuth time (ie the relative displacement of the radar device with respect to the point target in azimuth direction), f0 is the center frequency of the radar signal, T0 is the travel time of the radar pulse from the radar device to the point target and back for the shortest distance between the radar device and the point target, ie at the azimuth time t az = 0. This corresponds to 2R0in Fig. 1. Furthermore, f R a the Doppler rate, i.e., the rate of change over time or the time derivative of the Doppler frequency. The index a denotes the case where there is no snow on the Earth's surface and the radar pulses propagate only through air.

[0053] In a well-known manner, the Doppler rate is approximately given by the following equation: v e is the effective speed between the radar device and the point target, A o is the wavelength of the radar pulses in air, and c0 is the propagation speed of the radar pulses in air (i.e., the speed of light). As defined above, r0,a is the travel time of a radar pulse for the shortest distance between the radar device and the point target, assuming there is no snow on the point target.

[0054] For a point target covered with snow and for the same running time T0 = T o,a of the radar pulse results in the Doppler rate f R s depending on the Doppler rate for the case without snow as follows:

[0055] The term takes into account the refraction at the snow surface and the reduced propagation speed in the snow. The term depends on the variables defined above and, in particular, the snow depth Z s as follows:

[0056] Equations (6) and (7) result from a geometric derivation of the change in the Doppler rate f R s compared to the Doppler rate f R a for the case without snow. From the perspective of the point target, the Doppler rate describes the rate of change of the Doppler frequency at which the point target is observed. A point target under a layer of snow leads to a faster change in the Doppler frequency because the azimuth sweep is compressed. This results in a higher Doppler rate.

[0057] The higher Doppler rate can be derived by quantifying the compressed azimuth scan. This is illustrated in Fig. 3. This figure shows a schematic representation of the transmission of a radar pulse in the case of snow on the Earth's surface, viewed in the direction opposite to the ground-range direction y. Analogous to Fig. 2, Z denotes s the snow depth, L is the snow surface, GR is the earth's surface and h corresponds to the flight altitude of the radar device 100 above the snow surface L. The solid arrow AR3 indicates the radar beam deflected by the snow, ie the case E S > E a . In contrast, the arrow AR4 represents the case where there is no snow on the Earth's surface (ie E S = e a ). In the case without snow, the size Z scales swith the factor . E due to the higher propagation speed resulting from the absence of snow. For the radar beam shown in Fig. 3, the azimuth position r is thus obtained for the case with snow. 15 whereas, for the case without snow, the azimuth position for the radar beam under consideration is r2. This results in a compression of the azimuth positions for the case with snow. The ratio — rl describes the ratio of the Doppler rate for a point target with snow cover to the Doppler rate of the point target without snow, i.e., the following applies: The above equation (7) results from the geometric derivation of the ratio — according to Fig. 3, where 0 ( - the angle of incidence and 0 r the angle of refraction according to ri

[0058] Fig. 2. The correctness of equations (6) and (7) was verified by the inventors using a numerical ray tracing simulation for a snow-covered point target.

[0059] Taking into account equation (4), the following phase error results between the recorded signal and the signal after SAR processing:

[0060] For a SAR acquisition with a Doppler center frequency f DC (mean Doppler frequency) is not equal to zero, the phase error leads to a shift of the focused image in the azimuth direction (azimuth time), which can be approximated as follows:

[0061] Equation (9) is a well-known approximation for a shift in azimuth direction in a SAR image, which results from a deviation Af R the Doppler rate between the filter used for azimuth compression in SAR processing and the acquired signal for a SAR acquisition with the Doppler center frequency f DC A 0 results (see also document [2], equation (6)).

[0062] The factor is a function of the snow depth Z s (see equation (7)) and thus has a direct relationship to the snow-water equivalent (see equation (1)). Consequently, the azimuth shift is a direct measure of the snow-water equivalent. According to the invention, the azimuth shift according to equation (9) is used to determine the snow depth or the snow-water equivalent. For this purpose, two SAR images with different Doppler center frequencies are synthesized from a SAR acquisition. The SAR images with the different Doppler center frequencies are obtained by processing different parts of the Doppler spectrum of the SAR acquisition.

[0063] According to the above equations (9), (7) and (1), the snow depth or the snow-water equivalent can be obtained from the shifts of two SAR images with different Doppler center frequencies, as explained in more detail below.

[0064] 7 — 1. According to equation (9), t DC1 = f DC1 ■ - — the azimuth

[0065] JR,a

[0066] Shift for a frequency range with the Doppler frequency f DC1 and At DC2 =

[0067] 7 — 1 f DC2 ' 7 — denotes the azimuth shift for a frequency range with the JR,a

[0068] Doppler frequency f DC2 This results in an azimuth shift Ax (in meters) between the SAR images with the two Doppler center frequencies as follows: f R a is obtained from equation (5). The following relationship results from equation (10) above:

[0069] This gives a dependence of the shift of the image contents between the SAR images in the frequency ranges with the different Doppler center frequencies on the parameter <(. This parameter in turn depends on the snow depth according to equation (7). By rearranging equation (7) the following relationship is obtained:

[0070] From the shift Ax between the SAR images in frequency ranges with different Doppler center frequencies, one obtains the value from which the snow depth can be obtained using equation (12). The quantities contained in equation (12) besides the value are known with sufficient accuracy or can be calculated using Snell's law (size 0 r ) can be determined.

[0071] Assuming that the density of the snow is constant, the snow-water equivalent SWE is calculated based on equation (1) above as follows:

[0072] SWE = — ■ Z s (13) Pw V '

[0073] The invention is explained again below using a specific embodiment in which the use of two antennas with different beam directions in the SAR radar system achieves a good division of the acquired SAR raw data into two frequency ranges with different Doppler center frequencies. Fig. 4 shows a schematic representation of the structure of this SAR system. Instead of two antennas, a single antenna can also be used, which radiates in two different beam directions.

[0074] Analogous to Fig. 1, the radar device 100 moves along the azimuth direction x above the earth's surface GR. The point target detected during the overflight is indicated by a star and designated by reference symbol PT. The radar device 100 contains two antennas 1 and 2, which are not shown separately. The antenna 1 is a combined transmitting and receiving antenna, and its associated antenna beam is designated by reference symbol Al in Fig. 4. The main beam direction of the antenna beam, i.e., the radiation direction with the highest energy, is designated by reference symbol RI for the antenna beam Al. In contrast, the antenna beam for the antenna 2 is designated by A2 and its main beam direction by reference symbol R2. The beam direction RI of the antenna 1 is with a backward squint angle i / j binclined relative to the plane perpendicular to the azimuth direction. In contrast, the beam direction R2 of antenna 2 is inclined with a forward slant angle if relative to the plane perpendicular to the azimuth direction. In the embodiment described here, the two slant angles i / j b and if equal.

[0075] With the arrangement shown in Fig. 4, two opposing frequency ranges of the Doppler spectrum are simultaneously captured in the SAR raw data. In a conventional manner, the Doppler center frequency for antenna 1 with antenna beam Al is given as follows:

[0076] Analogously, the Doppler center frequency for antenna 2 with antenna beam A2 is given as follows:

[0077] Here, v denotes e the azimuth speed of the radar device and 2 corresponds to the wavelength of the radar radiation.

[0078] The forward squint angle if results in a positive Doppler center frequency, whereas the backward squint angle i / j b corresponds to a negative Doppler center frequency. The magnitudes of the center frequencies increase with larger squint angles, which in turn leads to a larger shift Ax in the azimuth direction, i.e., to a higher sensitivity in detecting snow depth or the snow-water equivalent.

[0079] As mentioned, the two squint angles are i b and if chosen to be equal, ie / DC2 = — foci- Consequently, the parameter can be calculated according to equation (11) above as follows:

[0080] From this, the snow depth can then be calculated according to equations (11) and (12) above, as well as the snow-water equivalent using equation (13) above.

[0081] Fig. 5 illustrates again the steps as based on the arrangement of Fig.

[0082] 4, the snow depth or the snow-water equivalent can be determined. First, SAR raw data RD is acquired in a conventional manner using radar device 100 from Fig. 4 and antennas 1 and 2. The corresponding Doppler spectrum DS of the raw data RD is shown schematically in a diagram in Fig. 5. The abscissa of the diagram denotes the Doppler frequency f D , whereas the ordinate of the range frequency f rg The two squint angles in the forward and backward directions result in two separate frequency ranges, FBI and FB2, in the Doppler spectrum DS. The frequency range FBI corresponds to the Doppler center frequency f DC1 and the frequency range FB2 of the Doppler center frequency f DC2 .

[0083] In step S1 of Fig. 5, the two frequency ranges FBI and FB2 are separated from the raw SAR data RD, which is achieved by a Fourier transformation followed by bandpass filtering. Subsequently, in step S2, the two frequency ranges FBI and FB2 are separately subjected to a conventional SAR processing with range compression and azimuth compression. In the case of no snow on the Earth's surface, the SAR image IM1' is obtained for the frequency range FBI, and the SAR image IM2' is obtained for the frequency range FB2. As can be seen, the two images are identical.

[0084] In contrast, if there is snow on the Earth's surface, there is a shift between the two images or their image contents in the azimuth direction. In Fig. 1, IM1 denotes the SAR image for the frequency range FBI in the case of a layer of snow and IM2 denotes the image for the frequency range FB2 in the case of a layer of snow. In the embodiment described here, the image IM1 corresponds overall to an image area IA. Analogously, the image IM2 corresponds overall to an image area IA. The images are usually divided into smaller image areas, i.e. the two images contain a plurality of corresponding image areas IA. Corresponding shifts in the image contents are then determined separately for the individual image areas.

[0085] As can be seen, in the case of snow cover, the image content of image IM1 (i.e., the point target PT from Fig. 4) is shifted in the azimuth direction opposite to the image content of image IM2. This is indicated by corresponding arrows AR, which represent the displacement of the point target compared to the point target without snow (shown in dashed lines). The greater the snow depth, the greater the opposite displacement between images IM1 and IM2. The displacement Ax between images IM1 and IM2, which corresponds to the value from equation (10), is determined by comparing these images in step S3. Subsequently, in step S4, the snow depth Z is calculated from the displacement Ax. s using the above equations (11) and (12) and the snow water equivalent SWE using the above equation (13).

[0086] The inventive method was tested by the inventors based on both simulated SAR raw data and real SAR raw data. Fig.

[0087] 6 to Fig. 9 show results from the simulation of SAR raw data for a point target on the Earth's surface and a snow-water equivalent of 1.0 m. Fig.

[0088] 6 and Fig. 7 refer to simulated SAR images with squint angles if and i bof +10° and -10°, whereby the SAR image for the squint angle of -10° is shown with solid contour lines and the SAR image for the squint angle of +10° is shown with dashed contour lines in Fig. 6 and Fig. 7. The position of the point target for the squint angle at -10° is labeled PI in Fig. 6 and Fig. 7, whereas the position of the point target for the squint angle at +10° is labeled P2 in Fig. 6 and Fig. 7. Fig. 7 shows an enlargement of the images from Fig. 6 at the corresponding positions Pl, P2 of the representation in Fig. 6. As can be seen, a shift in the azimuth direction does indeed occur between the point targets.

[0089] Fig. 8 and Fig. 9 again show the analogous representations to Fig. 6 and Fig. 7, but with larger squint angles of +20° and -20°. As can be seen, increasing the squint angle also increases the displacement between the detected point targets.

[0090] The inventors further conducted an analysis of the accuracy of determining the snow-water equivalent for the simulation just described. For this purpose, several instances of normally distributed noise for different SNR levels (SNR = signal-to-noise ratio) from 0 dB to 25 dB were added to each of the SAR images acquired at different squint angles in a Monte Carlo simulation. For each SNR level, 1,000 instances of noise were used. Subsequently, the shift between the images was measured using cross-correlation, and the snow-water equivalent (SWE) was determined from this.

[0091] Fig. 10 shows a diagram illustrating the result of the Monte Carlo simulation for the strabismus angles of ±10°. The solid line LI indicates the standard deviation (T S WE i n Dependence of the signal-to-noise ratio SNR, whereas the dashed line L2 represents the mean value ^S WE represents the snow-water equivalent minus the actual snow-water equivalent SWE (i.e., 1 m). As can be seen from Fig. 10, the standard deviation is very small compared to the snow-water equivalent of 1 m. The mean value of the snow-water equivalent also deviates only slightly from the actual value of 1 m.

[0092] As already mentioned, the inventive method was also tested using real SAR data from a natural environment including meadows, forests, and urban areas. For this purpose, phase errors corresponding to a specific SWE value were synthetically inserted into the real SAR data. For the natural scene, corresponding SWE values ​​were determined for image blocks with an extension of 80 m in range and 110 m in azimuth. The measurement is not based on the displacement measurement of point targets, but on the displacement measurement of extended natural scenes with contrast. The snow-water equivalent could also be determined with high accuracy for real SAR data.

[0093] The embodiments of the method according to the invention described above have a number of advantages. In particular, the absolute snow depth or the snow-water equivalent can be determined with high precision from SAR raw data using a single overflight. In contrast, currently known methods can only determine differences in snow depths using interferometric measurements based on SAR acquisitions from multiple overflights. Furthermore, the method according to the invention no longer has the disadvantage of interferometric measurements, in which temporal decorrelation effects can occur between two SAR acquisitions and which are subject to 2K phase ambiguity.

[0094] Bibliography:

[0095] [1] T. Guneriussen, K. A. Hogda, H. Johnsen, and I. Lauknes, “InSAR for estimation of changes in snow water equivalent of dry snow,” IEEE Trans. Geosci. Remote Sens., Vol. 39, no. 10, Seiten 2101-2108, Oct. 2001.

[0096] [2] M. Rodriguez-Cassola et al., "Doppler-Related Distortions in TOPS SAR Images," in IEEE Transactions on Geoscience and Remote Sensing, Vol. 53, no.

[0097] 1, Seiten 25-35, Jan. 2015

Claims

Patent claims 1. A method for computer-aided processing of SAR raw data (RD) originating from a radar device (100) which flies over the earth's surface (GR) in an azimuth direction (x), wherein the SAR raw data (RD) represent radar echoes of radar pulses (RP) during a single flyover over an area of ​​the earth's surface (GR), wherein the radar pulses (RP) are or were emitted by the radar device (100) and the radar echoes are or were received by the radar device (100) as radar pulses reflected at the earth's surface (GR), wherein the SAR raw data (RD) comprise a plurality of data samples containing a Doppler spectrum (DS), wherein a respective data sample belongs to an azimuth position along the azimuth direction (x) and to a range position along a range direction (R), wherein the range direction (R) is perpendicular to Azimuth direction,where a) from the SAR raw data (RD) a first frequency range (FBI) of the Doppler spectrum (DS) with a first Doppler center frequency (f, DC i) and a second frequency range (FB2) of the Doppler spectrum (DS) with a second Doppler center frequency ( / £> C2), wherein the first frequency range (FBI) is disjoint to the second frequency range (FB2); b) a first SAR image (IM1) is determined from the first frequency range (FBI) and a second SAR image (IM2) is determined from the second frequency range (FB2); c) a shift value (Ax) is determined for a respective image area (IA) of a number of image areas (IA) in the first SAR image (IM1), which shift value indicates by how much the image content in the respective image area (IA) from the first SAR image (IM1) is shifted in the azimuth direction (x) compared to the same image content in a corresponding image area (IA) from the second SAR image (IM2), wherein the respective image area (IA) and the corresponding image area (IA) represent the same area with respect to the azimuth direction (x) and the range direction (R); d) from the displacement value (Ax) a snow depth (Z s ) in the respective image area (IA).

2. Method according to claim 1, characterized in that in step d) the snow depth (Z s ) a value dependent on the snow depth is determined, which is preferably the snow water equivalent (SWE).

3. Method according to claim 1 or 2, characterized in that the snow depth (Z s ) in step d) is determined as follows: where Z s is the snow depth; where E S is the real part of the relative dielectric permittivity of snow; where h is the flight altitude of the radar device (100) above the snow surface; where θi is the angle of incidence of the radar pulses (RP) in the respective image area (IA); where θ r is the refraction angle of the radar pulses (RP) in the respective image area (IA) at the snow surface; where where Ax is the displacement value in meters in the azimuth direction (x); where v e is the azimuth speed of the radar device (100); where fDC1 the first Doppler center frequency (f DC i) is; where f DC2 the second Doppler center frequency (f DC 2) where f R a is the Doppler rate without snow in the respective image area (IA).

4. Method according to one of the preceding claims, characterized in that the SAR raw data (RD) originate from a radar device (100) comprising an antenna device which generates an antenna beam for transmitting and receiving radar radiation in a first beam direction (RI) and an antenna beam for transmitting and receiving radar radiation in a second beam direction (R2), wherein the first beam direction (RI) is at a first inclination angle (i / j b') is inclined relative to the plane perpendicular to the azimuth direction (x) and wherein the second beam direction (R2) is inclined at a second angle of inclination (t / ) relative to the plane perpendicular to the azimuth direction (x), wherein the first beam direction (RI) and the second beam direction (R2) differ from one another.

5. Method according to claim 4, characterized in that the first angle of inclination is a backward angle, so that the first beam direction (RI) lies behind the radar device (100) with respect to the movement of the radar device (100) in the azimuth direction (x), and the second inclination angle (if) is a forward angle, so that the second beam direction (R2) lies in front of the radar device (100) with respect to the movement of the radar device (100) in the azimuth direction (x).

6. Method according to claim 5, characterized in that the forward angle is between 2° and 40°, preferably between 5° and 25° and particularly preferably between 15° and 25° and / or that the backward angle is between 2° and 40°, preferably between 5° and 25° and particularly preferably between 15° and 25°.

7. Method according to claim 5 or 6, characterized in that the forward angle is the same as the backward angle.

8. Device for the computer-aided processing of SAR raw data (RD) originating from a radar device (100) which flies over the earth's surface (GR) in an azimuth direction (x), wherein the SAR raw data (RD) represent radar echoes of radar pulses (RP) during a single flyover over an area of ​​the earth's surface (GR), wherein the radar pulses (RP) are or were emitted by the radar device (100) and the radar echoes are or were received by the radar device (100) as radar pulses reflected at the earth's surface (GR), wherein the SAR raw data (RD) comprise a plurality of data samples containing a Doppler spectrum (DS), wherein a respective data sample belongs to an azimuth position along the azimuth direction (x) and to a range position along a range direction (R), wherein the range direction (R) is perpendicular to Azimuth direction, wherein the device is designed to carry out a method,in which: a) from the SAR raw data (RD) a first frequency range (FBI) of the Doppler spectrum (DS) with a first Doppler center frequency (f, DC i) and a second frequency range (FB2) of the Doppler spectrum (DS) with a second Doppler center frequency ( / £> C2), wherein the first frequency range (FBI) is disjoint to the second frequency range (FB2); b) a first SAR image (IM1) is determined from the first frequency range (FBI) and a second SAR image (IM2) is determined from the second frequency range (FB2); c) a shift value (Ax) is determined for a respective image area (IA) of a number of image areas (IA) in the first SAR image (IM1), which shift value indicates by how much the image content in the respective image area (IA) from the first SAR image (IM1) is shifted in the azimuth direction (x) compared to the same image content in a corresponding image area (IA) from the second SAR image (IM2), wherein the respective image area (IA) and the corresponding image area (IA) represent the same area with respect to the azimuth direction (x) and the range direction (R); d) from the displacement value (Ax) a snow depth (Z s ) in the respective image area (IA).

9. Device according to claim 8, characterized in that the device is designed to carry out a method according to one of claims 2 to 7.

10. A computer program product comprising a program code stored on a machine-readable medium for carrying out a method according to one of claims 1 to 7 when the program code is executed on a computer.

11. Computer program with a program code for carrying out a method according to one of claims 1 to 7, when the program code is executed on a computer.

Images