Ambiguity reduction in synthetic aperture radar imagery.

Abstract

A method for operating a synthetic aperture radar (SAR) to obtain SAR echo data for image formation includes the steps of: calculating a nadir ambiguity index for a platform's nadir; determining a frequency sweep direction sequence for successive pulses of a waveform transmitted by the SAR based on the nadir ambiguity index; obtaining a relative phase sequence for the successive pulses of the waveform; and encoding the waveform using the determined frequency sweep direction sequence and relative phase sequence.

Description

[Technical field]

[0001] The present invention is in the field of synthetic aperture radar imaging. [Background technology]

[0002] Synthetic Aperture Radar (SAR) can be used to image an area on Earth (also called a target area) by transmitting a radar beam and recording the return echo from the transmitted beam. SAR systems can be installed on airborne platforms such as aircraft as well as on satellites operated from space. SAR can operate in different modes such as strip map, spotlight, ScanSAR (Scanning Synthetic Aperture Radar) and TOPSAR (Progressive Scanning SAR for Earth Observation).

[0003] Typically, a SAR system transmits radio frequency radiation in pulses and records the returning echoes. The sampled data is stored for processing to form an image. The pulsed action of the SAR can result in ambiguities in the image, for example, due to radar echoes backscattered from the nadir or other points outside the target imaging area. These ambiguities can arise because of the difficulty of directing the radar beam perfectly only at the target imaging area. In reality, the radar beam has side lobes that also illuminate areas outside the desired imaging area, causing radar echoes from these "unknown" areas to be mixed with reflections from "clear" areas. These echoes of earlier and later transmitted pulses scattered from undesired areas may include the nadir, which is the point directly below the SAR platform (e.g., a satellite) at its current position. In this case, the SAR image is a combination of the clear image (the desired image), the partially focused unknown image, and the nadir.

[0004] One way to overcome the problem of ambiguity from unknown range regions is to increase the size of the antenna in elevation, which narrows the beam and reduces the beam sidelobes, as well as the backscattered signal from the unknown region. However, increasing the size of the antenna conflicts with the small satellite's size, weight, and power "SWAP" requirements and the need to image large ranges with high resolution.

[0005] Another method that can be used to suppress nadir ambiguities in particular is to tune the pulse repetition frequency (PRF) so that the nadir echo time falls outside the radar's receiving window. In most cases, this is impractical and imposes additional constraints on the PRF, which is already optimized to maximize swath width and minimize the azimuth ambiguity-to-signal ratio. Furthermore, unknown targets that are outside the blind range cannot be suppressed by PRF tuning. An alternative to applying a fixed or fine-tuned PRF is to use a staggered SAR system, where the time range to the preceding and succeeding pulses varies continuously, so that the ambiguities are located at different ranges for different range lines. Thus, the unknown energy is integrated incoherently in the Doppler domain, resulting in blurring. Unfortunately, the suppression rate of range ambiguities is very limited with typical system parameters, and additional signal processing algorithms are required to achieve equal range sampling in the azimuth direction.

[0006] Some ambiguity suppression methods focus on transmitting diverse waveforms to allow identification and suppression of ambiguities from the return signals, and then suppressing the remaining ambiguities through processing to isolate the unknown return signals. In the following, unless otherwise stated, the term "focusing" is used to refer to statistical or mathematical filtering processes, rather than, for example, optical focusing. An example of filtering is the convolution of the conjugate of the transmitted and received signals.

[0007] The basic idea of ​​waveform diversity is to gain the ability to "mark" or identify the transmitted pulse from which a particular return signal originates. To achieve this, the system needs to be able to transmit signals of different marks and identify the scattered signals accordingly. At least three different waveforms have been proposed in the literature: Up-and-Down Chirp (UDC), Azimuth Phase Coding (APC), and Frequency-Frequency Coding (CF).

[0008] UDC (Up-and-Down Chirp) waveform diversity can be used for nadir suppression and extract high quality SAR images. However, the energy is not suppressed but blurred in the range direction. This can result in range stripes appearing in the image, especially for targets with strong backscattering characteristics. Because the signal is blurred rather than suppressed, the total energy of the unknown signal is not significantly reduced. In fact, considering the total signal power of a given target, the suppression capability of UDC can be as low as 3dB for point targets and 0dB for extended targets.

[0009] To overcome some of these problems of UDC, several post-processing algorithms based on double focusing technique have been proposed in the literature. In these techniques, the raw data is focused according to the unknown regions. Then, the image of the unknown regions is thresholded, the complex data is suppressed, and the higher backscatter is assumed to represent the unknown targets. One drawback of this technique is that useful signals may also be lost. The final step is to focus the raw data back according to the distinct regions by focusing them. However, this algorithm can be computationally intensive, so a post-processing algorithm with less computational complexity is desired.

[0010] Another waveform diversity method is APC (Azimuth Phase Coding), where the phase of each transmitted pulse is alternated to shift the Doppler bandwidth of well-defined target signals out of the processing band. The idea is based on setting the PRF high enough so that well-defined and unknown Doppler bandwidths of the signal are separated. Unfortunately, this results in a narrower swath width and / or reduced azimuth resolution, both of which are undesirable for SAR imaging.

[0011] Cyclic Frequency Hopping (CF) is a method to generate orthogonal waveforms by periodically shifting the frequency of the transmitted pulse. However, in this case, the required rapid frequency hopping introduces practical issues such as rapid power drift, complex hardware implementation, and increased calibration load. In addition, SAR systems may have limited memory to store separate waveforms. For example, the TerraSAR-X satellite can only store up to eight different waveforms from a single acquisition.

[0012] Recently, there have been some efforts to combine UDC and APC to improve nadir suppression performance, but none of these waveforms are designed to address both nadir and range ambiguity suppression in SAR images. Some embodiments of the present invention described below address some of these issues. However, the present disclosure is not limited to addressing these issues, and some of the described embodiments may address other issues as well. Summary of the Invention

[0013] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter.

[0014] Disclosed below is a method of operating a Synthetic Aperture Radar (SAR) to obtain SAR echo data for image formation, the SAR being mounted on a platform that moves relative to the surface of the Earth and pointed at the surface of the Earth, the method including the steps of calculating a nadir ambiguity index relative to the nadir of the platform, determining a frequency sweep direction sequence for successive pulses of a waveform transmitted by the SAR based on the nadir ambiguity index, obtaining a relative phase sequence for the successive pulses of the waveform, and encoding the waveform with the determined frequency sweep direction sequence and relative phase sequence. As explained in more detail below, this encoding with frequency sweep direction and phase can be used to reduce ambiguity in the SAR image.

[0015] Any of the methods described herein may be implemented for operating a satellite already in orbit, and thus may be implemented in the form of a computing system configured to control the operation of the SAR. The computing system may be on-board, for example, a platform carrying the SAR system, or distributed, for example, between the platform and a ground station.

[0016] Also provided herein is a computer-readable medium containing instructions that, when implemented in a computing system forming part of a SAR operational system, cause the system to perform any of the methods described herein.

[0017] Also provided herein is a SAR system configured to transmit successive radio wave pulses to illuminate a target area according to any of the methods described herein.

[0018] Also provided is a pulsed radio waveform transmitted from a SAR system mounted on a platform moving relative to the surface of the Earth, the waveform being encoded with a frequency sweep direction sequence of successive emitted pulses, the frequency sweep direction sequence varying as a function of ambiguity at the nadir of the platform. The frequency sweep direction sequence may, for example, vary as a function of the range from the platform to the nadir. The waveform may be encoded according to any of the methods described herein.

[0019] A SAR system configured to transmit a pulsed waveform is also provided.

[0020] The waveform may be encoded with a relative phase sequence for successive pulses of radiation, which may vary with ambiguity of points in an unknown region other than nadir. The relative phase sequence may vary with range of points other than nadir from the platform.

[0021] In some embodiments of the present invention, a computer readable medium is provided that includes instructions in the form of an algorithm that, when implemented in a computing system that forms part of a satellite operating system, causes the system to perform any of the methods or processes described herein.

[0022] The features of the various aspects and embodiments of the invention may be combined as appropriate and in any combination with any aspect of the invention, as will be apparent to the skilled artisan. Embodiments of the present invention will now be described, by way of example only, with reference to the following drawings, in which: [Brief description of the drawings]

[0023] [Figure 1] 1 is a schematic perspective view of a satellite in orbit above the Earth; [Diagram 2] 1 is a schematic diagram of a satellite operating in space, a target area to be imaged, a nadir point, and several unknown area regions. [Figure 3a] 1 is a plot of range compression data for a clear point target and a point target in an unknown region. [Figure 3b] 13 is a plot of range compression data for a clear point target and an extended target in an unknown region. [Figure 4a] 1 is a flow chart of a method for extracting clear images from SAR data using a double double focusing method. [Figure 4b] 1 is a flow chart of a method for extracting clear images from SAR data using a delta focusing method. [Figure 5a] 13 is a plot of detection points extracted by thresholding the ratio of test cells to background in a focused nadir image. [Figure 5b] 13 is a plot of the sum of the ratios of the test subject cell to the background in each range bin of the in-focus nadir image. [Figure 6a] 10 is a flow chart illustrating an alternative method according to some embodiments of the present invention. [Figure 6b] 10 is a flow chart illustrating another alternative method according to some embodiments of the present invention. [Figure 7] 1 is a flow chart illustrating a method for detecting the nadir in SAR data according to some embodiments of the present invention. [Figure 8a] This SAR image shows a mountainous area with strong nadir echoes, unknown area returns, and strong scatterers. [Figure 8b] This is a SAR image showing the nadir return blurring in the range direction. [Figure 8c] This is a post-processed SAR image with the nadir completely suppressed. [Figure 8d] This is a post-processed SAR image with both nadir and range ambiguities completely suppressed. [Figure 9a] This is a graph showing nadir detection from SAR images collected with waveform diversity. [Figure 9b] An unidentified image of SAR data collected with waveform diversity. [Figure 9c] This is a graph showing ambiguity detection from an area where the range is unknown in a SAR image collected with waveform diversity. [Figure 10a] This SAR image was collected using waveform diversity and range striping. [Figure 10b] 10b is a graph comparing the total energy in range and azimuth angle for the central portion of FIG. 10a with the default image. [Figure 10c] A graph comparing the total energy in range versus azimuth angle for the right section of Figure 10a with the default image. [Figure 11a] SAR images with high incidence angles and high pulse repetition rates show ambiguities arising from unknown regions. [Figure 11b] The uncleared SAR image in Figure 11a does not suppress range ambiguity. [Figure 11c] The image in Figure 11a is an ambiguity-free SAR image in which range ambiguity is not suppressed. [Figure 11d] FIG. 11b is a comparative graph of the total energy in range and azimuth compared to the default image of FIG. 11a. Common reference numbers are used throughout the figures to denote like features. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] Embodiments of the present invention are described below by way of example only. These examples represent the best ways of practicing the invention currently known to applicant, but are not the only ways in which this may be accomplished.

[0025] Some embodiments of the present invention provide systems and methods for operating a Synthetic Aperture Radar (SAR) system to obtain images of an area on the Earth. For this purpose, the SAR may be mounted on a platform that travels relative to the surface of the Earth. For example, SAR systems are commonly mounted on satellites. However, the methods and systems described herein are not limited to space and may be performed using aircraft or other suitable platforms.

[0026] In the following description, the term clear signal is used to refer to a signal acquired from a target image region, also referred to herein as the "desired" image area. Unknown signal is used to refer to a signal acquired from an unknown region outside the desired imaging area region. Unknown signals may be mixed with clear signals and may cause ambiguity in the resulting image. Ultimately, it is desired to acquire an image of the clear region (target image area) with as few ambiguities as possible. According to some of the methods described in this disclosure, this may include acquiring an image of the unknown region, referred to in this disclosure as an unknown image. This refers to the SAR raw data that is focused with the parameters of the unknown region to acquire an image of that region. The unknown image itself is also valuable because it can provide an additional image of another area at little additional cost. Similarly, the nadir signal refers to a signal returned from a point directly below the satellite. The nadir is a special case of an unknown signal, and an image of the nadir region can also be created in the process of acquiring an image of the clear region.

[0027] FIG. 1 is a perspective view of a satellite 100 in orbit above the Earth as an example of a platform that may be used with the methods and systems described herein. The satellite includes a body 110 and "wings" 160. One or more antenna elements may be attached to the satellite's wings. The satellite 100 further includes a propulsion system 190, which is shown attached to the body 110 on the opposite side to the solar panels 150. The propulsion system generally includes thrusters 205, 210, 215, 220 that are operated to maintain the satellite 100 in a particular orbit. For example, the thrusters 205, 210, 215, 220 may be used to propel the satellite 100 in a particular direction relative to the Earth. As noted elsewhere herein, the methods described herein are particularly well suited for implementation in conjunction with a SAR onboard a satellite, but are not limited thereto.

[0028] The body 110 houses a computing system and control devices, as is well known to those skilled in the art. Also shown generally in Figure 1 is a ground station computing system 195 configured to post-process received SAR data. Some of the steps of the methods described herein may be implemented in the ground station computing system.

[0029] As known to those skilled in the art, it periodically alternates between a transmit mode in which pulses of radiation are directed toward the Earth's surface, and a receive mode in which radiation reflected from the Earth's surface is received.

[0030] As is known in the art, a SAR image is created by transmitting successive pulses of radio waves to "illuminate" a target scene, and receiving and recording the echoes of each pulse. The pulses can be transmitted and the echoes received by a single beam-forming antenna. When a SAR is mounted on a mobile platform, such as a satellite, and moves relative to the target, the position of the antenna relative to the target changes over time, causing the frequency of the received signal to change due to the Doppler effect. Signal processing of the successively recorded radar echoes allows the recordings from multiple antenna positions to be combined to form a Synthetic Aperture Antenna (SAR) to produce a high-resolution image.

[0031] The area imaged by a SAR is called its footprint. The direction along the SAR's flight direction is usually called the azimuth or along-track direction. The direction across the flight direction is usually called the range, elevation, or cross-track direction. The direction opposite the flight direction corresponds to the astern azimuth.

[0032] Referring to FIG. 2, a satellite 100 is shown moving along an azimuth flight path 200. The satellite is operating in a "side scan" mode, where the area to be imaged is not directly below the satellite, but to the side of the satellite's flight path. This is typical for SAR satellites, where bright specular reflections from objects directly below the satellite make it difficult to form an image of the nadir area. The shaded area 201 represents the area to be imaged (the clear area). Point 202 is the nadir point, i.e., the point directly below the satellite. Areas 204, 205, and 206 are unknown areas where radar reflections from the lobes of the radar beam may cause ambiguity in the SAR image. Point 203 is a point in the unknown area 204 adjacent to the clear area 201 where an image is desired. FIG. 2 shows the satellite 100 operating in a conventional strip map mode, where the SAR beam is swept along one swath along the ground as the satellite moves in orbit. However, examples according to the present disclosure are equally applicable to any SAR mode, such as spotlight mode, ScanSAR (Scanning Synthetic Aperture Radar) mode, and TOPSAR (Progressive Scanning SAR Topography) mode. The collected SAR data typically consists of echo signals from clear areas, unknown areas, and nadir, which correspond to clear images, unknown images, and nadir images, respectively.

[0033] Examples according to the present disclosure describe improved waveform sequences and the use of waveform diversity, in which up / down chirp waveform coding (UDC) and azimuth phase encoding (APC) are applied together to suppress both nadir returns and ambiguities arising from zones adjacent to the desired imaging area to produce improved SAR images.

[0034] With UDC, rather than transmitting radar pulses at a single frequency, the frequency of each pulse is swept up or down over the duration of the pulse, creating either an "up-chirp" or a "down-chirp." The signal transmitted by satellite 100, neglecting initial phase and power terms, can be written as:

number

[0035]

number

[0036] Here, st u and st d represent the transmitted signal with up- and down-chirp, respectively, where α is the chirp rate, t is the fast time (or time along the range direction), Tp is the pulse width, and red is a rectangular function.

[0037] The return echoes carry either an up or down "signature" to indicate whether the return is from a transmit pulse with an up chirp or a down chirp. For example, an up chirp is transmitted into the imaging area of ​​interest. Given the distance to the imaging area and the speed of light, the time at which the return echo is expected from that region is known. However, there may be returns from closer or more distant areas mixed in with the returns from the desired imaging area. For example, the nadir is much closer, so a return from a later transmitted pulse may appear along with a pulse that has traveled to the imaging area and returned. This is an example of ambiguity. If the sequence of up and down chirps is carefully chosen so that, for example, all of the clear image returns at a particular time are up chirps and the nadir returns are down chirps, it becomes possible to filter the nadir returns with a tailored filter.

[0038] The combined filter output of the down-chirp with the up-chirp reference signal is:

[0039]

number

[0040] The reverse case (combined filter output for up-chirp and reference signal for down-chirp) has the opposite phase sign in the index function. Thus, focusing according to a well-defined reference signal will result in the unknown signal being out of focus, with a pulse (2Tp) twice as wide and a chirp rate halved (α / 2) compared to the transmitted signals (1) and (2). Mathematically, focusing here is the convolution of the conjugates of the transmitted and received signals. Note that although chirps or pulses with either up or down linear frequency sweeps are described as examples, other types of frequency sweeps can be used as well, according to the current disclosure. Other examples of frequency changes that can be used to identify pulses include, but are not limited to, nonlinear frequency sweeps, triangular frequency sweeps, parabolic frequency sweeps, or periodic frequency sweeps.

[0041] Figure 3a shows a plot of the simulated combined filter output comparing a clear point target with an unknown point target, where the transmitted waveform is UDC coded. Figure 3b shows the same clear point target output with an unknown extended target (an 80 meter long target with a point target at each range sampling interval). The simulation parameters are shown in Table 1 below. It can be seen that the UDC waveform is able to suppress the point target by blurring its energy. However, if the backscatter of the target is strong enough, it is expected that range stripes will appear in the image. For the extended target, it can be seen from 3b that depending on the size of the target, UDC may not help significantly in reducing the unknown signal. To address this issue, further modifications to the waveform are proposed, as explained below.

[0042] [Table 1]

[0043] In an example according to the present disclosure, UDC is combined with azimuth phase coding (APC) to more effectively reduce ambiguities arising from nadir and unknown regions close to the desired imaging area, especially those arising from extended targets as mentioned above. The basic idea of ​​APC is to shift the Doppler spectrum of ambiguities arising from range unknown regions so that they can be mitigated during SAR focusing operations. However, applying APC alone has limitations such as narrow swath width and reduced azimuth resolution.

[0044] The following describes a method for calculating the platform nadir ambiguity index and determining a frequency sweep direction sequence based on the nadir ambiguity index. The waveform is then encoded using the determined frequency sweep direction sequence and the relative phase sequence (APC) for successive pulses of the waveform.

[0045] The nadir ambiguity index is a positive or negative integer. In other words, different frequency sweep direction sequences or UDC sequences are applied based on the first ambiguity index, which is the nadir return ambiguity index.

[0046] Furthermore, a different relative phase sequence or APC sequence can be applied based on a second ambiguity index, for example the ambiguity index of the unknown region (other than nadir) with the strongest reflection. Since the unknown region with ambiguity index equal to 1 is usually the strongest reflection, this can be used as the second ambiguity index.

[0047] This method of creating waveform diversity can be used to reduce ambiguities from both nadir reflections and unknown regions close to the desired imaging area. If the nadir region is outside the range of the radar echo return, both the UDC and APC portions of the waveform can be selected based on the ambiguity index of the unknown region where the strongest radar echo is expected to be (referred to herein as the range ambiguity index).

[0048] Determining the frequency sweep direction sequence may include selecting a frequency sweep direction sequence from a plurality of frequency sweep direction sequences.

[0049] The ambiguity index for the nadir or other region may depend on one or more of the slant distance, the estimated distance from the platform to the unknown point, and the pulse repetition rate of the waveform.

[0050] The ambiguity index for an unknown point assuming a flat Earth can be expressed as:

[0051]

number

[0052] The ambiguity index can be calculated for any point within the nadir and other unknown regions. Referring to FIG. 2, line 210 represents the distance to the far field of the imaged area (area 201), which in this example is R. Point 203 is a point within the unknown zone 204 that is outside the imaged area 201. The R of point 203n is the distance represented by line 211. In the example, point 203 has an ambiguity index of 1. In fact, all points contained in unknown area 204 will have an ambiguity index of 1. The ambiguity index indicates the order of the range ambiguities. The strongest ambiguity is usually the ambiguity arising from nadir point 202. Since unknown area 203 is the closest zone to clear area 201, a point with ambiguity index 1 will most likely cause the next strongest ambiguity signal (although this is not always the case). In this example, points in unknown area 205 will have an ambiguity index of -1. Points in unknown area 206 will have an ambiguity index of 2. For nadir point 202, the estimated distance R n is simply the height of the satellite above the ground, as shown by the distance represented by line 212. In what follows, the symbol N nadir is used to denote the nadir ambiguity index, and N range is used to indicate the ambiguity index of points in other unknown regions. The ambiguity index of the nadir point 202 depends on the shape of the scene, the distance to the target area being imaged represented by line 210, and the distance of the nadir point 202 from the satellite 100 (which corresponds to the height of the satellite above the ground).

[0053] Note that N at a particular point amb , depends on the location of the target area being imaged and may vary from image acquisition to image acquisition. For example, if unknown zone 206 is actually the target area being imaged, then the ambiguity index for nadir point 202 will be lower than in the example where area 201 is the target area being imaged. The ambiguity index for a point at a certain distance from the satellite may change multiple times during one orbit, since the satellite may be tasked with imaging areas closer or further from the flight path 200 during different parts of the orbit. Intuitively, N ambcan be thought of as indicating the spatial order of the unknown and clear regions. The farther an unknown region is from a clear region, the greater the N amb becomes higher. R and R n It is understood that the value of also varies with the satellite configuration and mission plan. For example, the antenna elevation pattern may have a greater effect on the received signal power than the range to the target. Thus, as mentioned above, the strongest ambiguities from unknown regions other than nadir will typically be the range ambiguity index N range = 1. In this region, the antenna gain is higher than in the other unknown regions, even though some of the other unknown regions are closer to the SAR platform. The ambiguities from the unknown regions are mainly N range = 1, in some embodiments of the present invention, a fixed range ambiguity index (N range >=1) and a varying nadir ambiguity index N nadir In the latter case, the waveform diversity is set according to R in Eq. n is the estimated distance to the nadir.

[0054] As shown in the example below, when a waveform is coded with both UDC and APC, both nadir reflections and reflections from other unknown regions can be suppressed. Nadir scatter is a bright target that falls within a few pixels in the SAR image. As a result, the nadir can be defined as a point target (in the range direction) and this can be effectively suppressed using UDC. The remaining ambiguity from the unknown range regions can be suppressed with APC.

[0055] In Table 2, three different waveform sequences combining UDC and APC are nadir (1st column) and odd N range(column 2). In these sequences, the UDC sequence is defined to suppress ambiguity at the nadir, and the APC is defined to suppress ambiguity from regions where the range is unknown. The ambiguity index is limited to 5, but can easily be increased for the same reasons.

[0056] [Table 2]

[0057] For example, N nadir is calculated to be 4. This means that the received signal is shifted by 4 pulses with respect to the transmitted signal. In this case, the nadir suppression works well because all the transmitted and received pulses have mismatched chirp directions (see Table 3).

[0058] [Table 3]

[0059] This means that nadir can be suppressed relatively easily. For unknown range regions, the strongest reflections will typically occur in the regions closest to the imaged region and the satellite, i.e., the unknown range regions with a range ambiguity index of 1. For a range ambiguity index of 1, all received pulses from the unknown regions of most interest are shifted by 1 relative to the transmitted pulse as follows:

[0060] [Table 4]

[0061] Thus, for the received range unknown signal, only 2 out of 8 pulses (U and D, ignoring the phase (π) coding for now) show mismatch with the transmitted signal, and 6 pulses (U and D) are in agreement. For this reason, in the example according to the present disclosure, the waveform is further coded with Azimuth Phase Coding (or APC) by adding a phase shift of 0 or π to help mitigate ambiguities from range ambiguity regions. The main idea of ​​APC is to shift the Doppler spectrum of the range ambiguities so that they are mitigated during the SAR focusing operation. To shift the Doppler spectrum by PRF (Pulse Repetition Frequency) / 2, 0,π,0,π,0,π,0,π,... phase differences are needed between the transmitted and received pulses. This means that N range When N is odd, this can be achieved if the transmitted up-and-down chirps are further modulated with 0, 0, π, π, 0 0, π π,... phase encoding (see Table 4 above). When considering phase, there is a mismatch in 6 out of 8, allowing post-processing to further identify and remove signals from the unknown odd range region. range If N is even and equal to 2, the transmit pulse can be modulated using APC to 0,0,0,π,0,0,0,π.... range If N is equal to 4, the pulse sequence can be modulated to 0,0,0,0,0π,0.π. So, in this example, N nadir Define the UDC pattern of the waveform using N range is used to define the APC pattern of the waveform. The combined waveform allows ambiguity suppression from the nadir and from unknown odd or even regions.

[0062] The waveform sequences are not limited to those mentioned above. Other sequences are possible. For example, in the case of up / down chirp (UDC) directional waveform coding, other frequency directional sequences are possible, such as: ●N nadir If is odd, the chirp direction sequence will be "UDUDUDUD...." or "DUDUDUDU...". ●N nadir If =2, the chirp direction sequence will be "UUDDUUDD...." or "DDUUDDUU...". ●N nadir If =4, the chirp direction sequence will be "UUUUDDDD...." or "DDDDUUUU...".

[0063] Here, "U" is for "up", "D" for "down" chirp modulation, and "D" for "down chirp modulation". The higher even numbers can be ignored since the power of these ambiguities is usually insignificant. Thus, the determination of the frequency sweep direction sequence or UDC may involve selecting a sequence from multiple possible sequences depending on the nadir ambiguity index.

[0064] In general, for phase waveform encoding (APC), the phase sequence can be determined by the following equation:

[0065]

number

[0066] Here, φ k is the phase of the kth pulse. Note that for the first Nabm phase, the starting phase of the waveform can be selected from 0 or π. For example, ●N range If is odd, the phase coding sequence can be selected as either: o '0,0,π,π,0,0,π,π...', o 'π,π,0,0,π,π,0,0...' ●N range If is 2, the phase coding sequence can be selected as either: o '0,0,0,π,0,0,0,π...' and shifted versions 'π.0,0,0,π,0,0,0,0...', '0π.0,0,0,π,0,0,0, and '0,0,π.0,0,0,π,0, o 'π,π,π,0,π,π,π,0...' and shifted versions When N range is 4, the phase coding sequence can be selected as one of the following: o '0,0,0,0,0,π,0,π' and shifted versions o '0,0,π,π,0,π,π,0' and shifted versions o '0,π,π,π,0,0,π,0' and shifted versions o 'π,π,π,π,π,π,0,π,0' and shifted versions

[0067] Thus, to account for range ambiguity indices other than 1, we see that the relative phase sequence can be determined based on whether the range ambiguity index is odd, 2, or 4, according to the example. One frequency sweep direction sequence can be used for all instances where N nadir is odd. Also, a larger set of frequency sweep direction sequences can be utilized for different even values ​​of N nadir. Although shifts of 0 and π are shown, the pulses do not necessarily need to be shifted by π, other values ​​such as -π / 2 and π / 2 are possible. Shifts less than π can also be performed, but the performance of suppressing ambiguities from regions where the range is unknown may not be as good.

[0068] Examples of U and D pulses have already been given in equations (1) and (2). For completeness, the definitions of U+π and D+π can be expressed as follows:

[0069]

number

[0070]

number

[0071] After the SAR data is collected, post-processing can be performed to suppress nadir and range ambiguities, for example by combining UDC and APC with frequency sweep direction sequences and / or relative phase sequences selected based on the ambiguity indicators.

[0072] The received raw echo data corresponds to clear regions, unknown regions, and nadir. Processing may include extracting the nadir and unknown data with a double focusing process.

[0073] Figures 4a and 4b show examples of two different post-processing algorithm flows. These figures show a post-processing method that uses double focusing to remove nadir ambiguities and ambiguities arising from unknown range regions. In general, the SAR data is first processed to detect and suppress nadir, and then the nadir plot is extracted. The data is then processed to detect and suppress the unknown images and extract the unknown range images. Finally, the SAR images of the clear regions are extracted. After this processing, the nadir ambiguities and ambiguities from other unknown range regions are essentially eliminated or significantly reduced.

[0074] The methods described herein are not limited to the order of operations shown, in particular, extraction of the missing image may occur before extraction of the nadir image, or vice versa.

[0075] Firstly, focusing on Fig. 4a, the input of the algorithm is the SAR raw data, which corresponds to data from nadir, unknown area, and clear area. The first operation 410 focuses the SAR data according to the nadir echo to obtain a focused image of the nadir. There are two major characteristics of the nadir in the image. First, the transmitted signal is reflected directly from the object at the nadir, resulting in high signal power. Second, the range deviates only within a narrow region in azimuth time, and is mostly within the same range bin in consecutive azimuth bins. In operation 412, the nadir is detected and suppressed. To detect the nadir, a range sliding window is applied to extract the ratio of the cell under test to the background. The result is shown in Fig. 5a, which shows the detection plot in the focused image of the nadir. This ratio is summed for each range bin to detect the nadir as shown in Fig. 5b. It can be clearly seen that the nadir range bin is between 6200-6500, and the plot outside this region may be useful signals.

[0076] Nadir detection has two advantages: first, it is less likely to suppress useful signals, and second, the satellite's height above ground is measured and can be used for radar altimetry purposes. Nadir ambiguities are then suppressed by dividing the data by the time-bandwidth product. Further, a nadir plot is extracted in operation 414.

[0077] In operation 416, the SAR data is defocused to extract the raw SAR data (without nadir echo). Defocusing is achieved by applying the conjugate of the filter used to focus the raw data according to the nadir parameters. Successive application of focusing and defocusing preserves phase and amplitude unless suppression is performed. The main challenge with this implementation is to preserve the desired signal that is not affected by nadir. To achieve this target, focusing and defocusing are implemented such that the full bandwidth of the signal is processed. Another challenge is to detect the nadir so that only the features affected by nadir are suppressed. Focusing includes range compression (RC), range upper limit migration correction (RCMC), and azimuth compression (AC). In this context, RC uses joint filtering and data with the reference pulse number shifted with the range ambiguity index relative to the transmitted pulse. RCMC is implemented as a phase multiplication. The reference function for AC is estimated with the corresponding range.

[0078] In operation 418, the SAR data is focused with a filter tuned to echoes with unknown range. In operation 420, range ambiguities are detected and suppressed. Detecting range ambiguities is a problem with many facets. The most important characteristic of range ambiguities is that the power of the signal is high enough that even an unfocused image of the target appears in a clear image. In this case, the Order Statistics Constant False Alarm Rate (or OSCFAR) method [1] can address the detection problem. However, OSCFAR can produce false alarms in areas dominated by clear targets. The Cell Averaging (CA) CFAR method [2] can reduce false alarms, but with the tradeoff of increasing missed detections. In some embodiments of the invention, the OSCFAR method is applied. The next step is the CACFAR method. The energy of the clear target is blurred in the range direction while focusing on the unknown target. As a result, instead of estimating the background in a ring, the background is estimated in the range direction, reducing false alarms.

[0079] In operation 422, the unknown image is extracted from the SAR data. The SAR data is then refocused in operation 424 and then focused according to the range distinct echoes in step 426 (using a filter tuned to the distinct echo signal) to extract a clear image from the SAR data with no nadir and range ambiguities. As before, defocusing is achieved by applying the conjugate of the filter used to focus the raw data according to the unknown region parameters. Successive application of focusing and defocusing preserves phase and amplitude unless suppression is performed.

[0080] FIG. 4b shows an alternative embodiment of the above method. Instead of double focusing, which includes defocusing and refocusing steps, the method described in FIG. 4b replaces these operations with a single focusing operation called "delta focusing". In other words, in operation 413, the SAR data (without upper limit) is delta focused according to the unknown echoes, instead of double focusing. Similarly, in operation 421, the SAR data is delta focused according to the clear echoes, instead of double focusing, to extract a clear image without ambiguity. The basic idea is that after focusing the SAR raw data according to the nadir parameters (operation 410 for both methods), the data is unfocused SAR data with different configurations for targets in unknown and / or clear areas, which can be focused with appropriate parameters to extract the unknown and / or clear SAR images. As a result, the computational load is approximately halved when using delta focusing. Waveforms encoded with UDC and APC are compatible with both post-processing methods (ie, double focusing and delta focusing).

[0081] 6a is a flow chart illustrating an alternative method according to some embodiments of the present invention, where the raw SAR data is first focused according to distinct echo signals in operation 510. Distinct images in the SAR are detected and suppressed in operation 512. The SAR data is then defocused (no distinct data) in operation 514, and then refocused according to unknown echo signals in operation 516. This allows the unknown images to be extracted from the SAR data.

[0082] FIG. 6b is a flow chart illustrating another alternative method according to some embodiments of the present invention. Here, the raw SAR data is first processed to remove the nadir from the SAR data and obtain a nadir plot (operations 502-506), and then defocused in operation 508. Operations 510-516, identical to those shown in FIG. 6a, are then performed to obtain an unknown image from the SAR data, but without the nadir. As before, in another embodiment, the defocusing 508 and focusing 510 operations of FIG. 6b can be replaced by a single delta focusing operation for computational efficiency. The ability to extract images of unknown regions in both processes 6a and 6b is an additional unexpected advantage of the disclosed method. Images of unknown regions provide additional images of a larger area that are useful to end users of the SAR data.

[0083] FIG. 7 is a flow chart showing a method for detecting nadir in SAR data using CACFAR. The first task is to determine the number of guard cells and background cells and the desired false alarm rate. The guard cells are placed adjacent to the cell under test (CUT), before and after it. The purpose of these guard cells is to prevent signal (nadir) components from leaking into the background cells and affecting the accuracy of the noise estimation. In some embodiments of the present invention, the number of guard cells and background cells are set to 5 and 15, respectively, and the desired false alarm rate is set to 0.001. However, it can be understood that these values ​​may vary depending on the specific requirements of the method. After focusing the SAR data according to nadir (operation 410 in FIG. 4a and 4b), a signal to background average ratio "R" is added for each range index in operation 610. In operation 612, the nadir peak is detected, and in operation 614, the nadir width is detected. The nadir start (N1) and end (N2) indexes relative to the nadir peak index are found using the function shown in Equation 7.

[0084]

number

[0085] Furthermore, as mentioned above, both OSCFAR and CACFAR are applied to detect range ambiguities. In some embodiments of the present invention, for OSCFAR, the desired false alarm rate is set to 0.001 and the noise power is estimated based on the selection of the Nth largest cell, where N is 3 / 4 times the number of SAR data samples. For CACFAR, which is then applied, the desired false alarm rate is the same as for OSCFAR, but the number of guard cells is set to 1000 and the number of background cells is set to N チャープ is set to -1000, where N チャープ is the pulse width x sampling rate.

[0086] The algorithm of the above method is derived below for the low squint case, but can be extended to the more general case. The baseband received signal of a well-defined target can be approximated as follows:

[0087]

number

[0088] Here, ω r and ωω a represent the antenna pattern in azimuth and elevation, respectively. A0 is the signal amplitude, η is the slow (or azimuth) time, and K a is the number of azimuth pulses, R(η) is the range to the target, R0 is the minimum range to the target, and X is the wavelength.

[0089] A first operation 410 of focusing according to the unknown pulse number halves the number of pulses in the clear signal while doubling the pulse width. After range compression and azimuth Fourier transformation, the range Doppler data can be expressed as:

[0090]

number

[0091] The range cell shift (RCM) term within the range envelope is expressed as a function of the nadir distance.

[0092]

number

[0093] The RCM can be corrected in the range-Fourier domain by linear phase multiplication.

[0094]

number

[0095] After RCMC, the signal is written as:

[0096]

number

[0097] The final step is azimuth compression to nadir range, where the number of azimuth pulses can be expressed as:

[0098]

number

[0099] Finally, the extracted image of the clear target after azimuth compression can be written as:

[0100]

number

[0101] As a result, the signals after being focused according to the parameters corresponding to the unknown region are SAR raw data that can be considered as collected with a different configuration, and there is no need to defocus and then refocus the signals, but instead can be directly focused to extract a clear image.

[0102] To validate the proposed range ambiguity suppression method, a series of SAR acquisitions were performed with the ICEYEOy SAR satellite in Espoo, Finland. The imaged scene contains a calm water surface expected to coincide with strong nadir echoes, unknown area reflections, and mountainous areas with strong scatterers, as shown in Figure 8a. The SAR image shown in Figure 8a was collected with waveform diversity using a combination of UDC and APC as described in the current disclosure, but no post-processing has yet been performed to remove ambiguities from the nadir and other unknown areas. The mission planning was performed to acquire a nadir line approximately in the center of the swath. The incidence angle was selected to be 37.3 degrees to ensure the observation of exaggerated ambiguities from range unknown areas. In the image shown in Figure 8a, it is clear that clear signals, nadir, and unknown signals are all contained within the SAR data. In this example, the ambiguity index for nadir is 5.

[0103] Figure 8b shows the same SAR image after processing to suppress ambiguities from regions of unknown nadir and range. We see that the nadir and range ambiguities are largely suppressed. However, there are range fringes in the center of the image consistent with nadir and fringes on the right side of the image consistent with strong range ambiguity reflections.

[0104] Further post-processing is applied to suppress the remaining range fringes. First, the nadir is detected, as shown in Figure 9a. The estimated nadir is 570005.8m, which is very close to the actual measurement. Strong scatterers labeled as nadir are suppressed by simply splitting the sample into time-bandwidth products. Then, we focus on the raw data without the nadir to extract a clear image. The results of both waveform diversity and post-processing are shown in Figure 8c. It was found that the range fringes in the center of the image are associated with the nadir and are completely suppressed.

[0105] The next operation is to detect and suppress range ambiguities. The unknown image is shown in Figure 9b, and the detection of range ambiguities is shown in Figure 9c. Comparing the detection results with the strong scatterers in the unknown image, we find that the algorithm is very good at detecting targets in the unknown range area, while it does not detect scatterers in the clear area as targets. Another observation is that even though the nadir was successfully suppressed in the previous operation, there is still a nadir portion that does not need to be suppressed. This part can be filtered using the nadir information extracted in the previous operation.

[0106] After detecting and suppressing range ambiguities, the SAR image is extracted and shown in Figure 8d. Qualitatively, it can be seen that the ambiguities arising from the nadir and range unknown regions are successfully removed. Unfortunately, quantifying the performance of range ambiguity suppression is not entirely straightforward. Figures 10a, 10b, and 10c show a comparison. Figure 10a displays a SAR image with range stripes. The energy of unknown targets is blurred in the range direction. Thus, the sum of the energy in the range direction is an indicator of the performance of the algorithm. Figures 10b and 10c show the graphs of range sum against nadir for area 1 (area surrounded by long dashed line and dots) in Figure 10a and range ambiguity (versus azimuth) for area 2 (area surrounded by short dashed line and dots) in Figure 10a, respectively, compared with the graph of range sum (versus azimuth) for the default image. The default image is an image acquired using waveform diversity, but prior to the processing step of suppressing nadir and range ambiguities using waveform diversity. After processing, it is observed that the nadir ambiguities are quantitatively and qualitatively suppressed in regions where the desired signal is dominated by the nadir return. In Figure 10c, the performance of the range ambiguity suppression is shown. Qualitatively, the range ambiguities appear to be significantly suppressed, however, the background reflections in the range unknown region are not low enough to quantitatively verify the suppression performance of more than 4 dB using this method.

[0107] Another experiment was designed with a much higher incidence angle and PRF to obtain more performance data. In this case, the nadir is not within the swath, but the range ambiguities are very strong, as shown in Figures 11a, 11b, and 11c. Clearly, the default image shown in Figure 11a is strongly affected by the range ambiguities. The unclear image shown in Figure 11b proves that the anomalies in the default image are the result of the range ambiguities. As can be seen qualitatively in Figure 11c, the range ambiguities in the desired image are dramatically suppressed. To quantify the power, the sum of the ranges in the area is compared to the default in Figure 11d. While the power is indeed suppressed, the background reflectivity is again very high, preventing the suppression ratio from being quantified at more than 8 dB, even though the method clearly works to remove the range ambiguities. Finally, strong targets in a clear area may also be suppressed as a result of false alarms.

[0108] In some embodiments of the present invention, a new nadir and range ambiguity suppression method is proposed. The method is based on using a waveform diversity based on UDC combined with APC and a double dual focusing technique that includes detection of nadir and range ambiguities. It is shown that it is possible to not only preserve the desired signal while suppressing nadir, but also to detect nadir in applications that require satellite altitude, altimetry, etc. Images with unknown range are also presented to prove that anomalies in non-unknown images are the result of range ambiguities. The method is demonstrated and verified by real SAR data.

[0109] The above describes a satellite suitable for performing any of the operational methods described herein. In the case of a satellite or other platform already in orbit, the methods described herein can be implemented by suitable control of the satellite, such as from the ground, using a suitable computing system. In other words, the SAR operates from the ground and some of the methods described herein may be implemented in software. Thus, the present invention may be provided with a computing readable medium including instructions that, when implemented by a processor in a computing system, cause the computing system to operate the SAR according to any of the methods described herein.

[0110] Some embodiments of the invention described herein provide a ground station computing system configured to operate a SAR according to any of the methods described herein.

[0111] In any of the embodiments of the present invention, the satellite may travel in low Earth orbit or be configured to travel in low Earth orbit.

[0112] Any of the computing systems described herein may be combined into a single computing system with multiple functions. Similarly, the functionality of any computing system described herein may be distributed across multiple computing systems.

[0113] Some operations of the methods described herein may be performed by software, for example in a machine-readable form, for example in the form of a computer program including computer program code. Thus, some aspects of the present invention provide a medium readable by a computing system that, when implemented in a computing system, causes the system to perform some or all of the operations of any of the methods of the present invention. The computer-readable medium may be in a transitory or tangible (or non-transitory) form, such as a storage medium, such as a disk, thumb drive, memory card, etc. The software may be adapted to run on a parallel or serial processor such that the method steps can be performed in any suitable order or simultaneously.

[0114] This application recognizes that firmware and software are separately tradable commodities of value. It is designed to include software that operates or controls on "dumb" or standard hardware to perform a desired function. It is also intended to include software that "describes" or defines the configuration of hardware, such as HDL (Hardware Description Language) software for designing silicon chips or configuring general purpose programmable chips to perform a desired function.

[0115] The above embodiments are largely automated: in some instances, a user or operator of the system may manually direct some of the method actions to be performed.

[0116] In embodiments of the present invention, the system may be implemented as any form of computing and / or electronic system, as described elsewhere herein. For example, a ground station may comprise such a computing and / or electronic system. A device such as herein may comprise one or more processors, which may be microprocessors, controllers, or any other suitable type of processor, for processing computer-executable instructions for controlling the operation of the device to collect and record routing information. In some examples, for example when using a system-on-chip architecture, the processor may include one or more fixed function blocks (also called accelerators) that implement parts of the method in hardware (rather than in software or firmware). Platform software, including an operating system or any other suitable platform software, may be provided in the computing-based device to enable the application software to run on the device.

[0117] As used herein, the term "computing system" is used to refer to any device having processing capability capable of executing instructions. Those skilled in the art will appreciate that such processing capability may be incorporated into many different devices, and thus the term "computing system" includes PCs, servers, smart cell phones, personal digital assistants, and many other devices.

[0118] It should be understood that the benefits and advantages described above may relate to one embodiment or to several embodiments, and the embodiments are not limited to those that solve any or all of the problems mentioned or that have the benefits and advantages mentioned.

[0119] Any reference to an "item" or "piece" refers to one or more of those items unless otherwise specified. As used herein, the term "comprising" means including the specified method steps or operations or elements, but such steps or operations or elements do not constitute an exclusive list and the method or apparatus may include additional steps or operations or elements.

[0120] Further, to the extent the term "comprising" is used in the detailed description or within the scope of the claims, it is intended that the term "comprising" have the same inclusiveness as the term "comprising," as the term "comprising" is interpreted as a transitional term within the scope of the claims.

[0121] The accompanying drawings illustrate exemplary methodologies. Although the methodologies are shown and described as a series of operations performed in a particular order, it is understood and should be understood that the methodologies are not limited by the order. For example, some operations may occur in a different order than described herein. Also, some actions may occur simultaneously with other actions. Furthermore, in some cases, not all operations may be required to implement the methodologies described herein.

[0122] Although the ordering of steps or actions of the methods described herein is exemplary, steps or actions may be performed in any suitable order, or simultaneously where appropriate. Further, steps or actions may be added or substituted, or individual steps or actions may be deleted, from any method without departing from the scope of the subject matter described herein. Aspects of any of the above embodiments may be combined with aspects of any of the other embodiments described above to form further embodiments.

[0123] The above description of the preferred embodiment is given by way of example only, and it should be understood that various modifications may be made by those skilled in the art. The above includes one or more exemplary embodiments. Of course, it is not possible to describe each possible modification and modification of the above device or method in order to describe the above aspects, but those skilled in the art will recognize that many further modifications and arrangements of the various aspects are possible. Therefore, the described aspects are intended to include all such changes, modifications, and variations that fall within the scope of the appended claims. List of references [1]Herman Rohling, “Radar CFAR Thresholding in Clutter and Multiple Target Situations,” IEEE Transactions on Aerospace and Electronic Systems, vol. 19, pp. 608-621, 1983. [2]X. Wen, X. Qiu,B.Han, C.Ding, B. Lei and Q. Chen, “A Range Ambiguity Suppression Processing Method for Spaceborne SAR with Up and Down Chirp Modulation”, Sensors 2018, 18, 1454.https: / / doi.org / 10.3390 / s18051454

Claims

1. 1. A method of operating a synthetic aperture radar (SAR) to obtain SAR echo data for forming an image, the SAR being mounted on a platform that moves relative to the surface of the Earth and is aimed at the surface of the Earth, the method comprising: calculating a nadir ambiguity index relative to the platform nadir prior to data acquisition from the target area to be imaged, the nadir ambiguity index being dependent on one or more of the oblique distance to the far field of the target area to be imaged, the estimated distance from the platform to the nadir, and the pulse repetition rate of the waveform; selecting a frequency sweep direction sequence from a plurality of frequency sweep direction sequences for successive pulses of a waveform transmitted to a target region imaged by the SAR based on the nadir ambiguity index; selecting a relative phase sequence for successive pulses of the waveform based on a range ambiguity index, the range ambiguity index depending on one or more of a slant distance to a far field of a target area to be imaged, an estimated distance from the platform to the point of uncertainty, and a pulse repetition rate of the waveform; and encoding a waveform using the selected frequency sweep direction sequence and relative phase sequence.

2. 2. The method of claim 1, wherein the same frequency sweep direction sequence is selected for all instances where the nadir ambiguity index is odd, and wherein a plurality of different frequency sweep direction sequences are selected for different even values ​​of the nadir ambiguity index.

3. 2. The method of claim 1, wherein the step of selecting relative phase sequences for successive pulses of a waveform comprises calculating range ambiguity indices for points in an unknown region other than nadir, and determining the relative phase sequences of the waveform based on the calculated range ambiguity indices.

4. The method of claim 3 , wherein the determination of the relative phase sequence depends on whether the range ambiguity index is odd or even.

5. 10. The method of claim 1, comprising processing received raw echo SAR data according to an unknown image and a clear image, the unknown image being a non-nadir image.

6. The method of claim 5 further comprising focusing the SAR image data using a filter aligned with the nadir echo.

7. detecting the nadir of the SAR data; and suppressing the nadir from the SAR data.

8. extracting a nadir from the SAR data; The method of claim 7 further comprising the step of: dual focusing the SAR data according to the missing echo signals.

9. The step of doubly focusing includes: defocusing using the conjugate of a filter tuned to the nadir echo signal; focusing the SAR data using a filter tailored to the missing echo signals to generate a focused missing image; detecting an out-of-focus image of the SAR data; The method of claim 8 , further comprising: suppressing out-of-focus images from the SAR data.

10. extracting a focused image of the unknown region from the SAR data; and double-focusing the SAR data according to the distinct echo signals; The step of double focusing the SAR data according to the distinct echo signals comprises: defocusing the SAR data; 10. The method of claim 9, including focusing the SAR data with a filter tuned to the well-defined echo signals to generate an in-focus unfocused image from the SAR data.

11. and further comprising focusing the SAR data using a filter tuned to the missing echo signals to generate a focused missing image, the focusing comprising: compressing the range using a filter tailored to the unknown echo signal; a range cell transition correction step, wherein the range cell transition term in the range envelope of the unknown echo signal is a function of the distance to the unknown region; 7. The method of claim 6, further comprising compressing the azimuth angle relative to the nadir distance, wherein the number of azimuth pulses of the missing echo signal is a function of the ambiguity index and the nadir distance.

12. detecting an out-of-focus image of the SAR data; suppressing out-of-focus images from the SAR data; extracting an unfocused image from the SAR data; and focusing the SAR data using a filter tuned to the distinct echo signals to obtain a focused, distinct image, wherein the focusing comprises: compressing the range using a filter tailored to the distinct echo signal; a range cell transition correction step, wherein the range cell transition term in the range envelope of the clear echo signal is a function of the distance to the unknown region; and compressing the azimuth angle relative to the nadir distance, wherein the number of azimuth pulses of the distinct echo signal is a function of the ambiguity index and the nadir distance.

13. further comprising the step of dual focusing the SAR data according to the distinct echo signals; The step of double focusing the SAR data according to the distinct echo signals comprises: defocusing the SAR data; and focusing the SAR data using a filter tuned to the distinct echo signals to generate a focused, distinct image from the SAR data.

14. 6. The method of claim 5, further comprising focusing the SAR data with a filter tuned to the distinct echo signals to produce a focused, distinct image.

15. detecting a clear, focused image of the SAR data; The method of claim 13 further comprising suppressing a clear, in-focus image from the SAR data.

16. further comprising the step of dual-focusing the SAR data according to the missing echo signals; The step of double focusing the SAR data according to the unknown echo signals comprises: defocusing the SAR data; and focusing the SAR data using a filter tuned to the distinct echo signals to produce a sharp, focused image.

17. focusing the SAR data using a filter tuned to the distinct echo signals to generate a sharp, focused image, the focusing comprising: compressing the range using a filter tailored to the distinct echo signal; a range cell transition correction step, wherein the range cell transition term in the range envelope of the distinct echo signal is a function of the distance to the distinct region; 7. The method of claim 6, further comprising compressing the azimuth angle relative to the nadir distance, wherein the number of azimuth pulses of the distinct echo signal is a function of the ambiguity index and the nadir distance.

18. detecting a clear, focused image of the SAR data; suppressing a clear focused image from the SAR data; and focusing the SAR data using a filter tailored to the missing echo signals to obtain a focused missing image, wherein the focusing includes: compressing the range using a filter tailored to the unknown echo signal; a range cell transition correction step, wherein the range cell transition term in the range envelope of the unknown echo signal is a function of the distance to the unknown region; 18. The method of claim 17, comprising compressing azimuth angles relative to the nadir distance, wherein the number of azimuth pulses of the missing echo signal is a function of an ambiguity index and a nadir distance.

19. A computing system configured to control a SAR to operate in accordance with the method of any one of claims 1 to 18.

20. A computer readable medium comprising instructions that, when implemented in a computing system forming part of a SAR operating system, cause the system to operate in accordance with the method of any one of claims 1 to 18.

21. A SAR system configured to transmit successive radio wave pulses to illuminate a target area according to the method of any one of claims 1 to 18.

22. 22. A pulsed radio waveform transmitted from the SAR system of claim 21 mounted on a platform that moves relative to the surface of the Earth.

Images