Method for detecting and resolving phase ambiguities in interferometric SAR data

Abstract

The invention describes a method for detecting and resolving phase ambiguities in interferometric SAR data. The SAR data are available in the form of interferograms (IGP, IGH1, IGH2) which are generated from images that are captured and provided by a multi-static SAR system (1). The SAR system (1) comprises the following radars, which, in order to capture the images, fly in a formation along an azimuth direction (AR): a first and a second radar (10) with an antenna aperture of a first size; wherein the first and the second radar (10, 20) have a first baseline distance (BL1) transverse to an azimuth direction (AR) of the SAR system; at least one auxiliary radar (30; 30-1, 30-2), designed only for receiving, having an antenna with an antenna aperture of a second size, which is smaller than the antenna aperture of the first size, wherein the at least one auxiliary radar (30; 30-1, 30-2) flies in formation with the first and the second radar (10, 20) in such a manner that there is a second baseline distance (BL2) between the radars (10, 20, 30; 30-1, 30-2) which is smaller than the first baseline distance (BL1). In the method, a primary interferogram (IGP) is generated from the images of the first and second radar (10, 20), a first auxiliary interferogram (IGH1) is generated from the images of the pair of radars (10 / 30; 30-1 / 30-2) that have the second baseline distance (BL2), and a second auxiliary interferogram (IGH2) is generated that differs from the first interferogram (IGH1). A discrepancy mask is generated by a pixel-by-pixel comparison of the phases which are wrapped and scaled by the respective ambiguity level and which result from the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2). Finally, the phase ambiguities are resolved in the primary interferogram (IGP) in the pixels that are marked as discrepant in the discrepancy mask.

Description

[0001] Methods for detecting and resolving phase ambiguities in interferometric SAR data

[0002] Description

[0003] The invention relates to a method for detecting and resolving phase ambiguities in interferometric SAR data, wherein the SAR data are in the form of interferograms generated from images acquired and provided by a multistatic SAR system.

[0004] SAR (Synthetic Aperture Radar) systems enable remote sensing of the Earth's surface by detecting radar pulses reflected from the Earth's surface, which are emitted by the SAR system. The SAR system is an active, coherent, and high-resolution imaging radar that operates on a moving platform in a sideways-oriented geometry. This well-known procedure is illustrated in Fig. 1.

[0005] Fig. 1 shows the geometry of a SAR system 1 for exploring the Earth's surface BO. The SAR system 1 comprises a satellite designated as platform P with a radar. The direction of movement of platform P is referred to as the azimuth (direction) AR. The radial distance of platform P from the Earth's surface BO to be explored is referred to as the slant range SR. The radar records a limited slant range interval that images an area of ​​the illuminated Earth's surface BO in the form of a strip parallel to the azimuth direction AR, which is referred to as the swath width SW.

[0006] The platform P, whose altitude PH above the Earth's surface BO is known, continuously transmits radar pulses toward the Earth's surface BO via a transmitting antenna while moving in the azimuth direction AR. The radar echo of each transmitted radar pulse is recorded by temporally sampling the radar radiation reflected from the Earth's surface BO at the slant distance extending perpendicular to the satellite's flight direction or azimuth direction AR.

[0007] As a result, a multitude of samples are obtained, with each sample corresponding to the radar return of a specific radar pulse and a range position. The assignment of a sample to a radar pulse is represented by an azimuth position. The transmitter and receiver of a SAR system (hereinafter also referred to simply as radar) are, for example, components of a combined transmit-receive antenna, which acts as the transmitter in transmit mode and the receiver in receive mode. In this case, the SAR system is a so-called single-aperture system, in which the radar returns are detected by only a single receiver.

[0008] During the analysis, only radar radiation information within the ground strip illuminated by the transmitted radar pulse is recorded. This strip width can be several kilometers, e.g., several tens or hundreds of kilometers. The width of the ground strip depends, among other things, on the length of the time window within which the backscattered radar echoes from a transmitted pulse are received by the receiver. This time window is called the echo window. The received echoes are processed (i.e., frequency converted, demodulated, digitized) and stored as raw data.

[0009] Echoes coming from distances beyond the imaged ground strip SW overlap and distort the main signal. These echoes are referred to as range ambiguities. An antenna pattern in the elevation direction is responsible for suppressing these range ambiguities, so the requirement for a maximum ratio of range ambiguities to signal leads to a minimum antenna height for the SAR system.

[0010] The raw SAR data is sampled along the azimuth direction AR at a frequency known as the pulse repetition frequency (PRF). A portion of the azimuth spectrum of the raw data is then processed to create the SAR image. This portion is referred to as the processed bandwidth. This sampling causes an aliasing effect, in which components outside the processed bandwidth insert themselves into it, overlaying and corrupting the main signal. These are known as azimuth ambiguities. The spectrum of the raw SAR data along the azimuth direction AR is modulated by the antenna pattern along the azimuth direction AR, so the requirement for a maximum ratio of azimuth ambiguity to signal leads to a minimum antenna length.

[0011] In so-called across-track SAR interferometry, two SAR images of the same area are acquired from different positions and combined to create a digital elevation model (DEM) of that area. Fig. 2 shows an interferometric SAR system 1 configured for this purpose, with two radars 10, 20 (satellites). Each of the radars 10, 20 acquires a respective SAR image, which are then combined. The distance between the two radars 10, 20 is referred to as the baseline B. Their projection orthogonal to the slant range SR, referred to here as Ri and R2, and azimuth direction AR is referred to as the orthogonal baseline B. ± designated.

[0012] If the two SAR images are acquired simultaneously, a bistatic configuration is used. The SAR images can also be acquired at different times, which is called a "repeat-pass" configuration. The two SAR images are combined pixel by pixel to create an interferogram according to equation (1):

[0013] V12 = u x u2* (1)

[0014] In equation (1) v 12 the pixels of the interferogram, u and u2 are the pixels of each of the two SAR images. The symbol represents the complex conjugate operation.

[0015] The phase of the interferogram is the phase difference between the two SAR images (hereinafter referred to as images). Since the trajectories of the radars 10, 20 are different, the two two-dimensional images are projections of the detected area in different coordinate systems. Therefore, a process called co-registration is carried out before the interferogram is formed. During co-registration, transformations are applied to align the two images. After the interferogram has been formed and the hat-earth phase correction has been applied, a process called multilooking is carried out in which neighboring interferogram pixels are averaged to reduce the uncertainty in the phase. Multilooking therefore represents a smoothing effect. However, this process results in a lower resolution of the DEM product.

[0016] The phase difference encoded in the interferogram is proportional to the height of the terrain according to equation (2):

[0017] In equation (2), HoA is the height of ambiguity, i.e. the height difference corresponding to a 2TT phase difference, j is the angle of incidence, 2 is the wavelength of the signal carrier, R is the slant distance and B ±the orthogonal baseline. Proportionality applies to the absolute interferometric phase. Since the phases are cyclic, the observed phases are the result of unwrapping the absolute phase in the [— TT, TI [ interval. Phase unwrapping is the process of reconstructing the absolute phase from the folded phases. After performing phase unwrapping, the absolute phases are converted into the digital elevation model of the imaged ground region using the relationship in equation (2). For a fixed degree of phase uncertainty, the smaller the ambiguity height, the higher the accuracy of the resulting digital elevation model, but the more difficult it is to perform phase unwrapping.

[0018] Performing phase unwrapping can result in incorrect absolute phase values. These errors are called phase ambiguities and affect the resulting digital elevation model in the form of elevation deviations that are multiples of the ambiguity height. For a fixed degree of phase uncertainty, the smaller the ambiguity height, the higher the accuracy of the resulting digital elevation model, but the more likely the occurrence of phase ambiguities.

[0019] To solve the problem of phase ambiguities, it is known to perform an additional bistatic acquisition over the same detection range, i.e., over the same ground region. This acquisition is performed with a different baseline and, therefore, a different ambiguity level, as can be seen, for example, in publication [1]. According to this proposal, the two interferograms are processed according to a dual-baseline phase unwrapping algorithm. The levels resulting from the independent unwrapping of the two interferograms are compared to detect phase unwrapping errors, which occur when the two levels differ by more than a certain threshold. A third interferogram with an even greater ambiguity level is formed by combining the two existing interferograms, where the levels resulting from the unwrapping of this interferogram are assumed to be without errors.These are then used to correct the discovered processing errors.

[0020] The additional overpass required to correct phase-delay errors increases the total time required to image a specific ground area. Due to the large time interval between the two overpasses, the SAR system's ability to quickly observe dynamic processes is limited. Furthermore, because the additional acquisition requires a different baseline, orbital maneuvers are required, adversely increasing the overall complexity of the SAR system.

[0021] Another way to resolve the phase ambiguities without requiring an additional overflight is to add another satellite to the SAR system, similar to the first two, with a large antenna aperture. However, this is undesirable for cost reasons.

[0022] The object of the invention is to provide a method for detecting and resolving phase ambiguities in interferometric SAR data that is functionally improved over the prior art approaches. A further object is to provide a correspondingly designed system.

[0023] These objects are achieved by a method according to the features of claim 1, a computer program product according to the features of claim 10, and a system according to the features of claim 11. Advantageous embodiments emerge from the dependent claims. A method for detecting and resolving phase ambiguities in interferometric SAR data is proposed, wherein the SAR data is in the form of interferograms. The interferograms are generated from images acquired and provided by a multi-static SAR system. The SAR system comprises the following radars, which fly in formation along an azimuth direction to acquire the images: a first radar with a transmitter, a receiver, and an antenna with an antenna aperture of a first size; a second radar with a receiver and an antenna with an antenna aperture of the first size.The first and second radars, which may be structurally identical, have a first baseline spacing transverse to an azimuth direction of the SAR system. In this respect, the first and second radars form a conventional SAR satellite system, such as is used for across-track SAR interferometry. The SAR system further comprises at least one auxiliary radar designed exclusively for reception and having an antenna with an antenna aperture of a second size. The antenna aperture of the second size is smaller than the antenna aperture of the first size. The at least one auxiliary radar flies in formation with the first and second radars such that a second baseline spacing is established between the radars, wherein the second baseline spacing is smaller than the first baseline spacing. A so-called CubeSat, for example, can be used as the auxiliary radar.CubeSats are characterized by an antenna aperture that is much smaller than that of conventional radars, such as those used as first and second radars.

[0024] According to the invention, the following steps are carried out in the process:

[0025] In step a), a primary interferogram is generated from the images of the first and second radars. The primary interferogram is generated as is usual for a bistatic SAR interferogram system. In step b), a first auxiliary interferogram is generated from the images of the pair of radars of the SAR system that have the second baseline spacing. As will become clear from the following description, the second, small baseline spacing can be formed between an auxiliary radar and, for example, the first radar. Alternatively, the second baseline spacing can also be formed between two auxiliary radars of the SAR system.

[0026] In a step c), a second auxiliary interferogram is then generated, which is different from the first interferogram. For this purpose, if the second baseline is formed between the auxiliary radar and the first radar, the second auxiliary interferogram can be generated from images of the pair of radars that have a third baseline spacing that is smaller than the first baseline spacing and greater than the second baseline spacing. According to this embodiment, the third baseline spacing is formed between the auxiliary radar and the second radar. If the second baseline spacing is formed between two auxiliary radars in a plurality of auxiliary radars, the second auxiliary interferogram is generated from the primary interferogram and the first auxiliary interferogram.

[0027] In step d), a phase development is generated for the primary interferogram as well as the first and / or second auxiliary interferogram. Subsequently, in step e), phases scaled by the respective ambiguity levels are generated by multiplying them by the assigned ambiguity level for the primary interferogram as well as the first and / or second auxiliary interferogram.

[0028] In step f), a discrepancy mask is then generated by pixel-by-pixel comparison of the previously determined scaled phases resulting from the primary interferogram and the first and / or second auxiliary interferogram. A respective pixel is marked as discrepant in the discrepancy mask if the compared, unwrapped phases scaled by the respective ambiguity level deviate from each other by more than a predetermined threshold value. The term "pixel-by-pixel comparison" in the present description is to be understood to mean that the pixels in the interferograms are in the same location, i.e., have the same xy coordinates, so that the image information of the same ground area is viewed.

[0029] In a step g), phase ambiguities in the primary interferogram are resolved in the pixels marked as discrepant in the discrepancy mask.

[0030] The combined radars enable the detection and resolution of phase ambiguities in a single pass of the radars (satellites). The relatively inexpensive CubeSats are configured for reception only and fly in formation with the bistatic SAR interferometers formed by the first and second radars, thus obtaining an additional interferogram with a short baseline required for the process.

[0031] The advantage of the proposed SAR system over conventional bistatic SAR interferometry systems is that it is comparatively low-cost and does not suffer from phase ambiguities. Compared to the conventional bistatic SAR interferometry system with an additional pass to resolve phase ambiguities, the advantage is that less time is required to image a specific ground area, as only a single pass of the SAR system is required. This does not preclude applications related to the imaging of rapidly changing scenes. Compared to a configuration with multiple passive receivers with an active transmitter and medium antenna apertures (as described, for example, in reference [2]), the proposed SAR system uses radars with a much smaller antenna aperture than passive receivers.

[0032] The small antenna aperture of at least one auxiliary radar leads to increased noise and greater range and azimuth ambiguity in the SAR images created with its data due to the lower reception power. However, the increased range and azimuth ambiguities are not so great that the performance for resolving phase ambiguities suffers. Since at least one auxiliary radar only receives, with pulses being transmitted by the first radar, which has correspondingly large antennas, the antenna pattern of the transmitter suppresses the ambiguities.

[0033] With at least one auxiliary radar, two interferograms are created in addition to the primary interferogram. The first auxiliary interferogram is an auxiliary interferogram with a small baseline. The second auxiliary interferogram, in contrast, is an auxiliary interferogram with a large baseline.

[0034] If the second auxiliary interferogram is generated from the primary interferogram and the first auxiliary interferogram, as is the case with at least two auxiliary radars, this can be done by:

[0035] In this equation (3) v primary , v auxl and v aux2 the pixels of the primary interferogram and the pixels of the first and second auxiliary interferograms. The ambiguity level is calculated as follows:

[0036] 1 > 1 1 (4).

[0037] HoA aux2 oA auxi oApril

[0038] In this equation (4) HoA primary , HoA auxl and HoA aux2the ambiguity levels of the primary interferogram (index "primary") and the ambiguity levels of the first and second auxiliary interferograms (index "aux1" and "aux2", respectively). The three interferograms are preferably processed using a scheme adapted to the Tan-DEM-X correction with two baselines, as described in reference [1]. This scheme is adapted to account for the fact that the additional auxiliary interferograms have lower coherence because they are formed from the images of the auxiliary radar(s), which are more noisy and have more ambiguities.

[0039] Conveniently, the first auxiliary interferogram comprises an ambiguity level that is at least twice the ambiguity level of the primary interferogram, wherein the ambiguity level is the height difference corresponding to a 27T phase difference. Preferably, the second auxiliary interferogram comprises an ambiguity level that is between half and twice the ambiguity level of the primary interferogram, wherein the ambiguity level is the height difference corresponding to a 2T phase difference.

[0040] It is advisable to subject the primary interferogram, the first interferogram, and the second auxiliary interferogram to phase processing independently of one another. It is also advisable to subject the primary interferogram, the first interferogram, and the second auxiliary interferogram to smoothing (multilooking) independently of one another. A larger number of smoothing steps can be used for the auxiliary interferograms to compensate for their lower coherence.

[0041] The discrepancy mask is generated by pixel-by-pixel comparison of the scaled phases resulting from the unwrapping of the primary interferogram and the auxiliary interferogram with a large baseline. If the scaled phases differ by more than a certain threshold, they are marked as discrepant, indicating errors in the phase unwrapping. In contrast to the phase unwrapping known from reference [1], the discrepancy mask is expediently smoothed, i.e., processed to group discrepant pixels into larger blocks. Such processing can be achieved, for example, by using DB SCAN (see reference [3]) or by spatial convolution with a kernel followed by thresholding. Smoothing serves to discard point-like discrepancies, which are false positives, and to remove gaps in the discrepancy mask, which are highly likely to be false negatives.

[0042] The higher coherence of the small-baseline auxiliary interferogram leads to greater uncertainty. Unlike the phase unwrapping method described in [1], the scaled phases resulting from the unwrapping of the small-baseline auxiliary interferogram are smoothed by spatial unwrapping with a kernel. The smoothing result is used to correct the detected unwrapping errors. The greater the uncertainty in the scaled phase, which is used as a reference for resolving the detected phase ambiguities, the higher the probability that the correction will lead to incorrect results. Smoothing thus serves to reduce the uncertainty in the scaled phases extracted from the small-baseline auxiliary interferogram and thus increase the probability of a successful correction.The resulting lower resolution for correcting the phase unwinding is unproblematic, since phase ambiguities generally occur over large areas.

[0043] The at least one auxiliary radar can be configured to receive a narrower bandwidth than the transmitted pulses, resulting in a smaller amount of data to be processed. The resulting lower range resolution is not critical, as phase ambiguities generally occur over large areas.

[0044] The second antenna aperture of the at least one auxiliary radar is expediently 50%, preferably 25% and most preferably 10% of the size of the first antenna aperture.

[0045] The invention further proposes a computer program product with program code stored on a non-volatile machine-readable medium for carrying out the method according to one or more embodiments when the program code is executed on a computer. Finally, the invention proposes a system for detecting and resolving phase ambiguities in interferometric SAR data, wherein the SAR data is in the form of interferograms generated from images acquired and provided by a multi-static SAR system, the SAR system comprising the following radars flying in formation to acquire the images along an azimuth direction: a first radar with a transmitter, a receiver, and an antenna with an antenna aperture of a first size; a second radar with a receiver and an antenna with an antenna aperture of the first size;wherein the first and second radars have a first baseline spacing transverse to an azimuth direction of the SAR system; and at least one auxiliary radar configured exclusively for reception, having an antenna with an antenna aperture of a second size that is smaller than the antenna aperture of the first size, wherein the at least one auxiliary radar flies in formation with the first and second radars such that a second baseline spacing is established between the radars, wherein the second baseline spacing is smaller than the first baseline spacing. The system is configured according to the invention to carry out the method according to one or more embodiments.

[0046] The invention is described in more detail below using an exemplary embodiment in the drawing. In the drawings:

[0047] Fig. 1 shows a geometry of a SAR-

[0048] System for detecting a ground area;

[0049] Fig. 2 shows a prior art geometry of a bistatic SAR interferometry system for detecting a ground area; Fig. 3 shows a first embodiment of a configuration of an SAR system according to the invention, in which an auxiliary radar is added to a bistatic SAR interferometry system;

[0050] Fig. 4 shows a second embodiment of a configuration of an inventive SAR system in which two auxiliary radars are added to a bistatic SAR interferometry system;

[0051] Fig. 5a and 5b antenna diagrams of a primary satellite of the bistatic SAR interferometry system and an auxiliary radar in azimuth and elevation directions;

[0052] Fig. 6 is a diagram illustrating the signal-to-noise ratios of the interferograms of a SAR system according to the invention in comparison;

[0053] Figs. 7a and 7b show three-dimensional models used to illustrate the method according to the invention for simulating a soil area;

[0054] Fig. 8a to 8c simulated SAR images for a first radar, a second radar and an auxiliary radar of the inventive SAR system according to the first embodiment in Fig. 3;

[0055] Figs. 9a to 9c show non-smoothed and smoothed interferograms generated from the SAR images according to Fig. 8 and the method according to the invention;

[0056] Fig. 10a to 10c show coherence estimates of the interferograms generated in Fig. 9a to 9c; Fig. 11a to 11c show a simulated error HE of the interferograms generated from a phase unfolding;

[0057] Fig. 12a and 12b show an exemplary discrepancy mask before and after a smoothing step;

[0058] Fig. 13a and 13b show an error in the primary interferogram resulting from the phase unwinding before and after the resolution of the phase ambiguities; and

[0059] Fig. 14 shows a flow chart of the method according to the invention.

[0060] Figures 3 and 4 show a first and a second embodiment of an inventive SAR system 1. Both embodiments comprise a first radar 10 and a second radar 20, which represent a primary and secondary satellite. The first radar 10 and the second radar 20 are satellites of a conventional bistatic SAR interferometry system and each comprise a transmitter, a receiver, and an antenna with a given antenna aperture; the second satellite does not necessarily have to be equipped with a transmitter. The antenna apertures of the first and second radars 10, 20 are the same. The first and second radars 10, 20 fly in the azimuth direction AR (perpendicular to the blade direction) to observe a ground region B, having a first baseline separation BL1 transverse to the azimuth direction AR.

[0061] The SAR system 1 according to the first embodiment in Fig. 3 additionally comprises an auxiliary radar 30, which can be referred to as an auxiliary satellite. The auxiliary radar 30 is preferably a so-called low-cost CubeSat, as known from the prior art. The auxiliary radar 30 is designed exclusively for reception and has an antenna with an antenna aperture that is smaller or significantly smaller than the antenna aperture of the first and second radars. The antenna aperture of the auxiliary radar 30 is expediently 50%, preferably 25%, and most preferably 10% of the antenna aperture size of the first and second radars 10, 20, respectively. The auxiliary radar 30 moves in formation with the first and second radars 10, 20 in the azimuth direction AR, wherein the auxiliary radar 30 has a second baseline spacing BL2 with respect to the first radar 10 that is smaller than the first baseline spacing BL1. The second baseline spacing is also referred to as a small baseline.With respect to the second radar 20, the auxiliary radar 30 has a third baseline BL3 that is larger than the second baseline BL2 and smaller than the first baseline BL1. The third baseline BL3 is also referred to as the mean baseline.

[0062] The first embodiment shown in Fig. 3 is characterized by a reduced required data volume and, as will become apparent later, by improved performance compared to the second configuration shown in Fig. 4. The auxiliary radar advantageously has a significantly lower mass in this embodiment than the first and second radars 10, 20. In this embodiment, it is necessary for the auxiliary radar to fly in formation with the first and second radars 10, 20, as explained.

[0063] In the second exemplary embodiment according to Fig. 4, two auxiliary radars 30-1, 30-2 are provided, with the second (small) baseline BL2 being formed between the two auxiliary radars 30-1, 30-2. The two auxiliary radars 30-1, 30-2 are each the CubeSats already mentioned and are designed exclusively for reception. The two auxiliary radars 30-1, 30-2 fly in formation with the first and second radars 10, 20 in the azimuth direction AR, with a distance ATS between the auxiliary radars 30-1, 30-2 and the first and second radars 10, 20, which is referred to as the "along-track" distance. However, this could also be an additional cross-track distance. This configuration is characterized by a higher data volume and lower performance compared to the first exemplary embodiment according to Fig. 3. However, this variant does not require having satellites with different mass differences in the same formation.The more auxiliary radars are provided, the greater the number of additional baselines available. This can increase the resolution of phase ambiguities in performance. In other words, the number of auxiliary radars is not limited to one (as in Fig. 3) or two (as in Fig. 4), but can also be greater than two. If a sufficiently large number of auxiliary radars are provided, SAR tomography could be used to resolve layover, i.e., when targets at different altitudes and ground positions appear superimposed within the same slope range. This is an effect that often occurs in cities and mountains, for example.

[0064] When flying over a ground area B to be observed, the first radar 10 emits radar pulses, which are received by the first and second radars 10, 20 and the auxiliary radar 30 (according to the first embodiment in Fig. 3) or the auxiliary radars 30-1, 30-2 (according to the second embodiment in Fig. 4). From these received data, respective SAR images are generated and provided in a conventionally known manner. Interferograms are generated from these images in a likewise known manner by pixel-by-pixel combination, as described in more detail below.

[0065] In the embodiment according to Fig. 3, a primary interferogram IGP is formed by combining the images of the first and second radars 10, 20. A first auxiliary interferogram IGH1 is formed by combining the images of the pair of radars with a small baseline separation BL2, i.e., by combining the images of the first radar 10 and the auxiliary radar 30. A second auxiliary interferogram IGH2 is formed by combining the images of the second radar 20 and the auxiliary radar 30, i.e., those radars between which the mean baseline BL3 is formed.

[0066] In the embodiment shown in Fig. 4, the primary interferogram IGP is also generated from the combination of the images of the first and second radars 10, 20. The first auxiliary interferogram IGH1 is generated from the combination of the images of the pair of radars with the small baseline separation BL2, i.e., the two auxiliary radars 30-1 and 30-2. The second auxiliary interferogram IGH2 is formed by combining the two aforementioned interferograms, i.e., the primary interferogram IGP and the first auxiliary interferogram IGH1. Equation (3) is used for this purpose.

[0067] Fig. 5 shows the frequency-dependent antenna patterns AM in the azimuth direction AR (Fig. 5a) and elevation (Fig. 5b) for the first radar 10 and the auxiliary radar 30. Dashed lines indicate a receive antenna pattern, while solid lines indicate a two-way antenna pattern. Each antenna pattern AM is plotted in [dB] versus the Doppler frequency f in [Hz] or the ground range GR in [km]. In the upper diagram according to Fig. 5a, frequency ranges are marked as a function of the pulse repetition frequency PRF. The frequency range between [-PRF / 2; PRF / 2] represents a processed bandwidth PBR. The areas to the left and right outside the frequencies are areas with ambiguity energy AE.

[0068] The antenna diagrams AM shown in Fig. 5 assume rectangular antennas for the first radar 10 and the auxiliary radar 30, with the first radar 10 having a height of 0.7 m and a width of 4.8 m. The auxiliary radar 30 has an antenna with a height of 0.3 m and a width of 1.0 m. This results in an azimuth ambiguity signal ratio (AASR) of -16.8 dB, while the auxiliary radar has an AASR of -8.6 dB. The lower signal power in the images of the auxiliary radar 30 leads to a lower signal-to-noise ratio (SNR), which results in a stronger SNR decorrelation in the interferogram in which they participate.

[0069] Fig. 6 shows the SNR decorrelation for the primary interferogram IGP and for the first auxiliary interferograms, where the first auxiliary interferogram according to the embodiment of Fig. 3 is labeled IGH1 and the first auxiliary interferogram according to the second embodiment of Fig. 4 is labeled IGH1', as a function of the SNR in the first radar. This assumes that the noise power is the same in all radars. The vertical lines in Fig. 6 mark the signal-to-noise ratio SNR for ground and rock backscatter in the X-band according to reference [4], assuming the TanDEM-X noise level presented in reference [5].

[0070] Simulated terrain surfaces are used for the further description of the inventive method and a figurative illustration. In the following explanations, a survey of a terrain comprising a truncated cone-shaped mountain with an inclination of 17° is assumed, whereby the survey is carried out with the SAR system shown in Fig. 3. The simulated terrain is shown in Fig. 7a). The ambiguity height for the primary interferogram IGP is 15 m, 52.5 m for the first auxiliary interferogram IGH1 with a small baseline BL2, and 21 m for the second auxiliary interferogram IGH2 with a large baseline BL3. The simulation considers an angle of incidence of 36° relative to the horizontal plane and ignores spectral shift decorrelation. The backscattering of the terrain is assumed to follow the mean backscattering from the backscattering model for soil and rock in X-band and HH polarization from Reference [4].The terrains are simulated such that the coherence in each interferogram is 0.8 before adding noise. The noise is added to the simulated terrains with a power equivalent to that of TanDEM-X at a similar angle of incidence. Due to the lower signal power due to the smaller antenna aperture of the auxiliary radar 30, this was scaled accordingly in the terrain of the auxiliary radar. Two first-order azimuthal ambiguities are added, originating from scenes whose terrain contains a pyramid, as can be seen in Fig. 7b). Otherwise, this has the same characteristics as the terrain of the main scene as shown in Fig. 7a.

[0071] The simulated images are shown in Fig. 8a) to c) for the first radar 10, the second radar 20, and the auxiliary radar 30. The azimuth direction AR is shown on the vertical axis, and the slant range SR is shown on the transverse axis, each in [km]. On the right side of Fig. 8c), a color scale representing an amplitude is visualized. The brighter the color or gray value in the images of Fig. 8a) to c), the greater the amplitude. The scale ranges from 0 to 4.

[0072] The resulting interferograms IGP, IGH1, IGH2 with smoothing and without smoothing (multilooking) are shown in Fig. 9a) to c), with the images in the upper row showing no smoothing and the images in the lower row showing smoothing.

[0073] The estimated coherences in the interferograms IGP, IGH1, and IGH2 are shown in Fig. 10a) to c). In all interferograms in Figures 9 and 10, smoothing and coherence estimation were performed using a moving average with a boxcar window of 5 x 5 pixels. On the right side of Fig. 10c), a color scale representing a coherence Coh is visualized. The brighter the color or gray value in the images of Fig. 10a) to c), the higher the coherence. The scale ranges from 0.0 to 1.0.

[0074] The wave-like pattern visible in the coherence estimate shown in Figures 10a) to c) is caused by azimuthal ambiguities. The low-coherence region near the center at the top of the truncated cone-shaped mountain is due to a bright tilt of the pyramids facing the respective radars 10, 20, 30 in the ambiguous scenes, which is superimposed on the less bright backscattering from the top of the truncated cone-shaped mountain in the main scene. This bright tilt can also be seen in the auxiliary radar image (see Fig. 8c)), where the azimuthal ambiguities are more pronounced. Furthermore, the first and second auxiliary interferograms IGH1, IGH2 in Figures 9 and 10 show low coherence on the slope facing away from the radar, which is due to the low backscattering from this slope due to the low angle of incidence.

[0075] The slope of the truncated mountain facing radars 10, 20, and 30 is undersampled in the primary interferogram IGP, as shown in Figure 9a. This results in very low estimated coherence, as shown in Figure 10a. The simulation was intentionally generated to accommodate this situation, resulting in aberrations in this region. Furthermore, phase ambiguities corresponding to an ambiguity height were artificially introduced in one quadrant of the scaled phase map resulting from the unwrapping of the primary interferogram IGP and the second auxiliary interferogram IGH2 with large baseline B13.

[0076] Fig. 11a) to c) shows errors HE resulting from the independent unwinding of each of the interferograms IGP, IGH1, and IGH2. In the unwrapped phases, scaled by the respective ambiguity levels, resulting from the unwinding of the primary interferogram IGP, significant errors can be seen on the slope of the mountain facing the first radar 10 and the second radar 20.

[0077] To detect these errors, the proposed method uses a discrepancy mask generated from the primary interferogram IGP and the second auxiliary interferogram IGH2 by performing a pixel-by-pixel comparison of the unwrapped phases scaled by the respective ambiguity levels. A pixel is marked as discrepant (D) in the discrepancy mask if the comparison result is greater than a specified threshold. Conversely, a pixel is marked as non-discrepant (C) if the comparison result is less than the specified threshold.

[0078] Figures 12a) and 12b) show the discrepancy mask obtained by pixel-by-pixel comparison of the unwrapped phases of the primary interferogram IGP and the second auxiliary interferogram IGH2, scaled by the respective ambiguity levels, with the large baseline BL3. Fig. 12a) shows the discrepancy mask before smoothing, with pixels marked as discrepant being shown in light color and pixels marked as non-discrepant being shown in dark color. On the scale shown to the right, a discrepancy value is shown as D and a consistency value (i.e., a non-discrepant value) as C. Fig. 12b) shows the discrepancy mask after preferential smoothing. Here, the pyramid is easily recognizable in the left half and the artificially inserted rectangle in the lower right half.

[0079] The smoothing is performed, for example, using DBSCAN (see reference [3]) with a radius of five pixels below the infinity norm and a threshold of eight pixels for classification as a core point. Finally, the resulting discrepancy mask is convolved from core and reachable points with a boxcar window of at most 5 x 5 pixels. Smoothing eliminates point-like artifacts and gaps. The smoothed discrepancy mask is able to detect 100% of the artificially introduced unfolding errors and 98.7% of the remaining errors. In contrast, the discrepancy mask without smoothing performs poorly.

[0080] Figures 13a) and b) show the errors HE resulting from the unwrapping of the primary interferogram before the resolution of phase ambiguities (Fig. 13a)) and after the resolution of phase ambiguities (Fig. 13b)) using the additional information from the auxiliary radar 30, specifically with respect to the true height of the imaged terrain. During the correction of the height errors, the scaled phases of the primary interferogram IGP are corrected in the regions defined by the discrepancy mask. In the example, a smoothed version of the unwrapping phase scaled by the ambiguity height was used, which results from the unwrapping of the first auxiliary interferogram IGH1 with a small baseline. The smoothing is achieved, for example, by a moving average with a 13 x 13 pixel boxcar window.Of the processing errors indicated by the smoothed discrepancy mask, 100% of the artificially introduced errors and 97.6% of the remaining errors were successfully corrected.

[0081] Fig. 14 shows a summary of the flow chart of the method according to the invention. In a step S1, respective images of a ground region are acquired by a first radar, a second radar, and at least one auxiliary radar. The first radar and the second radar represent primary radars, as used in a bistatic interferometry system. In a step S2, a primary interferogram is generated from the images of the first and second radars. In step S3, a first auxiliary interferogram is generated from the images of the pair of radars that have a small baseline separation. In the case of a single auxiliary radar, this could be, for example, the first radar and the auxiliary radar. In step S4, a second auxiliary interferogram is generated, which is different from the first auxiliary interferogram.For this purpose, for example, the images from the auxiliary radar and the second radar are combined. In step S5, a discrepancy mask is generated from the primary interferogram and the first and / or second auxiliary interferogram. This involves a pixel-by-pixel comparison of the unwrapped phases, scaled by the respective ambiguity levels, previously generated from the primary interferogram and the first and second auxiliary interferograms. Using the discrepancy mask, phase ambiguities in the primary interferogram are resolved in step S6.

[0082] List of reference symbols

[0083] 1 SAR system

[0084] 10 first radar

[0085] 20 second radar

[0086] 30 auxiliary radar

[0087] 30-1 first auxiliary radar

[0088] 30-2 second auxiliary radar

[0089] P Platform (radar system)

[0090] AR Azimuth direction

[0091] PH platform height

[0092] SR slant range

[0093] SW swath width

[0094] B Baseline orthogonal baseline

[0095] Ri slant distance

[0096] R2 slant distance

[0097] BO Floor

[0098] BL1 first baseline

[0099] BL2 second baseline (small baseline)

[0100] BL3 third baseline (middle baseline)

[0101] ATS Along-Track Distance

[0102] AM antenna diagram

[0103] MS main strip

[0104] AS ambiguity strip

[0105] PBR processed bandwidth

[0106] AE ambiguous energy

[0107] PRF pulse repetition rate

[0108] IGP primary interferogram

[0109] IGH1 first auxiliary interferogram

[0110] IGH2 second auxiliary interferogram HE error

[0111] D Discrepancy criterion met

[0112] C Discrepancy criterion not met

[0113] References

[0114] [1] M. Lachaise, T. Fritz and R. Barnier, "The Dual-Baseline Phase Unwrapping Correction Framework for the TanDEM-X Mission Part 1 : Theoretical Description and Algorithms," in IEEE Transactions on Geoscience and Remote Sensing, Vol.

[0115] 56, no. 2, pp. 780-798, Feb. 2018;

[0116] [2] M. Zink, G. Krieger, T. Amiot, "Interferometric Performance of a Cartwheel Constellation for TerraSAR-L," FRINGE Workshop, 2003, Frascati, Italy.

[0117] [3] M. Ester and H. Kriegei and J. Sander and X. Xu, "A density -based algorithm for discovering clusters in large spatial databases with noise," in Proc. KDD, p. 226-

[0118] 231, 1996.

[0119] [4] Fawwaz T. Ulaby und M. Craig Dobson, Handbook of Radar Scattering Statistics for Terrain, Artech, 2019.

[0120] [5] G. Krieger et al., "TanDEM-X: A Satellite Formation for High-Resolution SAR Interferometry," in IEEE Transactions on Geoscience and Remote Sensing, Vol.

[0121] 45, No. 11, S. 3317-3341, Nov. 2007.

Claims

Patent claims 1. A method for detecting and resolving phase ambiguities in interferometric SAR data, wherein the SAR data are in the form of interferograms (IGP, IGH1, IGH2) generated from images acquired and provided by a multi-static SAR system (1), wherein the SAR system (1) comprises the following radars flying in a formation along an azimuth direction (AR) to acquire the images: - a first radar (10) having a transmitter, a receiver and an antenna with an antenna aperture of a first size; - a second radar (20) having a receiver and an antenna with an antenna aperture of the first size, wherein the first and second radars (10, 20) have a first baseline spacing (BL1) transverse to an azimuth direction (AR) of the SAR system; - at least one auxiliary radar (30; 30-1, 30-2) designed exclusively for reception, having an antenna with an antenna aperture of a second size that is smaller than the antenna aperture of the first size, wherein the at least one auxiliary radar (30; 30-1, 30-2) flies in formation with the first and second radars (10, 20) such that a second baseline spacing (BL2) is established between the radars (10, 20, 30; 30-1, 30-2), the second baseline spacing (BL2) being smaller than the first baseline spacing (BL1); wherein the method comprises the following steps: a) generating a primary interferogram (IGP) from the images of the first and second radars (10, 20); b) generating a first auxiliary interferogram (IGH1) from the images of the pair of radars (10 / 30; 30-1 / 30-2) having the second baseline spacing (BL2); c) generating a second auxiliary interferogram (IGH2) different from the first interferogram (IGH1);d) generating a phase development for the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2); e) generating phases scaled by the respective ambiguity levels by multiplying them by the assigned ambiguity level for the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2); f) generating a discrepancy mask by pixel-by-pixel comparison of the scaled phases resulting from the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2), wherein a respective pixel in the discrepancy mask is marked as discrepant if the compared scaled phases deviate from each other by more than a predetermined threshold value; g) resolving phase ambiguities in the primary interferogram (IGP) in the pixels marked as discrepant in the discrepancy mask.

2. Method according to claim 1, characterized in that the first auxiliary interferogram (IGH1) comprises an ambiguity level which is at least twice as large as the ambiguity level of the primary interferogram (IGP), the ambiguity level being the height difference corresponding to a 2n phase difference.

3. Method according to claim 1 or 2, characterized in that the second auxiliary interferogram (IGH2) comprises an ambiguity level which is between half and twice the ambiguity level of the primary interferogram (IGP), the ambiguity level being the height difference corresponding to a 2TI phase difference.

4. Method according to one of the preceding claims, characterized in that the primary interferogram (IGP), the first and the second auxiliary interferogram (IGH1, IGH2) are each subjected to a phase processing independently of one another.

5. Method according to one of the preceding claims, characterized in that the primary interferogram (IGP), the first and the second auxiliary interferogram (IGH1, IGH2) are each subjected to smoothing independently of one another.

6. Method according to one of the preceding claims, characterized in that the second antenna aperture is 50%, preferably 25%, and most preferably 10%, of the size of the first antenna aperture.

7. Method according to one of the preceding claims, characterized in that the discrepancy mask is subjected to smoothing.

8. Method according to one of claims 1 to 7, characterized in that the second auxiliary interferogram (IGH2) is generated from the images of the pair of radars (20 / 30) having a third baseline spacing (BL3) which is smaller than the first baseline spacing (BL1) and greater than the second baseline spacing (BL2).

9. Method according to one of claims 1 to 7, characterized in that the second auxiliary interferogram (IGH2) is generated from the primary interferogram (IGP) and the first auxiliary interferogram (IGH1).

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

11. System for detecting and resolving phase ambiguities in interferometric SAR data, wherein the SAR data are in the form of interferograms (IGP, IGH1, IGH2) generated from images acquired and provided by a multistatic SAR system (1), wherein the SAR System (1) comprises the following radars flying in a formation to capture images along an azimuth direction (AR): - a first radar (10) having a transmitter, a receiver and an antenna with an antenna aperture of a first size; - a second radar (20) having a receiver and an antenna with an antenna aperture of the first size, wherein the first and second radars (10, 20) have a first baseline spacing (BL1) transverse to an azimuth direction (AR) of the SAR system; - at least one auxiliary radar (30; 30-1, 30-2) designed exclusively for reception, having an antenna with an antenna aperture of a second size that is smaller than the antenna aperture of the first size, wherein the at least one auxiliary radar (30; 30-1, 30-2) flies in formation with the first and second radars (10, 20) such that a second baseline spacing (BL2) is established between the radars (10, 20, 30; 30-1, 30-2), the second baseline spacing (BL2) being smaller than the first baseline spacing (BL1); wherein the system is designed to carry out the following steps: a) generating a primary interferogram (IGP) from the images of the first and second radars (10, 20); b) generating a first auxiliary interferogram (IGH1) from the images of the pair of radars (10 / 30; 30-1 / 30-2) having the second baseline spacing (BL2); c) generating a second auxiliary interferogram (IGH2) different from the first interferogram (IGH1);d) generating a phase development for the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2); e) generating phases scaled by the respective ambiguity levels by multiplying them by the assigned ambiguity level for the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2); f) generating a discrepancy mask by pixel-by-pixel comparison of the scaled phases resulting from the primary interferogram (IGP) and the first and / or second auxiliary interferogram (IGH1, IGH2), wherein a respective pixel in the discrepancy mask is marked as discrepant if the compared scaled phases deviate from each other by more than a predetermined threshold value; g) resolving phase ambiguities in the primary interferogram (IGP) in the pixels marked as discrepant in the discrepancy mask.

Images