Method for generating digital elevation models of a region under consideration on Earth using a system of multiple platforms with a synthetic aperture radar (SAR)

Abstract

A method and apparatus for generating a digital elevation model of a region under consideration on Earth or another planetary body is disclosed using a system of multiple platforms with a synthetic aperture radar (SAR) in a single pass, wherein the method comprises the following steps: providing a system of multiple SAR platforms arranged with multiple along-track and cross-track baselines, wherein at least one of the SAR platforms repeatedly transmits pulses in the direction of the region under consideration, e.g. in the oblique distance direction.The receiving SAR platforms receive the echo signals (raw data) and are equipped with antennas whose lengths in the along-track direction are shorter than the length required for the 3 dB Doppler bandwidth of the received signal to equal the pulse repetition frequency. The 3 dB Doppler bandwidth is defined as the width of the interval of Doppler frequencies for which the intensity of a ground-based target's response is at least half its maximum. Distance compression of the raw data is performed to obtain distance-compressed data. The distance-compressed data from all receiving SAR platforms are combined into a tomogram using 2D beamforming in the along-track and cross-track dimensions, and the digital elevation model is estimated from this tomogram.

Description

[0001] The invention relates to a method and apparatus using synthetic aperture radar (SAR) that generates a digital elevation model of a region of interest on Earth or another planetary body using a system of multiple platforms with synthetic aperture radar (SAR), e.g. SAR satellites, in a single pass of the platforms over the region of interest, comprising the following steps. Field of the invention and prior art

[0002] Synthetic aperture radars (SAR) belong to the class of active, coherent, high-resolution, imaging radars with various applications in remote sensing. As described in Fig.As shown in Figure 1, a SAR operates on a moving platform in a laterally oriented geometry. The direction of movement is called the azimuth direction, and the radial distance from the platform is called the slant range. The radar images a limited slant range interval, which, as shown in Fig. 1, images a region on the ground (Earth) in the form of a strip parallel to the azimuth direction, the so-called swath, by sending pulses of electromagnetic radiation at a frequency, the so-called pulse repetition frequency (PRF), in this direction and receiving an echo for each transmitted pulse.

[0003] Synthetic aperture radars (SAR) are also known from the following documents: DE 199 29 143 A1 and PEIXOTO, Maxwell Nogueira; VILLANO, Michelangelo: A CubeSat add-on for resolving phase unwrapping errors in single-pass SAR interferometry. In: Proceedings / EUSAR 2022 : 14th european conference on synthetic aperture radar. 25-27 July 2022. Berlin: Offenbach, 2022. pp. 664-669. - ISBN 978-3-8007-5823-4

[0004] Therefore, the raw SAR data is sampled along the azimuth using the PRF. However, only a portion of the Doppler spectrum (the azimuth spectrum) of the raw data is processed to create the SAR image. This portion is called the processed Doppler bandwidth. This sampling causes the aliasing effect, in which Doppler frequency components of the signal outside the interval [-PRF / 2, PRF / 2] fold into the processed Doppler bandwidth, superimposing and corrupting the main signal. These are called azimuth ambiguities. The Doppler spectrum of the raw SAR data is modulated by the antenna pattern along the azimuth, and the length of the interval of Doppler frequencies where the power is no less than 3 dB below that of the peak is called the 3 dB Doppler bandwidth.The azimuth sampling frequency—in this case, the PRF—must be high enough (and usually higher than the Doppler bandwidth) to meet the azimuth ambiguity-to-signal ratio requirements. SAR imaging can also be achieved if the pulses are transmitted at irregular pulse repetition intervals rather than at a constant pulse repetition frequency.

[0005] SAR images can also be created by combining data from a train of N SAR satellites tracking the same track. Either a single satellite transmits pulses, or pulse transmission occurs alternately between satellites, or multiple satellites transmit pulses simultaneously, characterized by mutually orthogonal waveforms. In all cases, the raw data from the N receivers can be combined to produce raw data sampled with an equivalent PRF N times greater than the PRF of the individual satellite. Therefore, with N satellites in a train formation, SAR images can be created with a PRF up to approximately N times lower than the system's Doppler bandwidth while still meeting azimuth ambiguity-to-signal ratio requirements. This allows the same swath width to be imaged using multiple antennas with smaller apertures.

[0006] Across-track SAR interferometry is a technique in which two SAR images of the same region are acquired from different positions, as in Fig. 2, and combined to create a digital elevation model (DEM) of the region. The distance between the tracks is called the across-track baseline B, and their projection B1 orthogonal to both the slant range and azimuth direction is called the orthogonal baseline.

[0007] The two images can be acquired simultaneously (i.e., in a single pass by two satellites), known as a bistatic configuration, or acquired at different times, known as a repeat-pass configuration. Many SAR systems can perform across-track interferometry in the repeat-pass configuration because it requires only a single satellite. However, this configuration suffers from the problem of temporal decorrelation, meaning the quality of the resulting DEM is degraded by changes in the scene (or atmospheric properties) between the two acquisitions.

[0008] The two images are combined pixel by pixel to create an interferogram according to v12=u1u2*, where v 12are the pixels of the interferogram, u1 and u2 are the pixels of each of the two images, and -* is the complex conjugate operation. The phase of the interferogram is then the phase difference between the two images. Because the traces are different, the two two-dimensional images are projections of the scene into different coordinate systems, so before the interferogram is created, a process called coregistration is performed, in which transformations are applied to align both images. After the interferogram is created, a process called multilooking is performed, in which neighboring interferogram pixels are averaged to reduce the uncertainty in the phase at the expense of a lower resolution of the DEM product.

[0009] The phase difference encoded in the interferogram is proportional to the height of the terrain, according to dϕ=2πh2πdh, h2π=nλR sin(θi)B⊥, where h 2π , the so-called ambiguity height, is the height difference corresponding to a 2π phase difference, θ i is the angle of incidence, λ is the wavelength of the carrier, R is the slant distance, B ⊥ is the orthogonal baseline, and n is 2 when the interferogram is formed from a bistatic configuration and 1 when it is formed from a repeat-pass configuration. This proportionality holds for the absolute interferometric phase, but the phases are cyclic, so the observed phases are the result of wrapping the absolute phase into, e.g., the [-π,π] interval. Phase unwrapping is the process of reconstructing the absolute phases from the wrapped phases. After performing phase unwrapping, the relationship in (2) is used to convert the absolute phases into a digital elevation model of the imaged region.

[0010] The phase unwrapping process can lead to incorrect absolute phase values. These are referred to as phase unwrapping errors and affect the resulting DEM in the form of height deviations that are many times the ambiguity level. For a fixed level of phase uncertainty, the smaller the ambiguity level, the higher the accuracy of the resulting DEM, but the more likely the occurrence of phase unwrapping errors.

[0011] To correct phase unwrapping errors, additional bistatic acquisitions can be performed over the same scene, but with different baselines and therefore with different levels of ambiguity [1]. The resulting interferograms can then be processed with a multi-baseline phase unwrapping algorithm, e.g., the one presented in [1], to generate DEMs without unwrapping errors.

[0012] The generation of DEMs requires clear, high-SNR SAR images that can be acquired with large antenna apertures. These requirements lead to large and expensive satellites. High-accuracy DEMs generated from a single pass of a bistatic SAR interferometer are prone to phase unwrapping errors. Bistatic SAR interferometers are therefore not suitable for the frequent monitoring of rapidly changing scenes or the generation of time series of DEMs, as correcting phase unwrapping errors requires additional satellite passes and orbital maneuvers between passes to change the baseline. Single-pass DEM generation could be achieved with a multistatic system consisting of at least three SAR satellites, but the cost of such a system would be very high due to the number and size of the satellites.

[0013] DEMs can also be generated using multiple trains of small-aperture satellites, but in this case a very large number of satellites is required.

[0014] An object of the present invention is to develop a method for generating digital elevation models of a region of interest on Earth using a simplified system of multiple platforms with a synthetic aperture radar (SAR).

[0015] To achieve the above-mentioned object, the invention proposes a method for generating a digital elevation model of a region to be observed on the Earth or another planetary body using a system of multiple platforms with a synthetic aperture radar (SAR), e.g. SAR satellites, in a single pass of the platforms over the region to be observed, which comprises the following steps. - Providing a system of multiple SAR platforms arranged with multiple along-track and cross-track baselines, - wherein at least one of the SAR platforms repeatedly transmits pulses in the direction of the region to be observed, i.e. in the slant range direction defined by the position of the platforms and the position of the region to be observed, at a specific pulse repetition frequency, and - at least some of the SAR platforms, i.e. the receiving SAR platforms, receive the echo signals, referred to as raw data, reflected from the region of interest and are equipped with antennas whose lengths in the along-track direction are less than the length required for the 3 dB Doppler bandwidth of the received signal to be equal to the pulse repetition frequency or the average pulse frequency in the case of non-uniform pulse repetition intervals, whereby the 3 dB Doppler bandwidth is defined as the width of the interval of Doppler frequencies for which the intensity of the response of a ground target is at least half of its maximum, - Performing range compression on the raw data received from each receiving SAR platform to obtain range-compressed data, - joint processing of the distance-compressed data of all receiving SAR platforms into a tomogram by 2D beamforming in the along-track and cross-track dimensions, and - Estimating the digital elevation model from the tomogram.

[0016] In one aspect of the present invention, the tomogram is processed to suppress radar ambiguities along the along-track and cross-track dimensions by utilizing spectral filters.

[0017] In another aspect of tomogram processing, estimating the digital elevation model from the tomogram involves performing multilooking of the tomogram.

[0018] According to a further aspect of the present invention, the step of multilooking the tomogram comprises taking the moving average of the intensity as an absolute value squared over the slant distance and along-track directions and, for each slant distance and along-track position, selecting the height corresponding to the maximum of the multilooked tomogram.

[0019] As mentioned above, the SAR platforms are equipped with antennas whose lengths in the along-track direction are smaller than the lengths required for the 3 dB Doppler bandwidth of the received signal to be equal to the pulse repetition frequency. In certain aspects of the present invention, the antenna lengths of the SAR platforms in the along-track direction are at least a factor of two or three or four or five or more smaller than the length required to achieve the 3 dB Doppler bandwidth of the received signal.

[0020] In another alternative embodiment of the present invention, the repeated transmission of the pulses occurs alternately among some of the SAR platforms.

[0021] Alternatively, the step of repeatedly transmitting pulses may also consist of multiple SAR platforms transmitting pulses with mutually orthogonal waveforms.

[0022] According to yet another aspect of the present invention, only a subset of the SAR platforms repeatedly transmit pulses, wherein the receiving SAR platforms have no pulse transmission capability and are intended only to receive echo signals.

[0023] The present invention proposes a method and apparatus for generating a DEM using multiple SAR systems with small antenna apertures flying in formation and arranged with multiple across-track and along-track baselines and dedicated processing (cf. Fig. 3). Furthermore, the system operates with a PRF that is much lower than the Doppler bandwidth. Pulse transmissions can be performed by a dedicated satellite, with all other satellites receiving the echoes, or pulse transmissions can be performed alternately among the satellites. Another alternative is for multiple satellites to transmit pulses simultaneously, characterized by mutually orthogonal waveforms. If only a subset of satellites transmit pulses, the other satellites can be manufactured without transmission capability, significantly reducing their cost.

[0024] The block diagram according to Fig. Figure 4 shows the main processing steps for generating the DEM model based on the raw data provided by the small satellites of the small satellite cluster.

[0025] According to one aspect of the present invention, the first step in processing for DEM generation is to perform range compression on the raw data from each satellite, i.e., to perform matched filtering along the slant range, tailored to the transmitted pulses. The range-compressed data from all satellites is then beamformed into a tomogram, which is a three-dimensional SAR image whose dimensions are slant range, azimuth, and elevation. The value of the tomogram at a given position is the result of a beamforming process in which the range-compressed data from all satellites is used to direct a beam to that position.The coefficients for this beamforming can be partitioned as the product of two components, one responsible for focusing the data along azimuth and one for focusing and steering the beam in elevation. One way to calculate the components responsible for focusing along azimuth is to follow the multi-channel reconstruction processing presented in [2]. One way to calculate the components responsible for steering the beam in elevation is to adjust them to compensate for the topographic phase expected from a target at the elevation in question. The resulting tomogram can also be post-processed to suppress azimuthal ambiguities, for example, by exploiting their unique signature to distinguish and remove them from the desired signal. The final DEM is then extracted from the tomogram.One method for this is to first multilook a tomogram over slant range and azimuth by averaging the squared absolute value of the data over different “looks” – the averaging can be done over a small sliding window (e.g. 5 × 5 pixels) in slant range and azimuth (each pixel is considered a different “look”) or by splitting the range and azimuth spectra of the tomogram into a number of subbands, forming a tomogram from each subband and then averaging over these tomograms (each tomogram is a different “look”) – and then, for each slant range and azimuth position, estimating elevation from the profile of the multilooked tomogram over elevation.

[0026] The multiple across-track baselines enable DEM generation with high accuracy and robustness to phase unwrapping errors. The multiple along-track baselines enable accurate DEM generation with a PRF much lower than the Doppler bandwidth, which in turn enables the use of smaller antennas and reduces satellite size and cost.

[0027] The advantages of the proposed system compared to conventional bistatic SAR interferometry are 1) the proposed system enables the generation of DEMs with the same performance (in terms of resolution, accuracy and swath range) as conventional interferometric SAR systems, but at a significantly lower cost due to the use of small satellites with small antenna apertures; 2) the proposed system does not suffer from phase unwrapping errors due to the presence of multiple across-track baselines; 3) the proposed system is more flexible, as the cluster of small satellites can be rearranged in various ways and used for different applications, such as along-track SAR interferometry and potentially single-pass SAR tomography; 4) the proposed system is more robust against hardware failures, since the system would be able to produce the products even after the loss of one or some receiver satellites, albeit with some loss of quality; 5) With the proposed system, it may be financially feasible to replace lost satellites due to their individual costs and size being lower. Compared to conventional bistatic SAR interferometry with an additional pass to correct phase unwrapping errors, the proposed system has the advantage of requiring less time to generate a DEM for a given area. Furthermore, since only a single pass of the satellite cluster is required, it does not preclude applications related to the observation of rapidly changing topography, as is the case when using two long-distance pass-throughs. 6) SAR imaging can be performed by transmitting pulses at a constant pulse repetition rate or at irregular pulse repetition intervals (average pulse repetition rate).

[0028] In the following, the invention is described in more detail with reference to the drawing, in which the following is shown: Fig. 1 shows the basic geometry of a SAR system, Fig. 2 shows the basic geometry of an interferometric across-track SAR system, Fig. Figure 3 shows a schematic view of the interferometric SAR system according to the invention for DEM generation, where a single transmitter (top left) or multiple transmitters (bottom left) can be used, and where the raw data from the cluster form an array of phase centers, one for each receiver-transmitter pair at each pulse, distributed in along-track and across-track (center) and processed to directly generate a DEM (right). Fig. 4 shows a block diagram of the technology for processing the data from the cluster of small satellites in particular to generate a DHM, Fig.Figure 5 shows an exemplary arrangement of 8 small satellite receivers for the distributed interferometric SAR system according to the invention, and Fig. Figure 6 shows in (a) the terrain topography and in (b) a multilooked tomogram at a certain slant distance formed from the data of a simulated acquisition performed by the considered distributed interferometric SAR system, where the black line in (b) represents the DEM generated by maximizing the tomogram.

[0029] An example of the present invention will now be described in more detail with reference to some of the figures already mentioned above as well as to further figures in the drawing.

[0030] In the following, a cluster of eight small satellites together with a dedicated transmitter is considered. The system parameters are listed in Table 1. The arrangement of the eight receivers is shown in Fig. 5 and Table 2. Table 1

[0031] Parameters of the distributed interferometric SAR system according to an example of the present invention. carrier frequency 9.65 GHz Orbit altitude 515 km Angle of incidence 36° Receiver antenna Planar, 0.5 m × 0.7 m (length × height) Transmitter antenna Planar, 2 m × 0.7 m (length × height) 3 dB Doppler bandwidth 8634 Hz processed Doppler bandwidth 8634 Hz PRF 3100 Hz Table 2

[0032] Along- and across-track position of the 8 small satellite receivers of the distributed interferometric SAR system according to this embodiment of the present invention. Recipient ID 1 2 3 4 5 6 7 8 Along-track position [m] 0,0 228,0 531,7 683,5 0,3 152,9 455,8 608,4 Across-track position [m] 0,0 75,9 0,0 151,7 455,2 303,5 379,3 455,2

[0033] The raw data acquired by the cluster over a homogeneous scene with a flat topography, including a pyramid at its center, were simulated. Noise was accounted for in the raw data with a signal-to-noise ratio of 6 dB. The data were then processed into a tomogram using 2D beamforming. This combined multichannel reconstruction (in azimuth) to recover a bandwidth equal to 3 times the PRF, azimuth compression, and low-pass filtering to the processed Doppler bandwidth, and Fourier beamforming (in elevation). The tomogram was then multilooking using a 5 × 5 sliding window. Fig.Figure 6 shows in (a) the terrain topography of the region of interest and in (b) the multilooked tomogram together with the terrain topography (dashed black line) and the DEM generated by maximizing the tomographic response (white line). The generated DEM shows good agreement with the underlying topography, and the standard deviation of the elevation error was 0.67 m. However, it should be noted that the DEM exhibits a spike at approximately -120 m in azimuth. Spikes like this are the result of an incorrect selection of an elevation ambiguity band by the tomogram maximization. These errors occur occasionally but can be corrected in various ways, e.g., by exploiting the high spatial correlation of the typical terrain to avoid strong localized elevation jumps or by increasing the number of small satellites. The above-mentioned standard deviation of the elevation error was evaluated excluding these spikes.

[0034] In the following, the present invention will be described again in connection with an embodiment.

[0035] As mentioned above, synthetic aperture radar (SAR) interferometry is an essential remote sensing technique with a wide range of applications. The investigation and monitoring of dynamic processes on the Earth's surface requires digital elevation models (DEMs) at short time intervals, making distributed and multistatic SAR systems a promising solution to this need. The present invention presents a concept for distributed SAR interferometry using a cluster of small satellites with small antenna apertures operating at a pulse repetition frequency much smaller than the Doppler bandwidth and capable of generating a single-pass DEM with high accuracy and robustness against phase unwrapping errors.The novelty of the proposed method lies in the fact that the DEM is extracted from a tomogram formed using all available data, without the need for the intermediate formation of SAR images. This allows for a reduction in the number of required satellites while achieving greater baseline diversity. A cluster of small satellites is a very attractive and cost-effective solution for the implementation of future interferometric SAR missions.

[0036] The study and monitoring of dynamic phenomena on Earth, such as ice melting, by satellite remote sensing requires continuous data time series and short repetition times. Synthetic aperture radar (SAR) interferometry is a powerful remote sensing technique capable of providing high-accuracy and high-resolution data for many such applications. However, while frequent repetitions are possible for SAR imaging from satellite constellations today, they are lacking for single-pass interferometric products, such as high-quality digital elevation models (DEMs). State-of-the-art interferometric SAR systems generally require multiple satellite overpasses of the same area to produce such products, limiting the sampling frequency of each generated time series.Even TanDEM-X, a formation flight mission capable of generating interferograms in a single overpass, requires additional overpasses with different baselines—the spatial separation between satellites—to produce DEMs robust to unwrapping errors and to eliminate layovers, e.g., in mountainous regions [1]. Furthermore, multi-pass systems must deal with the fact that the imaged scene and the behavior of the atmosphere change between different satellite overpasses. This can affect data quality (e.g., heavy rain between two overpasses alters the arrangement of soil and vegetation, causing decorrelation between images), introduce additional complexity (e.g., the different ionospheric delays between overpasses must be estimated and compensated), and even prevent the generation of an unambiguous product (e.g.,Snowfall events occurring between two overflights change the topography and may prevent the overflights from being used together to resolve phase-unwrapping errors).

[0037] With single-baseline across-track SAR interferometry, there is a trade-off between accuracy and robustness to unwrapping errors, with the former being achieved with larger baselines and the latter with smaller ones. If additional baselines are available, multiple interferograms can be created and combined to produce a final DEM with high accuracy and robustness. Furthermore, multi-baseline SAR tomography can potentially be used to resolve layover in DEMs and can also enable a wide range of applications, such as biomass measurements based on the vertical structure of forests.A formation with three or more satellites separated in the across-track direction would then be able to produce highly accurate DEMs in a single pass, avoiding the disadvantages and limitations of generating a product from data acquired at different times and enabling the creation of time series with frequent repetitions, supporting applications such as glacier or permafrost monitoring.

[0038] Instead of a formation of large satellites, the present invention proposes the use of a cluster of a larger number of small satellites with small antenna apertures, so that the data from each individual satellite is insufficient to create a unique SAR image, but the data from the entire cluster can be combined to produce a unique and highly accurate DEM. A cluster of small satellites can be a more cost-effective and flexible solution than a few large satellites and has the usual advantage of distributed systems: if some of the satellites in the cluster fail, the cluster can still produce products, albeit with some loss of quality, and it would be financially feasible to replace the failed satellites because their individual costs are low compared to those of the entire mission. Furthermore, a cluster of many small satellites may be suitable for other applications, such asAlong-track interferometry or tomography, flexibly rearranged in different formations.

[0039] Distributed SAR imaging can be performed using satellites flying in a platoon formation. SAR interferometry for robust DEM generation could then be performed using three or more satellite platoons, each generating a SAR image, and the usual SAR interferometric processing using these images. However, if the goal is to create a DEM, one should consider that the latter is characterized by a significantly lower information content compared to the SAR images used to create it. The local spatial correlation of a typical topography is indeed much greater than that of a SAR image, where spatial correlation is low due to speckle. This discrepancy is an indication that three or more complete platoons of small satellites are generating data beyond what is required for robust DEM generation.This observation was first exploited by proposing a CubeSat add-on to a bistatic SAR interferometer. This provides an additional noisy SAR image with strong azimuth ambiguities, which, despite its low quality, can be used to correct unwrapping errors in the DEM generated by the system. Therefore, the present invention proposes that the data of the entire cluster of small satellites be processed as a whole to directly generate a robust DEM from undersampled SAR data, without the intermediate step of generating high-quality SAR images. In this way, comparable DEM quality could be achieved with fewer small satellites, and the cluster does not need to be arranged in trains, allowing for more across-track baselines. TOMOGRAM-BASED DEM GENERATION

[0040] The proposed system concept is a cluster of small satellites with small antenna apertures, designed to generate robust and highly accurate DEMs. All or some of the satellites in the cluster can have pulse-transmitting capabilities and transmit pulses alternately or all simultaneously. Another option is a dedicated transmitter satellite—which can be an existing satellite opportunistically tracked by the cluster—so that the other satellites can only receive. As a result of the small antenna apertures, the proposed system observes a wide Doppler bandwidth, much larger than the pulse repetition frequency (PRF).Similar to the train formation used for SAR imaging, the proposed cluster must include along-track baselines that enable reconstruction of this wide Doppler bandwidth, but to enable robust DEM generation, it must also include a mix of across-track baselines. Large baselines should be preferred, as they contribute to elevation accuracy, but a sufficient number of small and medium-sized baselines should be included to provide robustness to the final DEM. As described in [the original text]. Fig. 3, the raw data from the cluster (two alternatives on the left side of Fig. 3) then a sparse array of phase centers distributed in along- and across-track (see in the middle of Fig. 3), and are processed to directly generate a DHM (see in Fig. 3 on the right), without the intermediate step of forming the SAR image.

[0041] As shown in the block diagram in Fig.As shown in Figure 4, a DEM can be generated from the data of the small satellite cluster by maximizing tomographic responses. That is, a multi-viewed tomogram can be formed from the range-compressed data of the entire cluster. For each pixel in range and azimuth, the DEM elevation is selected as the elevation whose value is largest in the multi-viewed tomogram. The tomogram can be generated from the array of phase centers provided by the cluster by beamforming in azimuth, including azimuth compression and reconstruction of the Doppler bandwidth larger than the PRF, using the along-track baseline, and in elevation using the across-track baseline.In addition, multilooking of the tomogram consists in averaging the squared size of the looks, which can be done as in conventional SAR interferometry with a sliding window in distance and azimuth or by dividing the data into frequency bands in distance and azimuth.

[0042] This DEM generation method is a generalization of conventional SAR interferometry, and in the case of a single baseline, the same DEM is equivalently obtained by maximizing the tomogram formed by Fourier beamforming in elevation with the two available images. More generally, in the case of multiple baselines, maximizing the tomographic response with Fourier beamforming in elevation is the maximum likelihood estimator of the elevation, assuming equal interferometric coherence in all baselines. This result is proven by the observation that, in this case, the log-likelihood function ln L(h|u1,...,uL)=C+∑l=1L−ulHejFhΓ−1e−jFhul equal to the multi-looked tomogram q(h)=1L∑l=1L|ql(h)|2=1L∑l=1LulHejFh11Te−jFhul ∵ql(h)=1Te−jFhul but for a constant and a linear factor, where h is the height, u lare the vectors of the values ​​of the focused data at the respective range and azimuth pixel for each satellite, l is the index of the look, L is the total number of looks, .T which denotes the transpose, .H denotes the transposed complex conjugate, r is the coherence matrix, e jFh is a diagonal matrix encoding the Fourier beamforming in elevation, C is a constant dependent on the coherence matrix, 1 is a vector whose entries are all 1, and q l (h) the different looks of the tomogram.

[0043] In the presence of volume scattering, the proposed DEM generation method will, similar to conventional SAR interferometry, provide heights relative to the phase center within the volume, albeit with some degradation of accuracy. However, the multiple baselines in the proposed system may enable tomographic applications such as estimating ground and treetop heights in a forest.

[0044] Interferograms formed from data from any pair of small satellites in the cluster are severely corrupted by azimuth ambiguities because the system operates with a PRF much lower than the Doppler bandwidth. The proposed processing technique is well suited to this scenario, as the tomogram is formed by coherently combining data from the entire cluster, allowing the suppression of azimuth ambiguities by exploiting the available along-track baselines. EXEMPLARY IMPLEMENTATION

[0045] This section presents an exemplary implementation of the proposed concept and a simulation of DEM generation by the tomographic response maximization method. A cluster of 8 small satellite SAR receivers, arranged as in Fig.5, and a dedicated transmitting satellite, all in helical orbits operating at the same altitude and frequency as TanDEM-X. The satellite arrangement evolves across the orbit but is approximately constant over the duration of an acquisition. The small satellite receivers have rectangular antennas 0.5 m long, much smaller than the 4.8 m of the TanDEM-X antenna, and the dedicated transmitting satellite has a rectangular antenna 2 m long. With these parameters, the system observes a 3 dB Doppler bandwidth of 8634 Hz, well above its PRF of 3100 Hz. CONCLUSION

[0046] The present invention proposes the concept of a distributed interferometric SAR system based on a cluster of small satellites with reduced antenna size, capable of generating a robust and accurate DEM in a single satellite pass, thus avoiding the disadvantages of using multiple temporally separated observations. A new DEM generation method is presented that does not require the acquisition of SAR images and thus does not limit the cluster to train formations, allowing the use of a smaller number of satellites than otherwise possible.

[0047] This concept is a promising solution for future Earth observation missions that require the generation of high-quality DEMs in a single overflight, and could also be of interest for planetary exploration missions.

[0048] Digital elevation models (DEMs) are used for a range of geospatial applications, including infrastructure planning and management, land-use planning, modeling of water flows or mass movements for landslide risk assessment, orthorectified map creation, geocoding of aerial photographs or satellite images, 3D visualization, open-pit coal mining monitoring, etc. Bibliography [1] M. Lachaise, T. Fritz and R. Bamler, “The Dual-Baseline Phase Unwrapping Correction Framework for the TanDEM-X Mission Part 1: Theoretical Description and Algorithms,” in: IEEE Trans. on Geosci. and Rem. Sens., Vol. 56, No. 2, pp. 780-798, Feb. 2018. [2] G. Krieger, N. Gebert and A. Moreira, “Unambiguous SAR Signal Reconstruction from Nonuniform Displaced Phase Center Sampling,” in: IEEE Geosci. and Rem. Sens. Lett., Vol. 1, No. 4, pp. 260-264, Oct. 2004.

Claims

[1] A method for generating a digital elevation model of a region of interest on Earth or another planetary body using a system of multiple platforms with a synthetic aperture radar (SAR), e.g. SAR satellites, in a single pass of the platforms over the region of interest, comprising the following steps - Providing a system of multiple SAR platforms arranged with multiple along-track and cross-track baselines, - wherein at least one of the SAR platforms repeatedly transmits pulses in the direction of the region to be observed, i.e. in the slant range direction defined by the position of the platforms and the position of the region to be observed, at a specific pulse repetition frequency, and - at least some of the SAR platforms, i.e. the receiving SAR platforms, receive the echo signals, referred to as raw data, reflected from the region of interest and are equipped with antennas whose lengths in the along-track direction are less than the length required for the 3 dB Doppler bandwidth of the received signal to be equal to the pulse repetition frequency or the average pulse frequency in the case of non-uniform pulse repetition intervals, whereby the 3 dB Doppler bandwidth is defined as the width of the interval of Doppler frequencies for which the intensity of the response of a ground target is at least half of its maximum, - Performing range compression on the raw data received from each receiving SAR platform to obtain range-compressed data, - joint processing of the distance-compressed data of all receiving SAR platforms into a tomogram by 2D beamforming in the along-track and cross-track dimensions, and - Estimating the digital elevation model from the tomogram. [2] Method according to claim 1, characterized by processing the tomogram to suppress radar ambiguities along the along-track and cross-track dimensions by exploiting spectral filters. [3] Method according to claim 2, characterized by that the step of estimating the digital elevation model from the tomogram includes performing multilooking of the tomogram. [4] Method according to claim 3, characterized bythat the step of multilooking the tomogram comprises a moving average of the intensity as an absolute value squared over the slant distance and along-track directions and, for each slant distance and along-track position, the selection of the height corresponding to the maximum of the multilooking tomogram. [5] Method according to one of claims 1 to 4, characterized by that the antenna lengths in the along-track direction are at least a factor of two or three or four or five or more smaller than the length required to achieve the 3 dB Doppler bandwidth of the received signal. [6] Method according to one of claims 1 to 5, characterized by that the repeated transmission of the pulses takes place alternately among some of the SAR platforms. [7] Method according to one of claims 1 to 5, characterized bythat the step of repeatedly transmitting pulses comprises multiple SAR platforms transmitting pulses with mutually orthogonal waveforms. [8] Method according to one of claims 1 to 7, characterized by that only a subset of SAR platforms transmit pulses repeatedly, with the receiving SAR platforms having no pulse transmission capability and being designed only to receive echo signals. [9] Apparatus for generating a digital elevation model of a region to be viewed on the Earth or another planetary body using a system of multiple platforms with a synthetic aperture radar (SAR), e.g. SAR satellites, in a single pass of the platforms over the region to be viewed, the apparatus being designed to carry out a method according to any one of claims 1-8.

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