Method and system for processing SAR raw data acquired by a SAR system

Abstract

The present disclosure describes a method for processing SAR raw data acquired by a SAR system (1) comprising a transmitting antenna and at least one receiving antenna, wherein the SAR system (1) is configured to alternately transmit up- and down-chirps (UDC), comprising the following steps: - Splitting the UDC-modulated SAR raw data (MD) into a first channel (CH1) that includes the data (UCD) of the up chirps, and a second channel (CH2) that includes the data (DCD) of the down chirps; - Performing range compression (RC) with a transfer function, where the transfer function is the complex conjugate of the respective transferred chirp simulation; - Performing an azimuth reconstruction (AR) with a reconstruction filter, wherein the reconstruction filter is calculated using the transfer function of an intrapulse (IP) effect taking into account a movement of the SAR system (1) during a transmit and receive operation, wherein the data obtained by azimuth reconstruction are output data (OD) representing range-compressed SAR raw data without IP effect; and - Providing the output data (OD) for further processing.

Description

[0001] The present invention relates to a method and a system for processing SAR raw data acquired by a SAR system having a transmitting antenna and at least one receiving antenna, wherein the SAR system is configured to transmit alternating up- and down-chirps (UDC).

[0002] Synthetic aperture radar (SAR) is a technique that increases the effective length of the physical antenna by taking advantage of the radar's motion, thus improving the system's azimuth resolution. The observation geometry of a synthetic aperture radar (SAR), which includes a radar antenna, is Fig. 1. The radar antenna at time t a,0 is shown as a rectangular planar antenna. The SAR system 1, which moves at a constant speed v smoving along an azimuth direction AZD (x), is equipped with a sideways-looking radar on a movable platform at height h. The dashed line NT indicates the so-called nadir track, which is the projection of the azimuth direction perpendicular to the Earth's surface. To move the radar antenna, it is mounted on a flying object (not shown), which is preferably a satellite but can also be an aircraft. The movement occurs along the azimuth direction AZD (x), which is determined by the antenna at time t a,1 is displayed. In this embodiment, the SAR system 1 is a combined transmitting and receiving device that transmits radar radiation in transmitting mode and receives radar radiation in receiving mode.

[0003] In transmit mode, SAR system 1 emits a radar beam RB based on a radar pulse RP at a specified angle toward the Earth's surface. The radar beam RB corresponds to the main lobe of the emitted antenna radiation and impinges on the Earth's surface. SAR system 1 transmits radar pulses RP (short: pulses) with a pulse duration τ p at a specific pulse repetition frequency (PRF). The majority of the energy of a given radar pulse RP or its radar beam RB is directed onto an approximately elliptical area FP on the Earth's surface. This area is usually referred to as the "footprint" of the radar device or the associated radar antenna, where W g the strip width of the area FP and L sa the length of the synthetic aperture.

[0004] In Fig.1 denotes SR, r0 the slant distance from the SAR system 1 to a point on the Earth's surface. This slant distance can be clearly converted into the so-called horizontal distance, the direction of which is Fig. 1 is designated GR. The horizontal distance GR corresponds to the projection of the slant distance SR onto the Earth's surface GR and is perpendicular to the azimuth direction x. In the following, the direction of the horizontal distance GR is also generally referred to as the range direction. The footprint FP has an extent in the range direction that corresponds to the displayed strip width W. g During the movement of SAR system 1, radar echoes RE of the radar pulses RP of the strip reflected from the Earth's surface are detected. For this purpose, SAR system 1 is switched to receive mode.

[0005] The principle of SAR measurement is based on the fact that a point on the Earth's surface GR is observed multiple times from different angles due to the movement of the SAR system 1. Due to the Doppler effect, a frequency shift occurs during the detection of the radar echoes, which can be appropriately evaluated, ultimately yielding amplitude and phase information for the points on the Earth's surface where the radar pulses are reflected, thus yielding an image point of the Earth's surface. The corresponding calculation of image points of the Earth's surface from the detected radar echoes is well known to those skilled in the art and will therefore not be explained further.

[0006] A typical SAR system 1 uses a chirp signal, i.e., a linearly frequency-modulated baseband signal. Depending on the sign of the exponential term, the transmitted pulse can be characterized as an up-chirp or a down-chirp. sup(tr)=rect[trτp]exp[j⋅π⋅|K|⋅tr2] sdown(tr)=rect[trτp]exp[−j⋅π⋅|K|⋅tr2] where t r is the range time (fast time) and |K| is the absolute value of the chirp rate K=Brτp where B r is the bandwidth of the transmitted chirp. The coordinates of radar system 1 are the azimuth and slant range, which correspond to the flight direction (azimuth direction AZD, x) and the observation direction (horizontal distance GR), respectively.

[0007] As already mentioned, the antenna footprint covers an area defined in the range direction (or transverse direction) by the strip width W g and in the azimuth direction by the length of the synthetic aperture L sa The emitted pulses are reflected back from the observed scene to the antenna (also called the sensor) with a certain time delay and are coherently demodulated, digitized, and stored as raw data.

[0008] The time between two transmissions is called the pulse repetition interval (PRI), which is the inverse of the PRF. Therefore, the sampling frequency of the raw SAR data in azimuth is determined by the system PRF (also called the operational PRF). The raw data is later processed to deconvolve the received echoes and obtain the reflectivity of the scene. After SAR processing, the energy of an individual point target is determined at its range and azimuth position. The range resolution of a radar is a function of the bandwidth of the transmitted signal, B r , and the azimuth resolution of a SAR sensor is equal to half the physical antenna length in azimuth, L a .

[0009] Typical SAR processing involves range compression, range cell migration correction (RCMC), and azimuth compression. Range compression is performed using a matched filter, which involves convolving the data with the complex conjugate of the transmitted signal. The range-compressed SAR data forms a hyperbolic curve spanning multiple range bins. This is due to the variation in distance between the point target and the sensor along the synthetic aperture. This effect is typically corrected using a range-dependent two-dimensional reference function, and the energy of a point target is confined to a single range bin. As in the range dimension, azimuth compression is applied using a matched filter to compress the energy of a point target to a single pixel.

[0010] To obtain a SAR image without ambiguities, the PRF of the system must be equal to or greater than the Doppler bandwidth B a PRF≥Ba≈2⋅vsLa. where v sthe platform's speed. Otherwise, azimuth ambiguities will occur in the focused SAR image due to Doppler spectrum aliasing. On the other hand, range ambiguities occur when echoes outside the main beamwidth in elevation and from different transmits reach the receiver at the same time despite their different flight times. To avoid range ambiguities, the SAR system can be designed to cover either a narrow swath with a higher PRF (allowing for finer azimuth resolution) or a wide swath with a lower PRF (forcing a coarser azimuth resolution). This represents the limitation of a conventional SAR system: the trade-off between azimuth resolution and swath width.

[0011] There are many system concepts (disclosed in references [R1]-[R3]) and processing strategies (disclosed in DE 10 2005 062 031 A1 and references [R4]-[R6]) to achieve high-resolution wide-angle imaging (HRWS). One way to overcome the limitation of a conventional SAR system is to generate alternating up- and down-chirps (UDC) during each transmission, i.e., to mark the pulses (as described, for example, in references [R7][R8]). Using this technique, the unique swath size of a monostatic single-channel SAR system can be doubled, or the azimuth resolution can be twice as fine with the same swath coverage by adjusting the antenna length. Since each pulse is labeled and compressed with its complex conjugate, the ambiguous signal compressed with the wrong filter is smeared along the range dimension (range ambiguity suppression).

[0012] Another approach to acquiring high-resolution SAR data from a larger swath is to reduce the operating PRF and suppress azimuth ambiguities by deploying multiple receiving units (as described in Reference [R6]). This can be achieved either with a single-platform SAR by splitting the antenna in the azimuth direction or with a multi-platform SAR constellation. Furthermore, both approaches can be combined in a multi-channel SAR system with up- and down-chirped modulation (as shown in [R9]).

[0013] Typical space-based SAR processors neglect the fact that the sensor moves during the transmission and reception process. In fact, the platform moves during the transmission and reception of the chirp signal, introducing a space-invariant phase known as the intrapulse (IP) effect, which can be expressed in the wavenumber domain as follows: HIP,down(fa,fr)=exp[−j⋅2π⋅fa|K|⋅fr] HIP,up(fa,fr)=exp[−j⋅2π⋅fa|K|⋅fr] where f a the Doppler frequency and f r is the range frequency vector (see Reference [R10]). For SAR systems without alternating transmit waveforms, this can lead to resolution losses in both azimuth and range and can be easily corrected using the complex conjugate of equations (5) or (6), as suggested in Reference [R10]. However, when an up / down sequence is used, the IP effect manifests itself in the form of additional azimuth ambiguities, which can be seen in the Fig. 2 and Fig. 3, which represents the impulse response function (IRF) as normalized intensity INT Norm including the maximum azimuth ambiguity in all range bins for a single-channel SAR system ( Fig. 2) and a multi-channel SAR system ( Fig. 3) show.

[0014] The right columns of the Fig. 2 and Fig.3 show the impulse response function (IRF) as normalized intensity INT Norm , where the azimuth ambiguities caused by the uncompensated IP effect are clearly observable, both for single-channel SAR systems ( Fig. 2, right column) as well as for multi-channel SAR systems ( Fig. 3, right column) with UDC modulation. The simulation parameters are listed in Table 1 (single-channel with TerraSAR-X parameters) and Table 2 (multi-channel with ROSE-L parameters). Table 1 Simulation parameters for the single channel simulation results shown in Fig. 2. parameter Value Altitude of the orbit 514 km Center frequency f0 9.65 GHz Chirp bandwidth 300 MHz Chirp duration 50 µs Processed Doppler bandwidth 2765 Hz PRF 4174 Hz Table 2 Simulation parameters for the multi-channel simulation results shown in Fig. 3. parameter Value Altitude of the orbit 693 km Center frequency f0 1.25 GHz Chirp bandwidth 65.2 MHz Chirp duration 48,61 µs Processed Doppler bandwidth 2600 Hz PRF 1378.18 Hz Number of azimuth channels (N) 5

[0015] The Fig. 2 and Fig. 3 also show the impulse response function (IRF) as a reference as normalized intensity INT Normof a system without UDC modulation and without IP effect (left columns of the Fig. 2 and Fig. 3). It is clearly visible that the IP-related ambiguities in the single-channel system are as high as those caused by the antenna pattern, and that the ambiguities in the multi-channel system are much higher than those caused by the antenna pattern. To express these results numerically, the maximum peak-to-ambiguity ratio (PTAR) in the single-channel system without UDC modulation and with IP effect are -30.60 dB and -33.16 dB, respectively, with the total azimuth ambiguity-to-signal ratio (AASR) being -20.42 dB and -23.69 dB, respectively. In the multi-channel system, the maximum PTAR values ​​without UDC modulation and with IP effect are -59.51 dB and -38.92 dB, respectively, with the total AASR being -40.13 dB and -29.50 dB, respectively.

[0016] The object of the present invention is to provide a method and a system for processing SAR raw data capable of compensating the intrapulse effect of Synthetic Aperture Radar (SAR) data acquired with up-chirp and down-chirp modulation.

[0017] These objects are achieved by the independent claims. Preferred embodiments are specified in the dependent claims.

[0018] According to a first aspect of the present invention, a method is proposed for processing SAR raw data acquired by a SAR system having a transmitting antenna and at least one receiving antenna, wherein the SAR system is configured to transmit alternating up- and down-chirps (UDC). The method comprises the following steps: - splitting the UDC-modulated SAR raw data into a first channel comprising the uplink chirps and a second channel comprising the downlink chirps; - performing a range compression with a transfer function, wherein the transfer function is the complex conjugate of the respective transmitted chirp replica; - performing an azimuth reconstruction using a reconstruction filter; and - Preparing the output data for further processing. Further processing can be performed by applying a conventional SAR focusing algorithm to obtain the fully focused SAR image. This algorithm typically performs range cell migration correction (RCMC) and azimuth compression.

[0019] The invention is characterized in that the reconstruction filter is calculated with the transfer function of an intrapulse (IP) effect, in particular an inverse of the transfer function of the intrapulse (IP) effect, taking into account a movement of the SAR system during a transmission and reception process, wherein the data obtained by azimuth reconstruction are output data that represent range-compressed SAR raw data without IP effect. The transfer function of the IP effect with a 2x2 matrix is ​​defined as H(fr,fa)=[HIP,up(fr,fa)HIP,down(fr,fa)HIP,up(fr,fa+PRF)HIP,down(fr,fa+PRF)] where H IP,up (f r , f a ) and H IP,down (f r , f a ) represent the IP effect for up and down chirps, expressed by HIP,up(fa,fr)=exp[j⋅2π⋅fa|K|⋅fr] HIP,down(fa,fr)=exp[−j⋅2π⋅fa|K|⋅fr] and PRF is half of the operating pulse repetition frequency PRF (PRFop ).

[0020] The invention proposes separating up- and down-chirped signals as new channels and incorporating the intrapulse effect into the transfer function to account for the impact of the IP effect on the performance of UDC-modulated SAR images.

[0021] According to a preferred embodiment, the division of the UDC-modulated SAR raw data into the first and second channels can be carried out before performing the range compression or after performing the range compression.

[0022] According to a further preferred embodiment, the range-compressed data of the first and second channels are transformed into a wavenumber domain using a 2D Fourier transform. In other words, the azimuth reconstruction takes place in the wavenumber domain, since the phase deviation due to the IP effect is space-invariant but dependent on the range and Doppler frequency.

[0023] In a further preferred embodiment, the data obtained by azimuth reconstruction are transformed back into the time domain by means of an inverse Fourier transformation.

[0024] Reconstruction filters can be calculated using various methods found in the literature. The choice of method for calculating the reconstruction filter depends heavily on the system under consideration, i.e., a single-channel SAR system or a multi-channel SAR system. A single-channel SAR system can be represented by a monostatic SAR system or a bistatic SAR system, which has a transmitting antenna and a receiving antenna. A multi-channel SAR system can be represented by a monostatic SAR system or a bistatic SAR system, which has a transmitting antenna and more than one receiving antenna (or receiving sections).

[0025] According to a further preferred embodiment, the reconstruction filter is calculated as follows P(fr,fa)=H(fr,fa)−1, i.e. the reconstruction filters are calculated as the inverse of the transfer function.

[0026] According to a further preferred embodiment, when the SAR system is a single-channel system, the transfer function is a matrix for each range and azimuth frequency, the inversion being analytically calculated as P(fr,fa)=1HIP,up(fr,fa)⋅HIP,down(fr,fa+PRF)−HIP,down(fr,fa)⋅HIP,up(fr,fa+PRF)[HIP,down(fr,fa+PRF)−HIP,down(fr,fa)−HIP,up(fr,fa+PRF)HIP,up(fr,fa)]

[0027] Using the transfer function specified above reduces the computational effort, as the matrix inversion does not need to be calculated. The output of the proposed technique is range-compressed raw SAR data. Subsequently, as mentioned above, any existing algorithm can be applied to obtain a fully focused SAR image.

[0028] According to a further preferred embodiment, if the SAR system is a multi-channel system with at least two receivers (also referred to as receiving channels), the transfer function depends on the range time as well as on the range and Doppler frequencies.

[0029] In particular, the transfer function of the IP effect of a multi-channel SAR system is defined by Hi,up(fr,fa;r0)=exp[−j.Δϕgeo,i(fr,fa;r0)]⋅HIP,up(fr,fa) Hi,down(fr,fa;r0)=exp[−j.Δϕgeo,i(fr,fa;r0)]⋅HIP,down(fr,fa) where Δϕ geo,i (f r , f a ; r0) is the phase deviation due to the geometric difference of a receiver i (receiving channel i) with respect to a reference receiving channel.

[0030] In a further preferred embodiment of a multi-channel SAR system, the azimuth reconstruction comprises the calculation of filters in the wavenumber domain for a reference range bin (P i,up / down (fr, f a ; r ref)), multiplying the data with these filters without adding them, and after transforming the data into the range-Doppler domain, calculating the range- and Doppler frequency-dependent residual filter.

[0031] The calculation of the range and Doppler frequency dependent residual filter includes in particular the calculation of ΔPi,up / down(fr,fa;r0(fa))=|ΔPi,up / down(fr,fa;r0(fa))||ΔPi,up / down(fr,fa;rref(fa))|⋅exp[j⋅Δφi(fr,fa;r0)] where the phase of the differential reconstruction filter is defined as Δφi(fr,fa;r0)=φi(0,fa;r0)−φi(0,fa;rref) where φ i (.) the phase of the reconstruction filter P i (.) is.

[0032] In addition, after summing the data of each receive channel, the Doppler spectrum is restored.

[0033] According to a second aspect of the present invention, a computer program product is proposed comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to one or more preferred embodiments as described above.

[0034] According to a third aspect of the present invention, a system is proposed for processing SAR raw data acquired by a SAR system having a transmitting antenna and at least one receiving antenna, the SAR system being configured to alternately transmit up- and down-chirps (UDC), comprising a processor configured to carry out the method according to one or more preferred embodiments as described above.

[0035] The invention and further advantages are explained in more detail with reference to the attached figures. Fig.Figure 1 shows the well-known geometry of a monostatic synthetic aperture radar (SAR) system. Fig. Figure 2 shows plots of an impulse response function (IRF) including the maximum of the azimuth ambiguity in all range bins of a single-channel SAR system without UDC modulation and with an IP effect due to missing compensation. Fig. Figure 3 shows the representation of an impulse response function (IRF) including the maximum of the azimuth ambiguity in all range bins of a multi-channel SAR system without UDC modulation and with an IP effect due to missing compensation. Fig. Figure 4 shows a schematic flow diagram of the proposed method for single-channel SAR systems according to a first embodiment, in which the data is range-compressed and then split into two processing channels before compensation of the IP effect. Fig.Figure 5 shows a schematic flow diagram of the proposed method for single-channel SAR systems according to a second embodiment, in which the data is separated into two channels and then range-compressed before compensating for the IP effect. Fig. Figure 6 shows a schematic flow diagram of the proposed reconstruction algorithm for multi-channel SAR systems according to a third embodiment, in which the data in each receive channel is first range-compressed and then separated into two channels before compensating the IP effect. Fig. Figure 7 shows a schematic flow diagram of the proposed reconstruction algorithm for multi-channel SAR systems according to a fourth embodiment, in which the data in each receive channel is first separated into two channels and then range-compressed before compensating for the IP effect. Fig.Figure 8 shows a schematic flow diagram of the proposed reconstruction algorithm for multi-channel SAR systems according to a fifth embodiment, in which the data in each receive channel is first range-compressed and then separated into two channels before compensating for the IP effect, which is advantageous for a single-platform SAR system. Fig. Figure 9 shows a schematic flow diagram of the proposed reconstruction algorithm for multi-channel SAR systems according to a sixth embodiment, in which the data in each receive channel is first separated into two channels and then range-compressed before compensating for the IP effect, which is advantageous for a single-platform SAR system. Fig.Figure 10 shows diagrams of an impulse response function (IRF) including the maximum of the azimuth ambiguity in all range bins of a single-channel SAR system without IP effect and with an IP correction according to the method of the present invention. Fig. Figure 11 shows diagrams of an impulse response function (IRF) including the maximum of the azimuth ambiguity in all range bins of a multi-channel SAR system without IP effect and with an IP correction according to the method of the present invention.

[0036] Azimuth ambiguities occur in a focused SAR image due to Doppler spectrum aliasing when an operational PRF is smaller than the Doppler bandwidth B aOn the other hand, range ambiguities occur when echoes outside the main beam width in elevation and from different transmissions reach the receiver at the same time despite their different flight times. To avoid range ambiguities, a SAR system, as used in conjunction with Fig. 1, can be designed either to cover a narrow swath with a higher PRF, allowing for finer azimuth resolution, or to cover a wide swath with a lower PRF, forcing a coarser azimuth resolution. This represents the limitation of a conventional SAR system, namely the trade-off between azimuth resolution and swath width.

[0037] As described in the introduction, one way to overcome the limitations of a conventional SAR system is to use alternating up- and down-chirps (UDC) during each transmission, i.e., to mark the pulses. Since each pulse is marked and compressed with its complex conjugate, the ambiguous signal compressed with the wrong filter is smeared along the range dimension, resulting in range ambiguity suppression. However, to date, conventional SAR processors neglect the fact that the platform-mounted sensor moves during transmission and reception. In fact, the platform moves during transmission and reception of the chirped signal, introducing a space-invariant phase, i.e., an intrapulse (IP) effect. However, when UDC modulation is used, the IP effect manifests as additional azimuth ambiguities if not properly accounted for.

[0038] The procedure described below deals with the compensation of the IP effect in SAR systems with UDC modulation.

[0039] Eliminating the IP effect differs for Nyquist-sampled data from a single channel and for a multi-channel system operating with a PRF below the Nyquist criterion. Therefore, two compensation techniques are essentially proposed. However, the basic idea of ​​both techniques is the same: eliminating the phase deviation for all channels using azimuth reconstruction. The term "channel" refers to data related to the different receivers or the different modulation (up-chirps or down-chirps).

[0040] The Fig. 4 and Fig. 5 show block diagrams of the processing approach for a single-channel SAR system. In the first embodiment of Fig.4 the UDC-modulated SAR raw data (short: data or input data) MD are either range-compressed (Block RC) with the complex conjugate of the transmitted chirp replica as Hr,up(fr)=FT{rect[trτp]exp[−j⋅π⋅|K|⋅tr2]} Hr,down(fr)=FT{rect[trτp]exp[j⋅π⋅|K|⋅tr2]} which also separates the input data MD into two channels CH1, CH2, where channel CH1 includes data from up-chirps UCD and channel 2 includes data from down-chirps DCD.

[0041] In the second embodiment of Fig. 5, the UDC-modulated SAR raw data MD are first separated into two channels (e.g. channel CH1: data from up-chirps UCD, e.g. odd samples; channel CH2: data from down-chirps DCD, e.g. even samples) and then range-compressed (block RC).

[0042] In both cases, the range-compressed data DCD and UCD are transformed into the wavenumber domain by a fast Fourier transform (block TR1).

[0043] Then, the azimuth reconstruction AR is performed with an inverse filter in the wavenumber domain, since the phase deviation due to the IP effect is space-invariant but range- and Doppler-frequency-dependent. The transfer function of the IP effect is defined with a 2x2 matrix as H(fr,fa)=[HIP,up(fr,fa)HIP,down(fr,fa)HIP,up(fr,fa+PRF)HIP,down(fr,fa+PRF)] where H IP,up (f r , f a ) and H IP,down (f r , f a ) represent the IP effect for up- and down-chirps, respectively (see (5) and (6)) and PRF is half of the operating PRF (PRF op ).

[0044] The reconstruction filters can be calculated using various methods found in the literature. The choice of method for calculating the reconstruction filter depends heavily on the system under consideration. Especially for a system with only one platform, the use of the inverse filter (nulling approach) can be chosen due to its simplicity. The reconstruction filters are calculated as the inverse of the transfer functions, as described, for example, in [R6]: P(fr,fa)=H(fr,fa)−1.

[0045] Since the transfer function of a single-channel system is a matrix for each range and azimuth frequency, the inversion can be calculated analytically as P(fr,fa)=1HIP,up(fr,fa)⋅HIP,down(fr,fa+PRF)−HIP,down(fr,fa)⋅HIP,up(fr,fa+PRF). [HIP,down(fr,fa+PRF)−HIP,down(fr,fa)−HIP,up(fr,fa+PRF)HIP,up(fr,fa)].

[0046] This approach reduces computational effort because matrix inversion does not need to be calculated. The output of the proposed technique is range-compressed SAR raw data (OD) that is in the frequency domain due to an inverse fast Fourier transform (block ITR).

[0047] The range-compressed SAR raw data (OD) can be further processed to obtain a fully focused SAR image. Any existing algorithm can be applied to obtain a fully focused SAR image.

[0048] In the case of a multi-channel SAR system with N receive channels RC1, ... RCN, the compensation approach becomes more complicated because the azimuth reconstruction must account for the phase deviations caused by the geometric differences of the multi-channel operation itself, as well as by the IP effect. This means that the overall transfer function depends on both the range time and the range and Doppler frequencies. This can be expressed as follows: Hi,up(fr,fa;r0)=exp[−j.Δϕgeo,i(fr,fa;r0)]⋅HIP,up(fr,fa) Hi,down(fr,fa;r0)=exp[−j.Δϕgeo,i(fr,fa;r0)]⋅HIP,down(fr,fa) where the first term of each equation (12) and (13) is the phase deviation due to the geometric difference of the receiving channel RCi (i = 1 ... N) with respect to a reference channel, and the second term is due to the IP effect. The phase of the geometric difference can be expressed as described in reference [R12]: Δϕgeo,i(fr,fa;r0)=2π⋅(f0+frfa⋅C0+C1⋅fa+c⋅C2f0+fr⋅fa2) where c is the speed of light and the coefficients C i are C0≈c0+λ⋅fDC22⋅ka+(λ⋅fDC+c1)22(λ⋅Ka+2c2) C1≈Ka⋅c1−2⋅fDC⋅c2λ⋅Ka+2c2+Δti C2≈c2λ⋅Ka⋅(λ⋅Ka+2c2) where f Dc and K a is the Doppler center of gravity or the rate and λ is the wavelength. The parameters c i in equations (15)-(17) are the coefficients of the deviation range history between the receiving channel RCi (i = 1 ... N) and the reference, which is approximated as a quadratic polynomial as described in reference [R12]: Δri(ta,bi;r0)=c0(bi)+c1(bi)⋅ta+c2(bi)⋅ta2 where t a is the azimuth time.

[0049] The 3D dependence of the phase deviation requires a more complex compensation technique. In this case, there are two ways to compensate for both effects. As a generalized approach (suitable for both multi-static and multi-channel systems), as shown in the single-channel case, the UDC-SAR raw data MD (RCi) from each receive channel RCi (i = 1 ... N) are either first range-compressed and then separated into two channels (third embodiment according to Fig. 6) or first separated into two channels and then range compressed (fourth embodiment according to Fig. 7).

[0050] As in the single-channel embodiments, in the third and fourth embodiments, the range-compressed data DCD and UCD of each receive channel RCi (i = 1 ... N) are transformed into the wavenumber domain by a fast Fourier transform (block TR1).

[0051] The number of receive channels RCi (i = 1 ... N) doubles to N * 2 and the PRF becomes half of the operational PRF op . Therefore, the calculation of the reconstruction filter for both processing schemes is done by solving the linear equations given by [R11] H(fr,fa;r0)=[H1,up(fr,fa;r0)⋯HN,down(fr,fa;r0)⋮⋱⋮H1(fr,fa+(2⋅N−1)⋅PRF;r0)…HN,down(fr,fa+(2⋅N−1)⋅PRF;r0)] P(fr,fa;r0)=H(fr,fa;r0)−1Pi,up−down(fr,fa;r0)=Pi,up / down(fr,fa;rref)⋅ΔPi,up / down(fr,fa;r0(fa))

[0052] The first step of the azimuth reconstruction is to set the filters in the wavenumber domain for a reference range bin (P i,up / down (f r f a ; r ref), block FC, marked only in channel CH2 of the receive channel RC1) and multiply the data with these filters without adding them. After the data has been brought into the range-Doppler domain by applying an inverse fast Fourier transform (RITR), the second step of reconstruction takes place, namely the calculation of the range- and Doppler frequency-dependent residual filter (block RESF), as described in [R11]: ΔPi,up / down(fr,fa;r0(fa)) =|ΔPi,up / down(fr,fa;r0(fa))||ΔPi,up / down(fr,fa;rref(fa))|⋅exp[j⋅Δφi(fr,fa;r0)] where the phase of the differential reconstruction filter is defined as Δφi(fr,fa;r0)=φi(0,fa;r0)−φi(0,fa;rref) where φ i (.) the phase of the reconstruction filter P i (.) is.

[0053] After the data are multiplied by (21) and summed (block SUM), the Doppler spectrum is recovered. As in the single-channel case, the output data of the proposed technique is range-compressed raw SAR data (OD) (short: output data), which is in the frequency domain due to an inverse fast Fourier transform (block ITR). Any existing algorithm can be applied to the output data (OD) to obtain a fully focused SAR image.

[0054] Since it has already been shown in the literature that the range-frequency dependence of the geometry-induced phase deviation only becomes significant in very high-resolution SAR systems and multistatic SAR constellations with large along-track baselines (see references [R11][R12]), the geometry-induced deviations and the IP effect can be corrected in two different steps, as in the fifth and sixth embodiments in the Fig. 8 and Fig.9. As mentioned in the previous approaches, the range compression (RC) and the uplink and downlink chirp separation can be performed in two channels CH1, CH2 in exchangeable steps. Subsequently, the IP effect in the wavenumber domain (block AR) can be compensated using Equation (11), and the geometry-induced phase deviation can be corrected in the range-Doppler domain using the inversion of the range-Doppler variant transfer functions (RITR) by neglecting the range frequency variation as follows: Hi(r0,fa;fr=0)=exp[−j.Δϕgeo,i(r0,fa)].

[0055] If orthogonal waveforms such as short-time shift orthogonal waveforms according to reference [R13] are used instead of UDC modulation, the same reconstruction strategy can be applied to compensate for the IP effect by modifying the transfer functions in equations (5) and (6) for each waveform accordingly.

[0056] The Fig. 10 and Fig. 11 show representations of the impulse response function (IRF) as normalized intensity INT Norm , a point target without IP effect (left illustrations in Fig. 10 and Fig. 11) or with corrected IP effect (right illustrations in Fig. 10 and Fig. 11) with the azimuth reconstruction in single-channel and multi-channel SAR systems, respectively. The simulation parameters used for the representations are listed in Table 1 (single-channel with TerraSAR-X parameters) and 2 (multi-channel with ROSE-L parameters). It can be seen that the proposed method significantly mitigates the azimuth ambiguities caused by the IP effect, so that they are either lower (single-channel SAR system, Fig. 10) or about the same size (multi-channel SAR system, Fig.11) how the antenna pattern-related azimuth ambiguities remain. The reason why the IP effect cannot be completely eliminated is the impossibility of compensating for the phase deviation in the frequency bands outside the original signal spectrum. ([−N2⋅PRFop,N2⋅PRFop]). Nevertheless, the invention succeeds in keeping the azimuth ambiguities at an acceptable level. References [R1] Griffiths, HD and P. Mancini, “Ambiguity Suppression In SARs Using Adaptive Array Techniques,” in: IEEE International Geoscience and Remote Sensing Symposium (IGARSS). Vol. 2. Espoo, Finland, 1991, pp. 1015-1018. [R2] Currie, A. and MA Brown, “Wide-swath SAR,” in IEEE Proceedings F - Radar and Signal Processing, 139.2, 1992, pp. 122-135. [R3] Callaghan, G. D. und I. D. Longstaff, „Wide-swath Space-borne SAR Using a Quad-element Array,“ in IEE Proceedings - Radar, Sonar and Navigation 146.3,1999, pp. 159-165. ISSN: 1350-2395. [R4] Suess, M., B. Grafmueller und R. Zahn, „A Novel High Resolution, Wide Swath SAR System“, in IEEE International Geoscience and Remote Sensing Symposium (IGARSS). Vol. 3. Sydney, NSW, Australien, 2001 pp. 1013-1015. [R5] Freeman, A. et al. „SweepSAR: Beam-forming on Receive Using a Reflector phased Array Feed Combination for Spaceborne SAR,“ in IEEE Radar Conference. Pasadena, USA, 2009, S. 1-9. [R6] Krieger, G., N. Gebert, und A. Moreira, „Unambiguous SAR Signal Reconstruction from Nonuniform Displaced Phase Center Sampling,“ in IEEE Geoscience and Remote Sensing Letters, 1.4, 2004, pp. 260-264 [R7] U. Stein und M. Younis, „Suppression of range ambiguities in synthetic aperture radar systems,“ The IEEE Region 8 EUROCON 2003. Computer as a Tool, Ljubljana, Slowenien, 2003, S. 417-421, Bd. 2. [R8] J. Mittermayer und J. M. Martinez, „Analysis of range ambiguity suppression in SAR by up and down chirp modulation for point and distributed targets,“ IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477), Toulouse, Frankreich, 2003, pp. 4077-4079 vol.6. [R9] H. Mo and Z. Zeng, „Investigation of multichannel ScanSAR with up and down chirp modulation for range ambiguity suppression,“ 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 2016, pp. 1130-1133. [R10] P. Prats-Iraola et al., „On the Processing of Very High Resolution Spaceborne SAR Data,“ in IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 10, pp. 6003-6016, Oct. 2014. [R11] N. Sakar, M. Rodriguez-Cassola, P. Prats-Iraola, and A. Moreira, „Azimut-Rekonstruktion Algorithm for Multistatic SAR Formations with Large Along-Track Baselines“, IEEE Transactions on Geoscience and Remote Sensing, vol. 58, no. 3, pp. 1931-1940, Mar. 2020. [R12] N. Sakar, M. Rodriguez-Cassola, P. Prats-Iraola, A. Reigber und A. Moreira, „Analysis of Geometrical Approximations in Signal Reconstruction Methods for Multistatic SAR Constellations With Large Along-Track Baseline,“ in IEEE Geoscience and Remote Sensing Letters, vol. 15, no. 6, pp. 892-896, June 2018. [R13] G. Krieger, „MIMO-SAR: Opportunities and Pitfalls,“ in IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 5, pp. 2628-2645, May 2014.

Claims

[1] A method for processing SAR raw data acquired by a SAR system (1) having a transmitting antenna and at least one receiving antenna, the SAR system (1) being arranged to transmit alternating up- and down-chirps (UDC), comprising the following steps: - splitting the UDC-modulated SAR raw data (MD) into a first channel (CH1) comprising the data (UCD) of the uplink chirps and a second channel (CH2) comprising the data (DCD) of the downlink chirps; - performing a range compression (RC) with a transfer function, wherein the transfer function is the complex conjugate of the respective transmitted chirp replica; - performing an azimuth reconstruction (AR) using a reconstruction filter; and - Providing the output data (OD) for further processing, characterized by , that - the reconstruction filter is calculated with the transfer function of an intrapulse (IP) effect taking into account a movement of the SAR system (1) during a transmission and reception process, whereby the data obtained by azimuth reconstruction are output data (OD) representing range-compressed SAR raw data without IP effect, and - the transfer function of the IP effect is defined with a 2x2 matrix as H(fr,fa)=[HIP,up(fr,fa)HIP,down(fr,fa)HIP,up(fr,fa)HIP,down(fr,fa+PRF)] where H IP,up (f r , f a ) and H IP,down (f r , f a ) represent the IP effect for up and down chirps, expressed by HIP,up(fa,fr)=exp[j⋅2π⋅fa|K|⋅fr] HIP,down(fa,fr)=exp[−j⋅2π⋅fa|K|⋅fr] and PRF half of the operating pulse repetition frequency PRF (PRF op ) is. [2] The method according to claim 1, wherein the splitting of the UDC-modulated SAR raw data (MD) into the first and second channels (CH1, CH2) can be performed before performing the range compression (RC) or after performing the range compression (RC). [3] A method according to claim 1 or 2, wherein the range-compressed data of the first and second channels (CH1, CH2) are transformed into a wavenumber range. [4] Method according to one of the preceding claims, wherein the data obtained by azimuth reconstruction are transformed into a frequency domain to represent the output data (OD). [5] Method according to one of the preceding claims, wherein the reconstruction filter is calculated as P(fr,fa)=H(fr,fa)−1. [6] A method according to any one of claims 1 to 5, wherein, when the SAR system is a single-channel system, the transfer function is a matrix for each range and azimuth frequency, the inversion being analytically calculated as P(fr,fa)=1HIP,up(fr,fa)⋅HIP,down(fr,fa+PRF)−HIP,down(fr,fa)⋅HIP,up(fr,fa+PRF). [HIP,down(fr,fa+PRF)−HIP,down(fr,fa)−HIP,up(fr,fa+PRF)HIP,up(fr,fa)]. [7] A method according to any one of claims 1 to 5, wherein, when the SAR system is a multi-channel system with at least two receivers, the transfer function depends on both the range time and the range and Doppler frequencies. [8] A method according to claim 7, wherein the transfer function of the IP effect is defined by Hi,up(fr,fa;r0)=exp[−j.Δϕgeo,i(fr,fa;r0)]⋅HIP,up(fr,fa)Hi,down(fr,fa;r0)=exp[−j.Δϕgeo,i(fr,fa;r0)]⋅HIP,down(fr,fa) where Δφ geo,1 (f r , f a; r0) is the phase deviation due to the geometric difference of a receiver i with respect to a reference receiving channel. [9] The method of claim 7 or 8, wherein the azimuth reconstruction comprises - Calculation of filters in the wavenumber range for a reference range bin (P i,up / down (f r , f a ; r ref )), - Multiplying the data with these filters without adding them, and - after transforming the data into the range-Doppler domain, calculation of the range and Doppler frequency dependent residual filter. [10] The method of claim 9, wherein the calculation of the range and Doppler frequency dependent residual filter comprises the calculation of ΔPi,up / down(fr,fa;r0(fa)) =|ΔPi,up / down(fr,fa;r0(fa))||ΔPi,up / down(fr,fa;rref(fa))|⋅exp[j⋅Δφi(fr,fa;r0)] where the phase of the differential reconstruction filter is defined as Δφi(fr,fa;r0)=φi(0,fa;r0)−φi(0,fa;rref) where φ i (.) the phase of the reconstruction filter P i (.) is. [11] A method according to claim 10, wherein the Doppler spectrum is restored after summing the data of each receive channel. [12] A computer program product comprising instructions which, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 11. [13] System for processing SAR raw data acquired by a SAR system (1) having a transmitting antenna and at least one receiving antenna, wherein the SAR system (1) is arranged to transmit alternating up- and down-chirps (UDC) and comprises a processor arranged to carry out the method according to one of claims 1 to 11.

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