Method for determining a vertical structure of a semi-transparent medium from SAR data of a SAR system

Abstract

A method for determining the vertical structure of a semi-transparent medium from SAR data from a SAR system is described. The SAR system comprises either one or more broadband radars with a bandwidth greater than 25% of the carrier frequency, or alternatively, one or more multiband radars with different frequency bands, where the upper frequency of the multiband radar is at least twice the lower frequency. The SAR system receives SAR data from at least two SAR acquisitions of an area whose vertical structure is to be determined. These two acquisitions are performed from different observation angles with known baselines relative to each other. A corresponding broadband SAR image (10B, 20B) is generated for each of the two acquisitions.From one or more distinct pairs of broadband SAR images (10B, 20B), a multitude of narrowband interferograms with different center frequencies are determined across the entire broadband frequency range. Narrowband interferograms with corresponding center frequencies from each of the multiple distinct pairs of broadband SAR images form a set of narrowband interferograms. From each set of narrowband interferograms, a corresponding frequency-dependent coherence profile is determined for different image regions. An inversion is then determined for each coherence profile. From the inversion, parameters characterizing the vertical structure are determined.

Description

[0001] The invention relates to a method and a device for determining a vertical structure of a semi-transparent medium from SAR data of a SAR system.

[0002] Synthetic Aperture Radar (SAR) systems enable remote sensing of the Earth's surface by detecting radar pulses reflected from the 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 with a side-facing geometry. A SAR image is generated from the acquired SAR data through a process known as SAR focusing. In the following, the term "acquiring a SAR image" refers to the acquisition of SAR data and its processing to generate a SAR image. The basic operating principle of SAR systems is well understood.In the following, the term SAR system is used in a general form and also includes a SAR system that is equipped with multiple radars on one or more platforms and can therefore enable multiple SAR recordings from different flight paths simultaneously.

[0003] SAR interferometry (InSAR) is used, among other things, to determine the topographic height of a scene from two SAR images of the same area taken from positions separated transversely, i.e., orthogonally to the flight direction of the SAR system. The spatial distance between the acquisition positions is called the baseline. The projection of the baseline in the direction orthogonal to the oblique distance of the area covered by the SAR radar is defined as the orthogonal baseline. In the following description, unless otherwise specified, the term baseline always refers to the orthogonal baseline.

[0004] When determining topographic height in an area containing semi-transparent media with multiple scattering, a problem arises: volumetric decorrelation occurs within the volume structure, negatively impacting the InSAR phase and impairing the accuracy of the height measurement. Examples of semi-transparent media with multiple scattering include forests and ice sheets. Therefore, when surveying such areas, additional measurements and processing are required to properly characterize the volume structure. Known methods include polarimetric SAR interferometry (PolInSAR) and SAR tomography.

[0005] To acquire SAR data for PolInSAR methods, SAR systems capable of transmitting differently polarized signals and receiving their reflected echoes with different polarizations are used. During the processing of the received signals, the variation in interferometric coherence across different polarizations, due to different scattering mechanisms, is used to characterize the volumetric properties and the subsurface topography. This method is performed using polarimetric SAR systems mounted on airborne or space-based platforms (satellites).

[0006] SAR tomography requires at least three, and typically five to ten, SAR images acquired from different positions across the SAR system. Using all of these SAR images, an array is created across the direction of flight (the so-called cross-track direction), enabling the creation of a three-dimensional radar image of the surveyed area. From this multitude of SAR images, multiple interferograms of the same scene with different baselines can be generated. Vertical scattering information can be obtained by inverting the interferograms, a technique known to those skilled in the art. Such data can be acquired using an airborne platform with multiple controlled flight paths over the same area. Alternatively, the data can be acquired using satellite-based SAR systems, which typically overfly the surveyed area multiple times.

[0007] The so-called InSAR coherence is used as a measure of the correlation between two images used for interferometry, as well as a quantity used in the inversion process. InSAR coherence can be modeled based on the volumetric decorrelation using the vertical scattering profile of the area to be investigated.

[0008] Determining the vertical structure of a region with a semi-transparent medium has so far been a complex and costly process. The use of PolInSAR methods requires a specialized hardware design for the SAR system capable of transmitting and receiving multiple polarizations, although the accuracy of the inversion result is limited.

[0009] SAR tomography requires a large number of SAR images, typically between five and ten. Simultaneously acquiring all SAR images therefore necessitates a fleet of aircraft with airborne sensors or a corresponding array of satellites, both of which are complex and expensive. SAR images acquired using the so-called repeat-pass method, i.e., by repeatedly flying over the area containing the vertical structure to be determined, result in temporal decorrelation. This can be significant when using a satellite-based SAR system due to the limited repetition rates. This restricts the accuracy of the inversion results.

[0010] Deviating from the procedures described above is not readily possible due to regulatory requirements regarding the transmission power, frequencies, and bandwidth of SAR systems, as well as the algorithms tailored to them. The maximum bandwidth that can be transmitted from airborne and space-based platforms is regulated. In the P- and L-bands, which exhibit high penetration due to their long wavelengths, the maximum transmission bandwidth from space is limited to 6 MHz and 85 MHz, respectively. Consequently, the information varying across wavelengths cannot be used to invert the vertical dispersion information.

[0011] From the publication PAPATHANASSIOU, Konstantinos P.; CLOUDE, Shane R.: “Single-baseline polarimetric SAR interferometry”, IEEE transactions on geoscience and remote sensing, Vol. 39, 2001, No. 11, pp. 2352-2363, a method for determining a vertical structure of a semi-transparent medium from SAR data using polarimetric SAR interferometry is known.

[0012] From the publication REIGBER, Andreas; MOREIRA, Alberto: “First demonstration of airborne SAR tomography using multibaseline L-band data”, IEEE transactions on geoscience and remote sensing, Vol. 38, 2000, No. 5, pp. 2142-2152, a method for determining a vertical structure of a semi-transparent medium from SAR data using SAR tomography is known.

[0013] From CN 1 15 291 217 A, a method for determining the vertical structure of a semi-transparent medium from SAR data is known. For this purpose, electromagnetic waves with different frequencies are used, and a "low-frequency polarized SAR image" and a "high-frequency polarized SAR image" are employed.

[0014] The object of the present invention is to provide a method and a device with which the determination of a vertical structure of a semi-transparent medium is functionally simplified.

[0015] These tasks are solved by a method according to the features of claim 1, a computer program product according to the features of claim 15, and a device according to the features of claim 16. Advantageous embodiments are set forth in the dependent claims.

[0016] A method for determining the vertical structure of a semi-transparent medium from SAR data from a SAR system is proposed. The semi-transparent medium may exhibit the property of multiple scattering, as occurs, for example, in forested areas or ice surfaces. The SAR system used to implement the method comprises either one or more broadband radars with a bandwidth greater than 25% of the carrier frequency, or alternatively, one or more multiband radars with different frequency bands, where the upper (cutoff) frequency of the multiband radar is at least twice as high as the lower (cutoff) frequency of the multiband radar. Aircraft, satellites, or drones (Unmanned Aerial Vehicles, UAVs) can be used as carriers for the SAR system's radars. The latter enable the exploration of the area under consideration from a significantly lower altitude compared to aircraft or satellites.The ability to launch UAVs vertically, without the need for runways, also enables exploration in complex environments. Furthermore, data collection over local areas can be performed at very high repetition rates and competitive costs. Due to their low cost and unmanned nature, multiple UAVs can easily be operated simultaneously.

[0017] The following steps are carried out in the method according to the invention:

[0018] In step a), the SAR system receives SAR data from at least two SAR images of an area whose vertical structure is to be determined. These at least two SAR images are acquired from different observation angles with known baselines relative to each other. The SAR data can optionally be acquired by one or more platforms using the known repeat-pass method, i.e., by acquiring SAR data over the area with successive SAR images. Alternatively, the SAR data can be acquired simultaneously by two or more platforms using the known single-pass method, in which case several radars are mounted on one or more platforms flying in formation (bi-static or multi-static configuration). In this case, it is sufficient for one of the radars to be able to transmit radar pulses and for all radars to be able to receive the reflected radar pulses.

[0019] In step b), a broadband SAR image is generated for each of the at least two SAR acquisitions. A "broadband SAR image" is one that utilizes the large transmission bandwidth employed by the radar. As described above, this bandwidth can exceed 25% of the carrier frequency in a broadband radar. A broadband SAR image generated by a multiband radar can be located in different frequency bands, meaning it may exhibit gaps between and / or within a frequency band.

[0020] In step c), a multitude of narrowband interferograms with different center frequencies are determined from one or more distinct pairs of broadband SAR images, hereinafter also referred to as InSAR pairs, across the entire broadband frequency range. Narrowband interferograms with corresponding center frequencies of each of the multiple distinct pairs of broadband SAR images constitute a set of narrowband interferograms. The narrowband interferograms can be obtained, for example, by filtering each pair of broadband SAR images using a window function with a given center frequency and a predetermined width, and processing the resulting narrowband SAR images in a known manner.

[0021] In step d), a corresponding frequency-dependent coherence profile is then determined from each set of narrowband interferograms for different image regions. This profile is called a coherence profile. The large number of frequency-dependent coherence profiles results from a corresponding large number of different image regions in a two-dimensional, spatial coordinate system of the area under consideration (without considering the height coordinate).

[0022] In step e), a known inversion is determined for each coherence profile (i.e., for each image region of the two-dimensional spatial coordinate system of the area under consideration). Finally, in step f), parameters characterizing the vertical structure can be determined from the inversion (i.e., for each image region of the two-dimensional spatial coordinate system of the area under consideration).

[0023] The present method enables a simple and cost-effective determination of the vertical structure of a semi-transparent medium that may exhibit multiple scattering. This determination of the vertical structure is made possible by the use of a SAR system with one or more radars possessing a wide normalized bandwidth, i.e., capable of transmitting and receiving signals with a bandwidth on the order of the radar carrier frequency. By generating broadband SAR images for each SAR acquisition and performing subsequent processing in which a multitude of narrowband interferograms with different center frequencies are determined from one or more distinct pairs of broadband SAR images across the entire broadband frequency range, the three-dimensional volume structure can be determined by inversion.

[0024] An advantage is that for volume structures with a semi-transparent medium, which attenuates the electromagnetic signal emitted by the SAR radar, two SAR images are sufficient if the extinction is constant across the frequencies of the radars under consideration. For volume structures characterized by frequency-dependent extinction, at least three SAR images of the area with the semi-transparent medium are required.

[0025] SAR imaging can be performed not only with aircraft and satellites, but also with UAVs, which simplifies the process of determining the vertical structure of the area with the semi-transparent medium. Due to the low flight altitude, the radar used according to the invention in UAVs can be operated with very low power in the milliwatt range.

[0026] The method is based on the finding that InSAR coherence is frequency-dependent. Existing SAR systems cannot exploit this relationship due to the narrowband characteristics of their radars. In contrast, the present invention enables the estimation of a coherence profile as a function of frequency, since it provides for the use of wide-bandwidth radars. The frequency profile of the coherence can then be used to characterize the vertical scattering profile.

[0027] In a suitable embodiment, the coherence profile is determined pixel by pixel. This allows for a precise determination of the vertical structure of a semi-transparent medium over a considered volume area.

[0028] Another advantageous embodiment provides that the center frequencies of two adjacent or successive narrowband interferograms are chosen such that the two narrowband interferograms partially overlap. In particular, the overlap between the two adjacent or successive narrowband interferograms is 50% or more.

[0029] To achieve high accuracy in determining the vertical structure of the semi-transparent medium, it is advantageous for the narrowband interferograms to be generated from narrowband images with slightly different bandwidths. It is also advantageous for the center frequencies of the two narrowband images used to form a given narrowband interferogram to differ, particularly slightly.

[0030] In the event that the volume structure to be investigated is characterized by a frequency-dependent extinction with the semi-transparent medium, it is advantageous if, in step a), SAR data from three (or more) SAR images of the area are received by the SAR system, wherein the three (or more) SAR images are carried out with two (or more) known baselines relative to each other.

[0031] In this configuration, it is also provided that in step b) a respective broadband SAR image is determined for each of the three (or more) SAR recordings and in step c) from the three different pairs of broadband SAR images that can be formed from them, a multitude of narrowband interferograms with different center frequencies are determined over the entire range of the broadband frequency, wherein narrowband interferograms corresponding to the center frequencies of each of the three pairs of broadband SAR images form a set of narrowband interferograms.

[0032] Step d) then provides that frequency-dependent coherence profiles are determined from each of the three sets of narrowband interferograms.

[0033] According to a further advantageous embodiment, in step f) the parameters characterizing the vertical structure are optionally determined by a Gauss-Newton method or by determining the mean squared error (MSE). Both methods are known in principle to those skilled in the art in connection with determining the inversion.

[0034] It is further advantageous to determine at least the height of the vertical structure and an extinction coefficient, or parameters characterizing the extinction coefficient, as parameters characterizing the vertical structure. The extinction coefficient indicates the attenuation of the electromagnetic signal by the medium of the vertical structure. In particular, it can be provided that, depending on the result of the estimation of a parameter characterizing the extinction coefficient, the extinction coefficient is assumed to be frequency-dependent or constant.

[0035] The invention further provides a computer program product comprising instructions which, when the program is executed by a computer, cause it to execute the method according to one of several embodiment variants.

[0036] Furthermore, the invention proposes a device for determining the vertical structure of a semi-transparent medium from SAR data of a SAR system comprising either one or more broadband radars with a bandwidth greater than 25% compared to the carrier frequency, or alternatively, one or more multiband radars with different frequency bands, where the upper frequency of the multiband radar is at least twice as high as the lower frequency of the multiband radar. The device includes a processor designed to perform the method according to one or more embodiments of the invention.

[0037] The invention is explained in more detail below with reference to exemplary embodiments shown in the drawing. The drawing shows: Fig. 1 a schematic representation illustrating the basic process of the method according to the invention; Fig. 2 a block diagram illustrating the multiband InSAR processing of SAR data according to the invention; Fig. 3 a block diagram showing the steps of an inversion procedure for determining characterizing parameters in the case of acquiring SAR data with a single baseline; Fig. 4 a block diagram showing the inversion using a Gauss-Newton method iteratively for the case where SAR data were acquired with a single baseline; Fig. 5 a block diagram showing the steps of an inversion procedure for determining characterizing parameters for the case of acquiring SAR data with two baselines; Fig. 6 a block diagram showing the inversion using the Gauss-Newton method iteratively for the case where SAR data were acquired with two baselines; Fig. 7 a schematic representation illustrating the geometry of a simulation with a semi-transparent medium modeled with point targets; Fig. 8 a coherence-frequency diagram derived from the simulated data of the Fig. 7 is generated; Fig. 9a and Fig. 9b a SAR image of the simulated data and a generated elevation map; and Fig. 10a and Fig. 10b a simulated area with a volume height varying with the distance to the ground and a created elevation map.

[0038] Fig. Figure 1 shows a schematic representation of the essential steps of the inventive method for determining the vertical structure of a semi-transparent medium 30. In the present schematic representation, the semi-transparent medium 30 consists, by way of example, of a plurality of trees 31, each of which has the same or different heights. These heights are to be determined for the area under investigation using the inventive method.

[0039] The determination is made from SAR data of a SAR system, which in this case consists of two platforms 10, 20 that simultaneously acquire the SAR data (“singlepass mode”). Both platforms are each equipped with a radar (not shown), whereby it is sufficient that one of the radars can transmit radar pulses and both radars can receive the reflected radar pulses.

[0040] In principle, the two platforms 10 and 20 can also be considered as one or more platforms that acquire the SAR data from the two positions depicted in successive SAR images ("repeat-pass mode"). In this case, the platforms should be equipped with radars capable of both transmitting radar pulses and receiving reflected radar pulses.

[0041] The radars can be configured as a broadband radar with a high bandwidth of more than 25% compared to the carrier frequency. Alternatively, the radars can be configured as one or more multiband radars with different frequency bands, where the upper (cutoff) frequency of the multiband radar is at least twice as high as the lower (cutoff) frequency of the multiband radar.

[0042] The following description assumes two platforms, 10 and 20. Platforms 10 and 20 fly over the area under investigation (also referred to as the scene) with the vertical structure 30 to be determined, as shown in the present example, at the same time.

[0043] Platforms 10 and 20 are depicted as unmanned aerial vehicles (UAVs) for illustrative purposes only. Platforms 10 and 20 could also be airplanes or satellites.

[0044] Each of platforms 10 and 20 provides a broadband SAR image (10B, 20B) from the SAR surveys of area 30, whose vertical structure is to be determined. The broadband SAR images were acquired with a known baseline between platforms 10 and 20. The broadband SAR images 10B and 20B are in Fig. 1 schematically represented by Fourier-transformed SAR data of the respective radar signals in a frequency range between f low and f high symbolized, where the Fourier transformation is performed with respect to the distance variable.

[0045] As will become apparent from the further description, frequency-dependent coherence profiles over the broadband frequency range, i.e., between f, are derived from the two broadband SAR images 10B and 20B. low and f high The profiles are called coherence profiles. From each frequency-dependent coherence profile KP, an inversion IKP is then determined in a known manner. After obtaining the inversion, the vertical structure and 30 characterizing parameters of the considered volume region can be determined.

[0046] To obtain the coherence profile KP, the following is done in Fig. The two described procedures were carried out. The first step S21, S22 consists of performing multiband InSAR processing of the two broadband SAR images 10B, 20B. The broadband SAR images 10B, 20B are each available as Fourier-transformed SAR data 10B, 20B and are represented as s1(f r ) and s2(f r ) denotes, where the Fourier transform is performed with respect to the distance variable and f r The distance frequency is represented. The SAR data 10B, 20B are filtered in steps S21, S22 using a window function W, which has a center frequency f. γ and a width f W This results in various, in particular partially overlapping, "narrowband" SAR images. The overlap of the narrowband SAR images is preferably 50% or more. The procedure is based on the center frequency f. γ repeatedly performed, which used the frequency of the received SAR signal 10B, 20B, which has a high bandwidth (fhigh - f low ) exhibits variations. The narrowband SAR images assigned to each other in steps S21 and S22 undergo a co-registration process, resulting in pre-processed SAR data in steps S23 and S24. 1,r (r) and s 2,r (r) can be obtained. The SAR data of each SAR acquisition can be focused into a SAR image either before or after the application of the narrowband filters for each narrowband data set, but in any case before co-registration. From the narrowband interferograms formed from these, the coherence γ̃(f) is determined in step S25. γ ) for the center frequency f γand each pixel is estimated. Estimating the coherence of a specific pixel requires multiple pixels, denoted as i in the formula sums in step 25, using neighboring pixels in addition to the pixel under consideration. By varying the center frequency across the wide bandwidth, the coherence profile KP is estimated for each pixel over the illuminated scene or captured area.

[0047] The three-dimensional mapping into vertical scattering profiles (IKP in Fig. 1) is achieved by pixel-wise inversion of the coherence profile KP. The vertical scattering profile g is usually used. v modeled with an extinction coefficient (σ) that takes into account the extinction of the electromagnetic signal by the medium of the vertical structure (the volume): gv(z)={exp[ln(10)102σzcosθ],0≤z≤hv0, otherwise where z is the vertical coordinate from the ground, θ is the angle of incidence of the SAR recording geometry, and hv to denote the height of the medium.

[0048] Coherence can be expressed as an integral over the vertical coordinate as γ(f)=ejϕ0(z0)∫0hvexp[j4πBcRssin θfz]gv(z)dz∫0hvgv(z)dz where B is the vertical baseline of an InSAR pair, Ø0 is the topographic phase with respect to ground level, c is the speed of light, and R s The oblique distance is the factor. Therefore, the absolute value of the model depends on the two parameters σ and h. v of the vertical profile. These two parameters σ and h v can be estimated by, for example, determining the values ​​with the lowest mean squared error.

[0049] In the case of frequency-dependent extinction, SAR data from at least three SAR acquisitions are required for inversion. These result in multiple frequency profiles with different (i.e., at least two) baselines. Thus, frequency-dependent coherence is obtained across the two orthogonal coordinates of an imaged scene for at least two different baselines.

[0050] To account for the large bandwidth and the change in the scattering profile depending on the frequency, the extinction coefficient σ - one of the parameters of the vertical profile - is modeled as a function of the frequency f: 2σ(f)=α30(f1 MHz)β[dBm] where α, β are coefficients that characterize the damping of the respective medium of the vertical structure under investigation.

[0051] The vertical scattering profile of the vertical structure can thus be determined using the three parameters α, β and h. v to be modeled according to: gv(z,f){exp[ln 1010(α30)(f1 MHz)βcos θ]0≤z <hv0 andernfalls

[0052] The coherence γ̃ can then be expressed as an integral over the vertical coordinate as γ(f,l)=ejϕ0(z0)∫0hvexp[j4πBlcRssin θfz]gv(z,f)dz∫0hvgv(z,f)dz where B l The orthogonal baseline of an InSAR pair indexed with l. Therefore, the absolute value of the model depends on the three parameters of the vertical profile α, β, and h. v These parameters are estimated by, for example, finding the set of values ​​with the least squared error.

[0053] Referring to the following block diagrams in the Fig. Sections 3 to 6 describe various examples for the implementation of the parameter search described above for the parameters characterizing the vertical structure.

[0054] Fig. Figure 3 shows a block diagram of the inversion method in a first example, which is applied in the case of SAR data acquired from two SAR images with a baseline. The parameter search scheme described here is then used when a constant extinction over the frequency can be assumed.

[0055] The estimate for the two parameters h v and σ can be calculated, for example, by determining the error for all possible valid parameter sets. The valid interval for h v is 0≤ h v ≤ h max , where h maxThe baseline is calculated in equation (6) below. An overview of the values ​​for the extinction coefficient σ is given in reference [2]. According to the overview shown there, a valid interval for σ, taking into account a certain margin of error, is given as 0 ≤ σ ≤ 3 with the unit [dB / m]. A block diagram of the exhaustive search method is given in Fig. 3 shown.

[0056] In step S31, coherence profiles γ(f; h) are calculated. v , σ) according to the coherence model in (2) for values ​​of the parameters h v and σ in the intervals 0 ≤ h v ≤ h maxand 0 ≤ σ ≤ 3 is generated with sufficiently small steps. In step S32, a pixel is selected from the InSAR data to be inverted. This yields the estimated coherence profile γ̃(f). In step S33, the mean squared error (MSE) between the estimated coherence profile and the coherence profiles generated by the coherence model is calculated for all values ​​of h. v and σ is calculated. In step S34, the parameters h v and σ with the lowest MSE is selected and stored. The procedure is performed iteratively across all pixels of the InSAR data.

[0057] Alternatively, parameter estimation methods based on the Gauss-Newton method can be used. An advantage of using the Gauss-Newton method is that the computational effort required to search for the parameters characterizing the vertical structure h is reduced. vand σ can be reduced. However, for the iterative search for the optimal parameters, the Gauss-Newton methods require the selection of the initial parameters for h. v and σ. The initial parameter for h v is in the interval 0 ≤ h v ≤ h max The one chosen is the one for which the MSE is lowest between the coherence profile calculated according to the coherence model of (2) under the assumption that there is no extinction (σ = 0) and the estimated coherence profile. Based on the initial value of the volume height, several sets of the initial parameters h are determined. v and σ for the Gauss-Newton method, where for each set of initial parameters h v The initial extinction parameter σ is the same as the one estimated in the previous step, while the initial extinction parameter σ is varied over the interval 0 ≤ σ ≤ 3 in sufficiently small steps. The Gauss-Newton method is iteratively performed for several sets of initial parameters with a common height h. vand different extinction coefficients σ. After each run of the Gauss-Newton method, the mean error and the updated parameters are recorded. The updated parameters h, which characterize the vertical structure, are then used. v and σ with the smallest mean squared error represent the result of the estimation. The procedure is shown in the block diagram in Fig. 4 shown.

[0058] In step S41, a pixel from the InSAR data is selected for inversion. The resulting estimated coherence profile γ̃(f) is used in step S42 to estimate the height (i.e., the first parameter characterizing the vertical structure) through a comprehensive search. The result h v0In step S43, this is used to generate initial values ​​for the comprehensive search. In step S44, the Gauss-Newton method is performed iteratively, and the least mean squared error (MSE) is determined. In step S45, the parameters h characterizing the vertical structure are determined. v and σ with the lowest MSE selected.

[0059] The block diagrams in the Fig. 5 and Fig. 6 describe the situation in which at least three SAR images have been taken over the area to be investigated with the vertical structure, so that at least two known baselines exist relative to each other.

[0060] The block diagram according to Fig. Section 5 considers the case of frequency-dependent extinction. The estimate for three parameters h v as well as α, β can be determined by calculating the error for all possible valid parameter sets. The valid interval for the height h vis 0 ≤ h v ≤ h max , where h max to calculate the larger baseline according to equation (6) below. Experimental values ​​for the parameters α, β representing the extinction coefficient σ are given in reference [1]. The valid interval for α, β, taking margins into account, is chosen to be 0 ≤ α ≤ 3 and 0 ≤ β ≤ 1. For the parameter β, which is less than 0.4, the frequency dependence of the extinction coefficient σ is negligible. Thus, if the result of the estimation for β is less than 0.4, the region is considered to have a constant extinction coefficient σ, whose value at the frequency f=fmax+fmin2 evaluated using equation (3). A block diagram of the comprehensive search procedure just described is shown in Fig. 5 shown.

[0061] In step S51, coherence profiles γ1(f; h) are calculated. v,σ) and γ2(f; h v , σ) according to the coherence model in (2) for two different baselines (denoted by the subscripts 1 and 2) and for values ​​of the parameters h v and σ in the intervals 0≤ h v ≤ h max and 0 ≤ σ ≤ 3 is generated with sufficiently small steps. In step S52, a pixel is selected from the InSAR data to be inverted. This yields the estimated coherence profiles γ̃1(f) and γ̃2(f) for the two baselines of the two available InSAR pairs. In step S53, the MSE is calculated between the estimated coherence profiles and the coherence profiles generated by the coherence model for all values ​​of h. vand σ is calculated, taking into account the coherence profiles for both baselines for the calculation of the MSE. In step S54, the parameters with the lowest MSE are found. In step S55, it is determined whether β > 0.4. If this is the case (path "Yes"), a classification as frequency-dependent is performed in step S56. If this is not the case (path "No"), a classification as a constant extinction σ is performed in step S56, the value of which is determined at the frequency. f=fmax+fmin2 evaluated using equation (3).

[0062] In the Fig. In the embodiment shown in Figure 6, a volume height value with the lowest error is determined based on the measured coherence profiles from the InSAR pair with the largest baseline. The coherence model, which assumes no extinction, is used to search for a height value with the lowest error. Using an initial volume height value, a set of initial parameters is defined for the Gauss-Newton method. The Gauss-Newton method is then iteratively performed for several sets of initial parameters with a common volume height and different combinations of α and β. After completion of each iteration of the Gauss-Newton method, the mean squared error and the updated parameters characterizing the vertical structure are stored. The updated parameters with the lowest error are the result of the estimation.Similar to the exhaustive search, the area is considered to have a constant extinction coefficient σ if the estimate result for β < 0.4. A block diagram of this procedure is shown in . Fig. 6 shown.

[0063] In step S61, one pixel from two InSAR pairs is selected for inversion. The resulting estimated coherence profile is derived from the InSAR pair with the highest baseline. γ1˜(f) In step S62, an exhaustive search is performed to estimate the volume height h0. The result h v0 This is used in step S63 to generate initial values ​​for the comprehensive search. A second coherence profile from the InSAR pair with the smaller baseline is then used. γ2˜(f) will be together with γ1˜(f) In step S64, the iterative Gauss-Newton method is used to determine the MSE. In step S65, the parameters that characterize the vertical structure and exhibit the smallest MSE are selected. A parameter β characterizing the vertical structure is compared to a threshold of 0.4 in step S66. If the estimated value β > 0.4 (path "Yes"), the region is considered frequency-dependent in step S67, i.e., a region with a constant extinction coefficient. If the comparison in step S66 is negative (path "No"), a classification with constant extinction coefficients is assumed for the region in step S68.

[0064] The following describes the selection of the baseline. During inversion, the coherence profiles estimated from the data with the largest baseline can be used to estimate the volume height. For a meaningful height estimation, the larger baseline is chosen such that the first minimum of the coherence profile lies within the frequency interval for which the coherence profile is provided. The larger baseline B1 should therefore be determined as follows: cRssinθ2phmaxfmax <B1<cRssinθ2phmaxfmin where R s the oblique distance is h max the maximum vertical height expected in the area of ​​interest, and f min and f maxThe minimum and maximum frequencies of the transmitted signal are specified. The factor p is an integer value that varies depending on the acquisition mode. The value of p is 1 for the repeat-pass method (monostatic configuration) and 2 for the single-pass method (bistatic or multistatic configuration).

[0065] For a monostatic configuration with a platform height h UAV of 100 m, an angle of incidence θ of 60°, a maximum volume height h max of 8 m and a transmission frequency of f min = 1 GHz to f max At 4 GHz, the minimum and maximum values ​​of the larger baselines are 0.81 m and 3.24 m, respectively. In a bi-static configuration, the minimum and maximum values ​​of the larger baselines are 0.405 m and 1.62 m, respectively.

[0066] The estimated coherence profiles, which were determined from the InSAR pair with the smaller baseline, are used to estimate the two parameters α and β of the frequency-dependent extinction coefficient σ(f) of the elevation profile.

[0067] For this reason, it is advantageous if the coherence profiles of the two baselines occupy a common area when mapped to the vertical wavenumber, i.e., when scaled by their respective baselines. A guideline for choosing the smaller baseline B2 could be that the coherence profile obtained with the smaller baseline overlaps by 50% with the coherence profile obtained with the larger baseline B1 when mapped to the vertical wavenumber. B2=fmax+fmin2 fmaxB1 This applies. Assuming a transmission frequency of f min = 1 GHz to f maxIf the baseline is 4 GHz and the larger baseline B1 is 3 m, then the second baseline B2 is 1.87 m.

[0068] During acquisition in a single pass, all platforms must maintain a safe distance from each other to avoid collisions. Proximity between platforms can be maintained without affecting the normal baseline conditions in equations (1) and (2) by introducing a baseline component parallel to the radar's range to the target. If additional platforms, such as drones, are available, an even shorter baseline should be targeted, e.g., B3=fmax+fmin2 fmaxB2.

[0069] The present procedure can be carried out, for example, with cost-effective unmanned aerial vehicles (UAVs), such as drones. However, the procedure can also be implemented without restriction with SAR systems that use airborne or satellite-based platforms.

[0070] In the Fig. Sections 7 to 10 present an example of the implementation of the described method, based on the generation of a set of simulated SAR data and its volumetric inversion. The case considered is one in which there is no frequency-dependent extinction and only two SAR images have been acquired, thus providing a baseline.

[0071] The geometry of the simulation is in Fig. Figure 7 shows 30 semi-transparent media modeled as point targets. The vertical structure of the semi-transparent medium 30 extends over a height h. v around the origin O. Assuming that M point scatterers are distributed within the region of interest, the distance-compressed signals in the frequency domain are modeled as follows: s1(fr)=∑m=1MAmexp[j4πcfrRm,1]s2(fr)=∑m=1MAmexp[j4πcfrRm,2]

[0072] In these equations, m is the index of the individual point spreaders and A m The complex amplitude of the point scatterers. The distance frequency was defined as a uniformly sampled variable from 1 GHz to 4 GHz. R m,1 and R m,2 These are the distances measured from each target to the antenna of platforms 10 and 20. The distances can be calculated using Rm,1=|Pant,1→−Ptgt,m→| and Rm,2=|Pant,2→−Ptgt,m→| are measured, whereby Pant,1→ and Pant,2→ to indicate the position of the antennas of platforms 10 and 20 and Ptgt,m→ the position of the m-th point spreader.

[0073] In the case of a radar, e.g. mounted on a drone, the altitude and tilt range of Pant,1→ 100 m or Pant,2→ Assumed to be 200 m. Accordingly, the angle of incidence at the center of the scene was 60°. The position Pant,2→ was defined as being 3 m from Pant,1→ is removed, specifically in the direction perpendicular to the viewing direction in relation to the center of the scene.

[0074] In this simple scenario, a uniform vertical dispersion was assumed. Therefore, A m The value was assumed to be constant, and the semi-transparent medium was modeled with random variables. The vertical positions of the point scatterers were therefore obtained as realizations of a uniform random variable whose limit refers to the given volume height.

[0075] The coherence estimation and the model for a volume height of 4.0 m are in Fig. 8 is shown, where the coherence estimation is given by γ est and the model with γ model are designated. The width of the frequency window f WThe range used for the estimation was 500 MHz and 3.5 m, respectively. It was assumed that the coherence profiles of approximately 100 neighboring pixels were used to estimate the coherence profiles of a given pixel. Despite the deviation caused by stochastic processes, the estimated coherence can be used to measure the volume height. By calculating the mean square difference between the coherence estimates using models with different heights for a given pixel, the volume height is estimated to be 3.9 m.

[0076] The estimation process can be repeated across the two dimensions of the scene to create a volumetric height map. Fig. Figure 9a shows an example of a SAR image with 100 azimuth bins and a 30 m distance range. The volume height was assumed to be 3.5 m. Fig. Figure 9b shows the result of the height estimation, which was iteratively determined for the entire scene, presented as a color-coded map, where lighter values ​​represent a greater height and darker values ​​a lesser height. The average estimated height is 3.546 m, while the standard deviation is 0.158 m.

[0077] Fig. Figure 10a shows an example with varying volume height above a scene under consideration. The simulated data were generated using a scene whose volume height changes slowly with distance from the ground. The maximum and minimum heights are 1 m and 4 m, respectively. The result of the height estimation is shown in Fig.Figure 10b is shown as a color-coded map, where light values ​​represent a height of approximately 4 m and dark values ​​represent a height of approximately 1.5 m. The maximum and minimum heights are 1 m and 4 m, respectively. The result of the estimation agrees with the simulated target, with the minimum height of the volume at both ends of the distance strip being 1.01 m and the maximum height of the volume in the middle of the strip being 4.24 m. The invention can also be applied to cases with multiple platforms and more complex vertical scattering profiles. References [1] LA Bessette and S. Ayasli, “Ultra-wideband P-3 and CARABAS II foliage attenuation and backscatter analysis,” Proceedings of the 2001 IEEE Radar Conference (Cat. No.01CH37200), Atlanta, GA, USA, 2001, pages 357-362, doi: 10.1109 / NRC.2001.923005. [2] J. David Ballester-Berman, “Reviewing the role of the extinction coefficient in radar remote sensing,” arXiv:2012.02609, 2020.

Claims

[1] A method for determining a vertical structure of a semi-transparent medium from SAR data of a SAR system comprising either one or more broadband radars with a high bandwidth of more than 25% compared to the carrier frequency or alternatively one or more multi-band radars with different frequency bands in which the upper frequency of the multi-band radar is at least twice the lower frequency of the multi-band radar, in which: (a) the SAR system receives SAR data from at least two SAR images of an area whose vertical structure is to be determined, the at least two SAR images being taken from different observation angles with known baselines relative to each other; b) a respective broadband SAR image (10B, 20B) is generated for each of the at least two SAR images; c) a plurality of narrowband interferograms having different center frequencies are determined from one or more different pairs of broadband SAR images (10B, 20B) over the entire range of the broadband frequency, wherein narrowband interferograms of corresponding center frequencies of the or each of the plurality of different pairs of broadband SAR images (10B, 20B) form a set of narrowband interferograms; d) a corresponding profile of the frequency-dependent coherence is determined from each set of narrowband interferograms for different image areas; (e) an inversion is determined for each coherence profile; and f) parameters characterising the vertical structure are determined from the inversion. [2] Method according to claim 1, characterized by that the coherence profiles are determined pixel by pixel. [3] Method according to claim 1 or 2, characterized bythat the center frequencies of two adjacent or consecutive narrowband interferograms are chosen such that the two narrowband interferograms partially overlap. [4] Method according to claim 3, characterized by that the overlap between the two narrowband interferograms is 50% or more. [5] Method according to one of the preceding claims, characterized by that the narrowband interferograms are generated from narrowband images with a slightly different narrowband width. [6] Method according to one of the preceding claims, characterized by that the center frequencies of the two narrowband images used to form a respective narrowband interferogram differ, in particular slightly. [7] Method according to one of the preceding claims, characterized bythat in step a) the SAR system receives SAR data from three SAR images of the area, the three SAR images being carried out with two known baselines relative to each other. [8] Method according to claim 7, characterized by that in step b) a respective broadband SAR image is determined for each of the three SAR images and in step c) from the three different pairs of broadband SAR images that can be formed therefrom, a plurality of narrowband interferograms with different center frequencies are determined over the entire range of the broadband frequency, wherein narrowband interferograms of corresponding center frequencies of each of the three pairs of broadband SAR images form a set of narrowband interferograms. [9] Method according to claim 7 or 8, characterized by that in step d) frequency-dependent coherence profiles are determined from each of the three sets of narrowband interferograms. [10] Method according to one of the preceding claims, characterized by that in step f) the parameters characterising the vertical structure are determined by a Gauss-Newton method or by determining the mean square error (MSE). [11] Method according to one of the preceding claims, characterized by that the parameters characterizing the vertical structure are at least - a height (h v ) of the vertical structure and - an extinction coefficient (σ) indicating the attenuation of the electromagnetic signal by the medium of the vertical structure, or parameters (α, β) characterising the extinction coefficient (σ) are determined. [12] Method according to claim 11, characterized by that, depending on the result of the estimation of a parameter (β) characterizing the extinction coefficient (σ), the extinction coefficient (σ) is assumed to be frequency dependent or constant. [13] Method according to one of claims 1 to 12, characterized by that the SAR data is determined by a platform using the repeat-pass method. [14] Method according to one of claims 1 to 12, characterized by that the determination of the SAR data is carried out by two or more platforms in a single-pass method, with the two or more platforms being configured in a bi-static or multi-static configuration. [15] A computer program product comprising instructions which, when executed by a computer, cause the computer to carry out the method according to any one of claims 1 to 14. [16] Apparatus for determining a vertical structure of a semi-transparent medium from SAR data of a SAR system comprising either one or more broadband radars with a high bandwidth of more than 25% compared to the carrier frequency or alternatively one or more multi-band radars with different frequency bands in which the upper frequency of the multi-band radar is at least twice as high as the lower frequency of the multi-band radar, the apparatus comprising a processor adapted to carry out the method according to any one of claims 1 to 14.

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