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) having a transmit antenna and at least one receive antenna, wherein the SAR system (1) is adapted to transmit alternating up- and down-chirps (UDC), comprising the steps of: - splitting the UDC modulated SAR raw data (MD) into a first channel (CH1) comprising the data (UCD) of the up-chirps and a second channel (CH2) comprising the data (DCD) of the down-chirps; - conducting a range compression (RC) with a transfer function, the transfer function being the complex conjugate of the respective transmitted chirp replica; - conducting an azimuth reconstruction (AR) with a reconstruction filter, the reconstruction filter computed with the transfer function of an intra-pulse (IP) effect considering a movement of the SAR system (1) during a transmit and receive event, the azimuth reconstructed data being output data (OD) that represent range-compressed SAR raw data without IP effect; and - providing the output data (OD) for further processing.

Description

[0001] P3120 00Deutsches Zentrum für Luft- und Raumfahrt e.V. Königswinterer Str. 522-524 53227 Bonn ____________________________________________________________________ Method and system for processing SAR raw data acquired by a SAR system ____________________________________________________________________ Description The present invention relates to a method and a system for processing SAR raw data acquired by a SAR system having a transmit antenna and at least one receive an- tenna, wherein the SAR system is adapted to transmit alternating up-and down-chirps (UDC). Synthetic Aperture Radar (SAR) is a technique that increases the effective length of the physical antenna by taking advantage of the radar’s motion, and consequently im- proves the azimuth resolution of the system. The observation geometry of a synthetic aperture radar 1 (SAR) comprising a radar antenna is depicted in Figure 1. The radar antenna at time,is depicted as a rectangular planar antenna. The SAR system 1 which moves with constant velocity along an azimuth direction AZD (x) is equipped with a side-looking radar on a moving platform at altitude . The dotted line NT indicates the so-called nadir track, which is the projection of the azimuth di- rection perpendicular to the earth's surface. To move the radar antenna, it is located on a flying object (not shown), which is preferably a satellite, but may also be an air- craft. Movement is along the azimuth direction AZD (x) is indicated by the antennaP3120 00at time,. The SAR system 1 in this embodiment is a combined transmitting and receiving device which emits radar radiation in transmitting mode and receives radar radiation in receiving mode. In transmit mode, the SAR system 1 transmits a radar beam RB based on a radar pulse RP to the earth's surface at a given angle. The radar beam RB corresponds to the main lobe of the emitted antenna radiation and falls on the earth's surface. The SAR system 1 transmits radar pulses RP (short: pulses) with a pulse duration at a certain Pulse Repetition Frequency (PRF). Most of the energy of a respective radar pulse RP or its radar beam RB is directed onto an approximately elliptical area FP on the earth's sur- face. This area is usually referred to as the "footprint" of the radar device or the asso- ciated radar antenna, where denoted the swath width of the area FP and denotes the synthetic aperture length.In Figure 1, , denotes the slant range from the SAR system 1 to a point on theearth's surface. This slant range can be clearly converted into the so-called ground range, the direction of which is denoted by GR in Fig. 1. The ground range GR corre- sponds to the projection of the slant range SR onto the earth's surface GR and runs perpendicular to the azimuth direction x. In the following, the direction of the ground range GR is also generally referred to as the range direction. The footprint FP has an extent in the range direction that corresponds to the swath width shown. During the movement of the SAR system 1, radar echoes RE of the radar pulses RP from the strip reflected on the earth's surface are detected. For this purpose, the SAR system 1 is switched to receive mode. The principle of SAR measurement is based on the fact that a point on the earth's sur- face GR is observed several times from different angles due to the movement of the SAR system 1. Due to the Doppler effect, a frequency shift occurs during the detec- tion of the radar echoes, which can be suitably evaluated, whereby amplitude and phase information and thus an image point of the earth's surface is ultimately ob- tained for the points on the earth's surface at which the radar pulses are reflected. TheP3120 00corresponding calculation of image points of the earth's surface from the detected ra- dar echoes is sufficiently known to the skilled person and is therefore not explained further in detail. A typical SAR system 1 uses a chirp signal, which is a baseband linear frequency modulated signal. Depending on the sign in the exponential term, the transmitted pulse can be characterized as up- or down-chirp as where is the range time (fast time) and | | is the absolute value of the chirp rate(3) where is the bandwidth of the transmitted chirp. The coordinates of the radar sys- tem 1 are the azimuth and the slant-range, which corresponds to the flight direction (azimuth direction AZD, x) and the observation direction (ground range GR), respec- tively. As mentioned above, the footprint of the antenna covers an area which is character- ized with the swath width, in the range (or cross-track) direction and with the synthetic aperture length, , in the azimuth direction. After a certain time delay, the transmitted pulses reflect back to the antenna (also referred to as sensor) from the ob- served scene and are coherently demodulated, digitalized and stored as raw data. The time between two transmit events is called pulse repetition interval (PRI), which is the inverse of the PRF. Therefore, the sampling frequency of the SAR raw data in azimuth is determined by the system PRF (also referred to as the operational PRF).P3120 00The raw data is later processed to deconvolve the received echoes to retrieve the scene reflectivity. After the SAR processing, the energy of a single point target is lo- cated at its range and azimuth position. The range resolution of a radar is a function of the bandwidth of the transmitted signal, , and the azimuth resolution of a SAR sensor is equal to the half of the physical antenna length in azimuth, . A typical SAR processing undergoes range compression, range-cell migration cor- rection (RCMC) and azimuth compression. The range compression is done via matched filter, which is the convolution of the data with the complex conjugate of the transmitted signal. The range compressed SAR data forms a hyperbolical curve that crosses over several range bins. The reason for that is the change of the distance between the point target and the sensor along the synthetic aperture. This effect is usually corrected by a range-variant two-dimensional reference function and the en- ergy of a point target becomes confined to a single range bin. As in the range dimen- sion, the azimuth compression is applied with a matched filter to compress the en- ergy of a point target into a single pixel. To acquire an ambiguity-free SAR image, the system PRF must be equal or greater than the Doppler bandwidth where is the platform velocity. Otherwise, azimuth ambiguities occur in the fo- cused SAR image due to the backfolding of the Doppler spectrum. On the other hand, the range ambiguities occur when echoes outside the main beamwidth in eleva- tion and from different transmit events reach the receiver at the same time despite their different flight time. To avoid range ambiguities, the SAR system can be either designed to cover a narrow swath with a higher PRF (which potentially allows for a finer azimuth resolution) or to cover a wide swath with a lower PRF (which forces a coarser azimuth resolution). This represents the limitation of a conventional SAR system, namely, the trade-off between azimuth resolution and swath width.P3120 00There are many system concepts (disclosed in references [R1]-[R3]) and processing strategies (disclosed in DE 102005062031 A1 and references [R4]-[R6]) to achieve high resolution wide-swath (HRWS) imaging. One way of overcoming the limitation of a conventional SAR system is alternating up- and down-chirp (UDC) in each transmit event, i.e., marking the pulses (as disclosed, for example, in references [R7][R8]). By employing this method, the unambiguous swath size of a monostatic single-channel SAR system can be doubled, or the azimuth resolution can be twice as finer for the same swath coverage if the antenna length is adjusted. Since each pulse is marked and compressed with its complex conjugate, the ambiguous signal com- pressed with the wrong filter becomes smeared along the range dimension (range ambiguity suppression). Another approach towards acquiring high resolution SAR data from a larger swath is to reduce the operational PRF and suppress the azimuth ambiguities by employing more receive units (as disclosed in reference [R6]). This can be achieved either with a single-platform SAR by splitting the antenna in azimuth direction or with a multi- platform SAR constellation. Furthermore, both approaches can be combined together in a multi-channel SAR system with up- and down-chirp modulation (as shown in reference [R9]). Typical spaceborne SAR processors neglect the fact that the sensor moves during the transmit and receive events. In fact, the platform moves during the transmission and the reception of the chirp signal and introduces a space-invariant phase, known as in- tra-pulse (IP) effect, that can be expressed in the wavenumber domain as P3120 00where is the Doppler-frequency and is the range-frequency vector (see refer- ence [R10]). For SAR systems without alternating transmitted waveforms, it may re- sult in resolution loss both in azimuth and range, and it can be easily corrected with the complex conjugate of equations (5) or (6), as suggested in reference [R10]. How- ever, in case an up / down sequence is used, the IP effect shows itself as additional az- imuth ambiguities, which is illustrated in Figures 2 and 3 showing the impulse re- sponse function (IRF) as normalized intensity INTNorm including the maximum of the azimuth ambiguity in all range bins for a single channel SAR system (Figure 2) and a multi-channel SAR system (Figure 3). The right columns of Figures 2 and 3 show the impulse response function (IRF) as normalized intensity INTNorm, where the azimuth ambiguities introduced by the un- compensated IP effect can be clearly observed, both for single channel (Figure 2, right column) and multi-channel (Figure 3, right column) SAR systems with UDC modulation. The simulation parameters are listed in Table 1 (single channel with Ter- raSAR-X parameters) and 2 (multi-channel with ROSE-L parameters). Parameter ValueOrbit altitude 514 km Center frequency 9.65 GHz Chirp bandwidth 300 MHz Chirp duration 50 μs Processed Doppler bandwidth 2765 Hz PRF 4174 HzTable 1 Simulation parameters for the single channel simulation results shown in Figure 2. Parameter ValueOrbit altitude 693 kmP3120 00Center frequency 1.25 GHz Chirp bandwidth 65.2 MHz Chirp duration 48.61 μs Processed Doppler bandwidth 2600 Hz PRF 1378.18Hz Number of azimuth channels 5 ()Table 2 Simulation parameters for the multi-channel simulation results shown in Figure 3. The plots in Figures 2 and 3 also show as reference the impulse response function (IRF) as normalized intensity INTNormof a system without UDC modulation and without any IP effect (left columns of Figures 2 and 3). As it can be clearly seen, the IP related ambiguities in single-channel system go as high as the ones due to the an- tenna pattern and the ambiguities in multi-channel system are much higher than the ones related to the antenna pattern. To put these results in numbers, the maximum Peak-to-Ambiguity-Ratio (PTAR) in the single-channel system without UDC modu- lation and with IP effect are –30.60 dB and -33.16, where the total Azimuth-Ambigu- ity-to-Signal-Ratio (AASR) values are -20.42 dB and -23.69 dB, respectively. In the multi-channel case, the maximum PTAR without UDC modulation and with IP effect are -59.51 dB and -38.92 dB, where the total AASR values are -40.13 dB and -29.50 dB, respectively. It is an object of the present invention to provide a method and a system for pro- cessing SAR raw data which are able to compensate the intra-pulse effect from Syn- thetic Aperture Radar (SAR) data acquired with up- and down-chirp modulation. These objects are solved by the independent claims. Preferred embodiments are set out by the dependent claims.P3120 00According to a first aspect of the present invention, a method for processing SAR raw data acquired by a SAR system having a transmit antenna and at least one re- ceive antenna is suggested, wherein the SAR system is adapted to transmit alternat- ing up- and down-chirps (UDC). The method comprises the steps of:- splitting the UDC modulated SAR raw data into a first channel comprisingthe up-chirps and a second channel comprising the down-chirps;- conducting a range compression with a transfer function, the transfer functionbeing the complex conjugate of the respective transmitted chirp replica; - conducting an azimuth reconstruction with a reconstruction filter, where the reconstruction filter is computed with the transfer function of an intra-pulse (IP) ef- fect, in particular an inverse of the transfer function of the intra-pulse (IP) effect, considering a movement of the SAR system during a transmit and receive event, the azimuth reconstructed data being output data that represent range-compressed SAR raw data without an IP effect; and- providing the output data for further processing. Further processing may con-tinue by applying any conventional SAR focusing algorithm in order to retrieve the fully focused SAR image. This algorithm usually performs the range-cell migration correction (RCMC) and azimuth compression. According to the invention, a separation of up- and down-chirp signals as new chan- nels and including the intra-pulse effect in the transfer function equation is suggested to consider the impact of the IP effect on the performance of UDC modulated SAR images. According to a preferred embodiment, splitting the UDC modulated SAR raw data into the first and second channel may be executed before conducting the range com- pression or after conducting the range compression. According to a further preferred embodiment, the range compressed data of the first and second channel are transformed into a wavenumber domain via a 2-D FourierP3120 00transform. 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 depend- ent on range frequency and Doppler-frequency. According to a further preferred embodiment, the azimuth reconstructed data are transformed back to time domain via an inverse Fourier transform. According to a further preferred embodiment, the transfer function of the IP effect is defined with a 2x2 matrix as where , , and , , represent the IP effect for up- and down-chirp, respectively, as expressed by and PRF is the half of the operational pulse repetition frequency PRF ( ). Thereconstruction filters may be computed by various different methods that can be found in the literature. The choice of the reconstruction filter computation method highly depends on the considered system, namely a single-channel SAR system or a multi-channel SAR system. A single channel SAR system may be represented by a monostatic SAR system or a bistatic SAR system having one transmit antenna and one receive antenna. A multi-channel SAR system may be represented by a mono- static SAR system or a bistatic SAR system having one transmit antenna and more than one receive antennas (or receiving portions). According to a further preferred embodiment, the reconstruction filter is computed asP3120 00, , ,i.e., the reconstruction filters are computed as the inverse of the transfer function. According to a further preferred embodiment, if the SAR system is a single channel system, the transfer function is a matrix for each range and azimuth frequency, where the inversion is computed analytically as , Using the above given transfer function reduces the computational complexity since the matrix inversion does not need to be computed. The output data of the proposed technique is range-compressed SAR raw data. Afterwards, as mentioned above, any existing algorithm can be applied to retrieve a fully focused SAR image. According to a further preferred embodiment, if the SAR system is a multi-channel system having at least two receivers (also referred to as receive channels), the trans- fer function depends on range time, as well as on the range and Doppler frequencies. In particular, the transfer function of the IP effect of a multi-channel SAR system is defined by ,, ; exp j. , , ; , ,wherein , , ; is the phase deviation due to the geometrical difference ofa receiver (receive channel ) with respect to a reference receive channel.P3120 00In a further preferred embodiment of a multi-channel SAR system, the azimuth re- construction comprises computing filters in the wavenumber domain for a referencerange bin ( , / , ; ), multiplying the data with these filters withoutadding them together, and after the data are transformed to the range-Doppler do- main, computation of the range and Doppler frequency dependent residual filter. In particular, the computation of the range and Doppler frequency dependent residual filter comprises computing where the phase of the differential reconstruction filter is defined as where . is the phase of reconstruction filter . .In addition, after the data of each receive channel is summed up, the Doppler spec- trum is recovered. According to a second aspect of the present invention, a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to one or more preferred embodi- ments as described above, is suggested. According to a third aspect of the present invention, a system for processing SAR raw data acquired by a SAR system having a transmit antenna and at least one re- ceive antenna is suggested, wherein the SAR system is adapted to transmitP3120 00alternating up- and down-chirps (UDC), comprising a processor, which is adapted to execute the method according to one or more preferred embodiments as described above. The invention and further advantages will be explained more detailed by the accom- panying figures. Fig. 1 shows the generally known geometry of a monostatic synthetic aperture ra- dar (SAR) system. Fig. 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 compensa- tion. Fig. 3 shows plots 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 compensa- tion. Fig. 4 shows a schematic flow chart view of the proposed method for single-chan- nel SAR systems according to a first embodiment, where data are range compressed and then separated into two processing channels before the IP effect compensation. Fig. 5 shows a schematic flow chart view of the proposed method for single-chan- nel SAR systems according to a second embodiment, where data are sepa- rated into two channels and then range compressed before the IP effect com- pensation.P3120 00Fig. 6 shows a schematic flow chart view of the proposed reconstruction algorithm for multi-channel SAR systems according to a third embodiment, where the data in each receive channel are first range compressed and then separated into two channels before the IP effect compensation. Fig. 7 shows a schematic flow chart view of the proposed reconstruction algorithm for multi-channel SAR systems according to a fourth embodiment, where the data in each receive channel are first separated into two channels and then range compressed before the IP effect compensation. Fig. 8 shows a schematic flow chart view of the proposed reconstruction algorithm for multi-channel SAR systems according to a fifth embodiment, where the data in each receive channel are first range compressed and then separated into two channels before the IP effect compensation which is advantageous for a single platform SAR system. Fig. 9 shows a schematic flow chart view of the proposed reconstruction algorithm for multi-channel SAR systems according to a sixth embodiment, where the data in each receive channel are first separated into two channels and then range compressed before the IP effect compensation which is advantageous for a single platform SAR system. Fig. 10 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 IP effect and with an IP correction according to the method of the present invention. Fig. 11 shows plots 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.P3120 00Azimuth ambiguities occur in a focused SAR image due to the backfolding of the Doppler spectrum, in case an operational PRF is smaller than the Doppler bandwidth . On the other hand, the range ambiguities occur when echoes outside the main beamwidth in elevation and from different transmit events reach the receiver at the same time despite their different flight time. To avoid range ambiguities, a SAR sys- tem as described in conjunction with Figure 1 can be either designed to cover a nar- row swath with a higher PRF, which potentially allows for a finer azimuth resolution, or to cover a wide swath with a lower PRF, which forces a coarser azimuth resolu- tion. This represents the limitation of a conventional SAR system, namely, the trade- off between azimuth resolution and swath width. As described in the introductory portion, one way of overcoming the limitation of a conventional SAR system is alternating up- and down-chirp (UDC) in each transmit event, i.e., marking the pulses. Since each pulse is marked and compressed with its complex conjugate, the ambiguous signal compressed with the wrong filter becomes smeared along the range dimension resulting in a range ambiguity suppression. How- ever, up to now conventional SAR processors neglect the fact that the sensor mounted on a platform moves during the transmit and receive events. In fact, the platform moves during the transmission and the reception of the chirp signal and in-troduces a space-invariant phase, i.e., intra-pulse (IP) effect. However, in case UDCmodulation is used, the IP effect shows itself as additional azimuth ambiguities if not properly accounted for. The method described below addresses the compensation of the IP effect in SAR sys- tems with an UDC modulation. The removal of the IP effect differs for a single channel Nyquist sampled data and a multi-channel system operated with a PRF lower than the Nyquist criteria. Therefore, two main compensation techniques are proposed. Nevertheless, the basic idea of both of the techniques is common, namely, removing the phase deviation from allP3120 00channels with the azimuth reconstruction. The term “channel” means data relating to the different receivers or the different modulation (up-chirps or down-chirps). Figures 4 and 5 show block diagrams of the processing approach for a single channel SAR system. In case of the first embodiment of Figure 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 (7) ,exp | | which also separates the input data MD into two channels CH1, CH2, where channel CH1 comprises data of up-chirps UCD and channel 2 comprises data of down-chirps DCD. In case of the second embodiment of Figure 5, the UDC modulated SAR raw data MD are first separated into two channels (e.g., channel CH1: data of up-chirps UCD, e.g. odd samples; channel CH2: data of down-chirps DCD, e.g. even samples) and then range compressed (block RC). In both cases the range compressed data DCD and UCD are transformed into the wavenumber domain by a Fast Fourier transformation (block TR1). Then, the azimuth reconstruction AR with an inverse filter takes place in the wave- number 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 de- fined with a 2x2 matrix asP3120 00 where , , and , , represent the IP effect for up- and down-chirp respectively (see (5) and (6)), and PRF is the half of the operational PRF( ).The reconstruction filters may be computed by various different methods that can be found in the literature. The choice of the reconstruction filter computation method highly depends on the considered system. Especially for a single platform system, the usage of the inverse filter (nulling approach) may be chosen due to its simplicity. The reconstruction filters are computed as the inverse of the transfer functions as dis- closed, for example, in reference [R6]: ,, . (10)Since the transfer function of a single channel system is a matrix for each range and azimuth frequency, the inversion can be computed analytically as This approach reduces the computational complexity since the matrix inversion does not need to be computed. The output of the proposed technique is range-compressed SAR raw data OD (short output: data) which are in the frequency domain due to an inverse Fast Fourier transformation (block ITR).P3120 00The range-compressed SAR raw data OD may be processed further in order to re- trieve a fully focused SAR image. Here, any existing algorithm can be applied to re- trieve a fully focused SAR image.In the case of a multi-channel SAR system having receive channels 1, … ,the compensation approach becomes more complicated since the azimuth reconstruc- tion has to consider the phase deviations caused by the geometrical differences of the multi-channel operation itself, as well as the IP effect. This implies that the complete transfer function depends on range time, as well as on the range and Doppler fre- quencies. This can be expressed as ,, ; exp j. , , ; , , (12) where the first term of each equation (12) and (13) is the phase deviation due to thegeometrical difference of the receive channel RC ( 1 … ) with respect to a ref-erence channel and the second term is due to the IP effect. The phase of the geomet- rical difference can be expressed as disclosed in reference [R12]: where is the speed of light and the coefficients are P3120 00where and are the Doppler centroid and rate, respectively, and is the wave- length. The parameters in equations (15)-(17) are the coefficients of the range his-tory deviation between the receive channel RC ( 1 … ) and the reference whichis approximated as the quadratic polynomial as disclosed in reference [R12]: where is the azimuth time. The 3-D dependencies of the phase deviation require a more elaborate compensation technique. In this case, there are two possible ways for compensating both effects. As a more generalized approach (suitable for both multi-static and multi-channel sys-tems), as shown in the single channel case, the UDC SAR raw data MD (RC ) fromeach receive channel RC ( 1 … ) are either first range compressed and then sep-arated into two channels (third embodiment according to Figure 6), or first separated into two channels and then range compressed (fourth embodiment according to Fig- ure 7). As with the single channel embodiments, in both, the third and fourth embodiments,the range compressed data DCD and UCD of each receive channel RC ( 1 … )are transformed into the wavenumber domain by a Fast Fourier transformation (block TR1).The number of receive channels RC ( 1 … ) doubles to *2 and the PRF be-comes half of the operational . Hence, the reconstruction filter computation for both of the processing schemes is done by solving the linear equations given by [R11]P3120 00 ,; , ; (20), / , ; , / , ; , / , ;The first step of the azimuth reconstruction is to compute the filters in the wave-number domain for a reference range bin ( , / , ; , block FC, onlymarked in channel CH2 of receive channel RC1) and multiply the data with these fil- ters without adding them together. After the data are brought to the range-Doppler domain by applying an inverse Fast Fourier transformation RITR, the second step of the reconstruction takes place, which is the computation of the range and Doppler frequency dependent residual filter (block RESF) as disclosed in reference [R11]: , / , ;(21) where the phase of the differential reconstruction filter is defined as ,; 0, ; 0, ; (22)where . is the phase of reconstruction filter . .After the data are multiplied with (21) and summed up (block SUM), the Doppler spectrum is recovered. As in the single-channel case, the output of the proposed tech- nique is range-compressed SAR raw data OD (short output: data) which are in the frequency domain due to an inverse Fast Fourier transformation (block ITR). AnyP3120 00existing algorithm can be applied to the output data OD to retrieve a fully focused SAR image. Since it is already shown in the literature that the range-frequency dependency of the geometry related phase deviation becomes significant only for very-high resolution SAR systems and multi-static SAR constellations with large along-track baselines (see references [R11][R12]), the geometry related deviations and the IP effect can be corrected in two different steps as shown in the fifth and sixth embodiments illus- trated in Figures 8 and 9. As mentioned in the previous approaches, the range com- pression RC and up- and down-chirp separation into two channels CH1, CH2 can be done in interchangeable steps. Afterwards, the IP effect can be compensated in the wavenumber domain (block AR) with equation (11) and the geometry related phase deviation can be corrected in the range-Doppler domain with the inversion of the range-Doppler-variant transfer functions (RITR) by neglecting the range-frequency variation as Note that if the orthogonal waveforms such as short-term-shift-orthogonal wave- forms according to reference [R13] are used instead of UDC modulation, the same reconstruction strategy can be applied to compensate the IP effect by modifying transfer functions in equations (5) and (6) for each waveform accordingly. Figures 10 and 11 show plots of the impulse response function (IRF) as normalized intensity INTNormof a point target without IP effect (left plots of Figures 10 and 11) and corrected IP effect (right plots of Figures 10 and 11) with the azimuth recon- struction in single channel and multi-channel SAR systems, respectively. The simu- lation parameters used for the plots are listed in Table 1 (single channel with Ter- raSAR-X parameters) and 2 (multi-channel with ROSE-L parameters). It can be seen that the proposed method mitigates significantly the azimuth ambiguities caused by the IP effect, such that they remain either less (single channel SAR system, FigureP3120 0010) or around the same level (multi-channel SAR system, Figure 11) as the antennapattern related azimuth ambiguities. The reason for not removing the IP effect com- pletely is the impossibility of compensating the phase deviation in the frequency binsoutside of the original signal spectrum (,). Nevertheless, theinvention manages to keep the azimuth ambiguities within an acceptable level.

[0002] P3120 00References [R1] Griffiths, H. D. 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 M. A. Brown, “Wide-swath SAR,” in IEEE Proceedings F - Radar and Signal Processing, 139.2, 1992, pp. 122–135. [R3] Callaghan, G. D. and 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, and R. Zahn, “A Novel High Resolution, Wide Swath SAR System,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS). Vol. 3. Sydney, NSW, Australia, 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 Con- ference. Pasadena, USA, 2009, pp. 1–9. [R6] Krieger, G., N. Gebert, and A. Moreira, “Unambiguous SAR Signal Recon- struction from Nonuniform Displaced Phase Center Sampling,” in IEEE Geo- science and Remote Sensing Letters, 1.4, 2004, pp. 260–264 [R7] U. Stein and M. Younis, "Suppression of range ambiguities in synthetic aper- ture radar systems," The IEEE Region 8 EUROCON 2003. Computer as a Tool., Ljubljana, Slovenia, 2003, pp. 417-421 vol.2. [R8] J. Mittermayer and 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, France, 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 Inter- national Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 2016, pp. 1130-1133.P3120 00[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, “Azimuth Reconstruction 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 and 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

P3120 00Claims1. A method for processing SAR raw data acquired by a SAR system (1) having atransmit antenna and at least one receive antenna, wherein the SAR system (1) is adapted to transmit alternating up- and down-chirps (UDC), comprising the steps of: -splitting the UDC modulated SAR raw data (MD) into a first channel(CH1) comprising the data (UCD) of the up-chirps and a second channel (CH2) comprising the data (DCD) of the down-chirps; -conducting a range compression (RC) with a transfer function, the trans-fer function being the complex conjugate of the respective transmitted chirp replica; -conducting an azimuth reconstruction (AR) with a reconstruction filter,the reconstruction filter computed with the transfer function of an intra- pulse (IP) effect considering a movement of the SAR system (1) during a transmit and receive event, the azimuth reconstructed data being output data (OD) that represent range-compressed SAR raw data without IP ef- fect; and -providing the output data (OD) for further processing.

2. The method according to claim 1, wherein splitting the UDC modulated SARraw data (MD) into the first and second channel (CH1, CH2) may be executed before conducting the range compression (RC) or after conducting the range compression (RC).

3. The method according to claim 1 or 2, wherein the range compressed data ofthe first and second channel (CH1, CH2) are transformed into a wavenumber domain.P3120 004. The method according to any of the preceding claims, wherein the azimuth re-constructed data are transformed into a frequency domain to represent the out- put data (OD).

5. The method according to any of the preceding claims, wherein the transfer function of the IP effect is defined with a 2x2 matrix aswhere , , and , , represent the IP effect for up- anddown-chirp, respectively, as expressed byand PRF is the half of the operational pulse repetition frequency PRF ( ).

6. The method according to any of the preceding claims, wherein the reconstructionfilter is computed as<sub>, , .

7. The method according to any of the claims 1 to 6, wherein, if the SAR systemis a single channel system, the transfer function is a matrix for each range and azimuth frequency, where the inversion is computed analytically as<sub>P3120 008. The method according to any of the claims 1 to 6, wherein, if the SAR systemis a multi-channel system having at least two receivers, the transfer function depends on range time, as well as on the range and Doppler frequencies.

9. The method according to claim 8, wherein the transfer function of the IP effect is definedwherein , , ; is the phase deviation due to the geometrical differenceof a receiver i with respect to a reference receive channel.

10. The method according to claim 8 or 9, wherein the azimuth reconstructioncomprises -computing filters in the wavenumber domain for a reference range bin<img src='' class="img-anchor img-center" img-id="IMGF000027_0002" / >-multiplying the data with these filters without adding them together, and- after the data are transformed to the range-Doppler domain, computationof the range and Doppler frequency dependent residual filter.

11. The method according to claim 10, wherein the computation of the range and Doppler frequency dependent residual filter comprises computingwhere the phase of the differential reconstruction filter is defined as ,; 0, ; 0, ;where . is the phase of reconstruction filter . .P3120 0012. The method according to claim 11, wherein after the data of each receive chan-nel is summed up, the Doppler spectrum is recovered.

13. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to perform the method accord- ing to any one of claims 1 to 12.

14. A system for processing SAR raw data acquired by a SAR system (1) having atransmit antenna and at least one receive antenna, wherein the SAR system (1) is adapted to transmit alternating up- and down-chirps (UDC), comprising a processor, which is adapted to execute the method according to any of claims 1 to 12.

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