Patent Publication Number: US-8994584-B2

Title: Autofocus-based compensation (ABC) system and method for a hovering ground moving target indication (GMTI) sensor

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims the benefit of U.S. Provisional Patent Application No. 61/495,783 filed on Jun. 10, 2011, herein incorporated by reference in its entirety. 
    
    
     GOVERNMENT INTEREST 
     Governmental Interest—The invention described herein may be manufactured, used and licensed by or for the U.S. Government. 
    
    
     BACKGROUND OF THE INVENTION 
     i) Field of Invention 
     Embodiments of the present invention generally relate to motion compensation, and in particular to an autofocus-based compensation (ABC) systems and methods for a ground moving target indication (GMTI) sensor. 
     ii) Description of Related Art 
     Various military and non-military organizations use moving target indication (MTI) radar systems—both ground-based and airborne. Most of these systems process data in the frequency domain, detecting the Doppler shift induced on a transmitted waveform by the radial velocity of the moving target. Since they process target returns appearing at specific Doppler frequencies, it is important that their relative spatial location be precisely specified throughout the entire processing interval. Without accurate position information, processing algorithms cannot correct for phase errors introduced by platform motion. This is generally not an issue for stationary, ground-based systems; but it is critically important for airborne systems, including the helicopter-based multi-channel system that was considered. 
     In a typical hovering airborne GMTI radar system, a post-processor uses simultaneously collected platform position and orientation information to correct for motion-induced errors in the measured signal phases. This motion compensation (MOCOMP) system performs well provided that the position measurement system produces high-precision outputs. If, however, the position measurements are imprecise; then the downstream GMTI algorithm may be unable to detect specific targets of interest. This may be especially true when the target of interest has low radar cross section (RCS) and is moving at low speed. The small amount of energy available in its GMTI signature would likely smear across multiple Doppler bins, making it indistinguishable from large sidelobes of the main clutter ridge concentrated near the 0 Hz Doppler bin. 
     BRIEF SUMMARY OF THE INVENTION 
     According to one embodiment, a method for autofocus based compensation of range data acquired from an object in motion is provided. The method may include: receiving range data; steering at least one receive beam of the range data in a desired direction; transforming the range data into the range domain; determining the width of a main clutter lobe; excluding data that is not part of the main lobe clutter response; transforming the main-lobe clutter response into the range domain; calculating a phase correction term; and applying the phase correction to the original range data. 
     According to another embodiment, a system for autofocus based compensation for range data acquired from an object in motion is provided. The system may include: a processor configured to: receive range data; steer at least one receive beam of the range data in a desired direction; transform the range data into the range domain; determine the width of a main clutter lobe; exclude data that is not part of the main lobe clutter response; transform the main-lobe clutter response into the range domain; calculate a phase correction term; and apply the phase correction to the original range data. 
     According to yet another embodiment, a computer-readable storage medium having computer-readable instructions, that when executed by a processor, implement a method for autofocus based compensation of range data acquired from an object in motion is provided. The method executed by the computer-readable instructions may include: receiving range data; steering at least one receive beam of the range data in a desired direction; transforming the range data into the range domain; determining the width of a main clutter lobe; excluding data that is not part of the main lobe clutter response; transforming the main-lobe clutter response into the range domain; calculating a phase correction term; and applying the phase correction to the original range data. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only a few embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. These embodiments are intended to be included within the following description and protected by the accompanying claims. 
         FIG. 1  illustrates a schematic of one platform system which may be used with embodiments of the present invention. 
         FIG. 2  illustrate a functional block diagram of an autofocus-based compensation (ABC) system according to an embodiment of the present invention. 
         FIG. 3  illustrates emulation outputs showing the effect of uncompensated, constant-velocity aircraft motion on Doppler frequency estimation 
         FIG. 4  illustrates effects of imposing an undetected, non-linear position error onto the uncorrupted or uncompensated data. 
         FIG. 5  illustrates various examples of uncorrected range-Doppler imagery. 
         FIG. 6  shows a generally block diagram of the basic PGA algorithm. 
         FIG. 7  shows a plot of the mean difference between compensated and uncompensated MTS mainlobe widths for each of the data cubes. 
         FIG. 8  illustrates plots showing distorted and corrected responses from MTSs. 
         FIG. 9  is a plot showing the standard deviation calculated for each of the several MTS responses in the scene. 
         FIG. 10  illustrates the mean difference between positive and negative Doppler frequency estimates as a function of positive Doppler bin index. 
         FIG. 11  illustrates the mean difference for several target responses. 
         FIG. 12  illustrates a block diagram of the ABC algorithm processing method according to an embodiment of the present invention. 
         FIG. 13  illustrates block diagrams of GMTI system showing incorporation of the ABC processing step. 
         FIGS. 14 and 15  illustrate examples of range-Doppler data before and after ABC processing. 
         FIG. 16  illustrates the distortion of a point-target response produced by an artificially introduced slant-range motion component. 
         FIG. 17  shows the compensated point-target response after ABC processing. 
         FIG. 18  illustrates shows the relative uncompensated aircraft offset in the slant-plane as a function of CPI pulse number. 
         FIG. 19  illustrates applying a phase shift to input data. 
         FIG. 20  illustrates schematics showing elimination of the “non-main-lobe clutter” response. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the present invention generally relate to motion compensation, and in particular to, an autofocus-based compensation (ABC) systems and methods for a GMTI sensor. 
       FIG. 1  illustrates a schematic of one platform system  100  which may be used with one or more embodiments of the present invention. System  100  may be implemented as part of a modified DARPA FORESTER system as shown. However, it will be appreciated that other antenna array-based systems might also be used, such as, Northrop Grumman&#39;s ARTEMIS system, in other embodiments. 
     The Defense Advanced Research Projects Agency (DARPA) recently developed the Foliage Penetrating, Reconnaissance, Surveillance, Tracking, and Engagement Radar (FORESTER) system. The foliage penetration (FOPEN) requirement dictates that the system&#39;s operational frequencies are low, which results in small Doppler frequency shifts. In addition, the system must detect partially concealed dismounts with small radar cross section (RCS) moving at relatively slow speeds. The FORESTER system includes a suite of sensors for measuring the platform&#39;s position, velocity, yaw, pitch, and roll, enabling it to realize a long coherent processing interval (CPI) and produce high-resolution Doppler measurements. 
     Ideally, the FORESTER system would hover motionlessly during a CPI, but this may be an unrealistic expectation for such a (relatively) long interval. Inevitably, a certain amount of platform drift introduces phase distortions into the received signal resulting in blurred range-Doppler imagery. Typically, a post-processor uses simultaneously collected platform position and orientation information to correct for these motion-induced errors in the measured signal phases. If the platform position measurement system fails to correct for all the errors, then alternative motion compensation (MOCOMP) solution to obtain high-quality MTI data may be required. 
     As shown in  FIG. 1 , a platform  110  may be a rotary positioner craft, such as an A160 Hummingbird helicopter unmanned aerial vehicle (UAV). When deployed, this platform  110  may hover and track ground moving objects and targets. 
     An antenna array  120  is mounted, and/or otherwise designed, to be carried underneath or by the platform  110 . For instance, it may be housed in large “pod” transversely mounted on the platform  110  in some embodiments. The antenna array  120  can be positioned to provide desired surveillance of a certain sector or area, and then electronically scanned across that sector. FORESTER, for example, is a multi-channel system which includes an array of 16 active elements. In some embodiments, the antenna array  120  may be maintained at a predetermined azimuth using a drive controller. 
     An onboard electronics system  130  may be provided within the platform  110 , which include that includes the radar transmitter, receiver, and signal processor. For instance, it may be housed within the fuselage of the platform  110 . Doppler range data may be collected by the antenna array  120  and processed by the electronics system  130 . The collected Doppler data may be communicated remotely, via radio frequency (RF) communications, to a control station  140 , such as a fixed command station, a mobile vehicle-platform and/or to other platforms including ground-, aerial-, satellite-, or sea-based platforms. Accordingly, the system  100  provides target tracking, data display, and operator control capability. 
     In other embodiments, the platform  110  might be an aerial moving vehicle, such as an airplane, helicopter, UAV, dirigible, balloon, blimp, or other aircraft. Or the platform could be a marine vehicle such as a submarine, ship, boat, hovercraft, etc, or a space-based platform such as a satellite or spacecraft. Radar or other electromagnetic ranging may be used in some instances. In the case of an underwater vehicle, sonar (an acronym for SOund Navigation And Ranging) may be used, which employs sound waves rather than electromagnetic (EM) radiation. 
       FIG. 2  illustrate a functional block diagram of an autofocus-based compensation (ABC) system  200  according to an embodiment of the invention. 
     The system  200  generally includes antenna array/Doppler hardware systems  210 , transmit/receive electronics  220 , communication electronics  230 , and system controller  240 . 
     The antenna array/Doppler hardware systems  210  may include an array of antenna elements. As noted above, FORESTER, for example, is a multi-channel system which includes an array of 16 active elements. It uses 1024 samples collected during a relatively long CPI, and this relatively high Doppler resolution enables it to detect and track slowly moving dismounts. Each of the 16 channels collects 1024 samples at each range gate, yielding a data cube of size 1024 (number of CPI pulses)×16 (number of array elements)×nRange (number of range gates=2048 for this data set). All of the channels also collect coherent data simultaneously permitting various, beamforming strategies. Other Doppler hardware systems may be conventional. 
     The transmit/receive (T/R) electronics  220  include electronic systems needed to transmit and receive radar information to and from the antenna array. For instance, the T/R electronics  220  include various modulators, phase shifter, power amplifiers and harmonic filters for generating and transmitting signals for 16 channels (corresponding to 16 antennas of the antenna array  220 ). Similarly the T/R electronics  220  may include limiters, pre-selectors, low noise amplifiers (LNA), down-convertors and analog/digital (A/D) convertors for receiving and pre-processing signals received from the antenna array. Such electronics are generally known and will not be discussed further herein. 
     The communication electronics  230  include uplink and/or downlink communication systems for wireless communications between the platform and the control station. Various known RF communication frequency bands and protocols may be used. System control data, flight data, Doppler range data, Inertial Navigation System (INS)/Global Position System (GPS) data are some types of data which may be transmitted and received via the communications electronics  230 . 
     The system controller  240  includes electronics for controlling the flight of the platform and providing range tracking. In this embodiment, range tracking uses Doppler radar. But, it should be appreciate that radar, sonar, or other EM ranging techniques could also be used. As shown, the system controller  240  includes an ABC processing unit  241  which include an ABC application  242 , processor(s)  243 , memory  244 , support circuits  245 , and input/output (I/O) interfaces  246 . Status and control information may be exchanged between the various elements. 
     The ABC processing unit  241  is coupled to the processor(s)  243  for executing the ABC application  242  that is configured to process Doppler range data and to provide correction of errors in the Doppler range data that are induced by platform movement. The ABC application  242  may be software (firmware) created using any number of programming languages. Application  242  may include one or more modules having processor-executable instructions. Of course, it will be appreciated that any number of hardware implementations, programming languages, and operating platforms may be used. As such, the description or recitation of any specific hardware implementations, programming language, and operating platforms herein is exemplary only and should not be viewed as limiting. 
     Alternatively or additionally, the application  242  may be a stand-alone application running on a computer which interfaces with the platform control systems, for example, though a remote network connection, or via a computer readable storage media (i.e., flash memory, DVD/CD-ROM, floppy disk, removable or permanent hard drive, etc.). In some implementations, the application may be a “plug-in” application that is incorporated into a third-party software application. Other configurations may also be implemented. 
     Methodology and algorithms for performing ABC processing in the absence of precise vehicle position measurements is disclosed herein. As a starting point the inventors evaluated a synthetic aperture radar (SAR) autofocus technique, and further extended this techniques to the problem of a moving platform. 
     The nature of the moving target indication (MTI) signature distortion due to different types of platform motion is further discussed below. The ABC processing was developed by the inventors based on their research on SAR autofocus considerations which may be performed, at least in part, by the ABC processing unit  241 . 
     The processor(s)  243  may include one or more microprocessors as known in the art. In some implementations, software code (instructions) may be stored on a computer or machine-readable storage media having computer or machine-executable instructions executable by processor(s)  243 . In some implementations, the processor(s)  243  may be a programmable processor, such as, for example, a field-programmable gate array (FGPA) or an application-specific integrated circuit (ASIC) processor. 
     The memory  244  may include one or more of the following: random access memory, read only memory, magneto-resistive read/write memory, optical read/write memory, cache memory, magnetic read/write memory, and the like, as well as signal-bearing media, excluding non-transitory signals such as carrier waves and the like. 
     The support circuits  245  may include conventional cache, power supplies, clock circuits, data registers, I/O devices, and the like. An input/output (I/O) interface  246  may be directly coupled to the memory  244  or coupled through the supporting circuits  245 . The I/O interface  246  may also be configured for communication with input devices and/or output devices, such as, network devices, various storage devices, mouse, keyboard, display, and the like. 
     The ABC processing was applied and tested in order to document its effectiveness using moving target simulators (MTSs) in measured FORESTER data. Various appropriately defined metrics and measured responses from canonical targets were determined to quantify observations. Results demonstrate that the ABC processing does not distort canonical target responses sharpened by the measurement-based motion compensation algorithm. 
     The range data may be electronic data which includes distance or range values (i.e., “Range gate”) at a particular frequency bands (i.e., “bins”). In some embodiments, the data may be stored and/or output as a matrix, multi-dimensional (e.g., 2-D or 3-D) array or other dataset. While certain embodiments disclosed herein are described with respect to Doppler range data, it should be appreciated that in other embodiments, sonar or radar data could be similar used similar to Doppler range data. 
     Experiments were performed by the inventors to determine the impact of imprecisely measured platform position on the frequency domain signatures required for MTI. Without precise platform position information, the phase relationships measured by the radar during a CPI was shown to be distorted, and the resulting target signatures were displaced and/or smeared in the range-Doppler plane. This typically led to missed or inaccurately located detections. 
     In particular, the experiments focused on MTSs at bearing angles of nearly 0° (relative to a line perpendicular to the array axis) using a non-adaptive beam-steering algorithm. The data from all 16 channels was coherently added together. This approach narrowed the effective beamwidth of the antenna to approximately 7°, enabling reasonable autofocus-based MOCOMP corrections to be implemented without adversely impacting downstream processing steps (such as those based on space-time adaptive processing concepts). During the experiments, the initial beamforming step proved important as preliminary attempts to formulate a MOCOMP solution for each individual channel failed due to the wide range of measured mainlobe Doppler frequencies in each channel. The narrower effective beamwidth output by the beamformer reduced the range of bearing angles included for mainlobe clutter determination, thereby reducing the undesirably large spread of mainlobe Doppler frequencies. This played an important role in estimating MOCOMP correction parameters via analysis of Fast Fourier transforms (FFT) calculated across the 1024 time-domain samples. It was the frequency-domain representation—provided by the FFT—that suitably concentrated the energy of moving targets, enabling determination of suitable MOCOMP corrections. 
       FIG. 3  illustrates emulation outputs showing the effect of uncompensated, constant-velocity aircraft motion on Doppler frequency estimation. For example,  FIG. 3(   a ) shows original FORESTER data.  FIG. 3(   b ) show a distorted images in which a Doppler shift is introduced by the uncompensated, constant-velocity aircraft motion in the data of  FIG. 3(   a ). In these images, the MTS response should appear as point targets in the range-Doppler plane. The imagery in  FIG. 3(   a ) was generated by first steering the beam to 0° (as measured perpendicular to the antenna array axis) and then performing an approximate MOCOMP. 
       FIG. 3(   c ) shows the frequency domain shift introduced by hypothesized, unmeasured aircraft positions. Here, the MTS Doppler signatures extracted from the range gate are indicated by the dashed ellipses.  FIG. 3(   d ) is an expanded (zoomed in) view of a portion of the plot in  FIG. 3(   c ). The vertical, dashed line (in both the imagery and the plots) indicates the frequency bin corresponding to zero Doppler; the final plot shows a zoom of the plot to the left. Based on the available Doppler resolution, the inventors expect an offset of slightly more than 20 frequency bins. 
     Following motion compensation, a new phase shift was introduced—at each CPI pulse—due to the undetected aircraft motion within the data collection plane (i.e., slant-range vs. cross-range) illustrated in  FIG. 3(   e ). This new, corrupted range-Doppler image and the original uncorrupted image constitute the graphics in  FIGS. 3(   a ) and  3 ( b ). In these images, the MTS responses should appear as point targets in the range-Doppler plane. The linearity of the unmeasured trajectory shown in  FIG. 3(   e ) implied that the undetected velocity was constant across the entire CPI, and the constant velocity produced the frequency domain shift evident in the aforementioned figures. Here, undetected aircraft position offsets as a function of CPI pulse number. 
       FIG. 4  illustrates the effects of imposing an undetected, non-linear position error onto the uncorrupted or uncompensated data of  FIG. 3 .  FIG. 4(   a ) shows original Doppler range data.  FIG. 4(   b ) shows the distortion produced in the range-Doppler imagery by this undetected, non-constant velocity, and differences between this imagery and that of  FIG. 3(   a ) are immediately apparent. So-called “smearing” of the point-like MTS responses was noticed as being introduced by the uncompensated, non-linear aircraft trajectory. The increase in the width of the clutter mainlobe was noticed, particularly in samples greater than 100 dB. 
     In  FIG. 4(   c ), the frequency-domain plots are again extracted from the range gate containing MTS responses—as indicated by the dashed ellipses.  FIG. 4(   d ) is an expanded (zoomed in) view of a portion of the plot in  FIG. 4(   c ). The vertical, dashed line (in both the imagery and the plots) indicates the frequency bin corresponding to zero Doppler; the final plot shows a zoom of the plot to the left, emphasizing the smearing introduced by the uncompensated down-range acceleration. In  FIG. 4(   e ), the uncompensated aircraft trajectory is now non-linear, indicating the presence of an undetected acceleration in the down-range direction. Undetected aircraft position offsets as a function of CPI pulse number. The extent of the range offset ensures that the MTS never moves out of a single range gate (e.g., less than 3.75 m). The acceleration component of  FIG. 4  has resulted in Doppler-domain “smearing” of the MTS point-like target responses. 
     Doppler-domain distortions arising from non-linear motion can have serious repercussions, as evidenced by the plots in  FIG. 4(   c ) sand  4 ( d ). The peak MTS signal levels realized in this instance fall approximately 6 dB below those realized prior to distortion, and this represents a significant reduction in target-to-clutter ratio—especially in view of the fact that low-RCS dismount targets are of interest. In addition, large signal levels within the clutter mainlobe clearly spread away from the zero-Doppler bin, potentially obscuring low-velocity targets. 
       FIGS. 5(   a )- 5 ( d ) illustrate various examples of uncorrected range-Doppler imagery in FORESTER data for data cubes  10 ,  16 ,  64 , and  52 , respectively. Qualitative comparison with  FIG. 3(   a ), for example, reveals the differences due to uncompensated motion. It is apparent that there are artifacts due to both smearing and frequency shifting. In  FIG. 5 , the Doppler bins have been interpolated by a factor of 4. 
     For instance, the inventors believed that the SAR imaging community has also recognized certain problems associated with uncompensated platform motion. One MOCOMP algorithm considered by the inventors, i.e., the phase gradient autofocus (PGA) algorithm, appeared in the late 1980s and has been successfully applied to a wide variety of SAR imagery. After careful consideration of current MTI problems, the inventors recognized that the fundamental MOCOMP problem is similar to that of the SAR community in some regards. A goal is to reduce or eliminate phase errors due to unmeasured aircraft motion. Thus, the inventors considered the effects of uncompensated aircraft motion on SAR image processing and the incorporation of autofocus techniques to ameliorate these effects. 
     The spatial resolution within a SAR image depends mainly upon two factors: (i) the transmitted bandwidth for downrange (or “cross-track”) resolution, and (ii) the synthetic aperture length—expressed in terms of the transmitted wavelength—for cross-range (or “along-track”) resolution. As documented in earlier descriptions of the time-domain, back-projection algorithm, cross-range resolution may be obtained by coherently integrating pulses from range gates corresponding to a particular image pixel. That is, for every along-track position within a synthetic aperture, the round-trip time of flight for the radar signal from a specified radar position to a particular image coordinate is calculated. Then all of the data samples extracted at the appropriate delay for each aperture position (i.e., the sample corresponding to the round-trip time of flight) are coherently added. This process may be repeated at each pixel of the processed image to obtain the desired SAR image. Errors in the recorded aircraft position produce errors in the estimated signal time of flight, and these are the errors that SAR autofocus routines, such as phase gradient autofocus (PGA) algorithm, attempt to eliminate. 
     Realizing that a time delay at a specific transmitted frequency corresponds to a phase shift, the inventors recognized that unwanted deviations from the known aircraft trajectory produce phase deviations that must be detected and eliminated during image formation. The PGA accomplishes this by using large target responses within the focused SAR image to adaptively estimate the phase distortion produced by the undetected aircraft motion. 
       FIG. 6  shows a generally block diagram of the basic PGA algorithm as modified by the inventors. The basic PGA algorithm is discussed by Jakowatz, C. V et al. in “Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach,” Kluwer Academic Publishers, Boston, 1996, pp. 251-269, herein incorporated by reference. 
     From the block diagram and the detailed discussion therein, it was realized that, following the initial circular shift and windowing, all targets should appear as nearly point-like responses. Since the target signatures also are centered, there should be no additional frequency-domain phase terms arising from time shifts. That is, following cross-range decompression (the FFT step), each target sample summed across the synthetic aperture should have the same phase, thereby producing the largest coherent sum. The PGA phase correction terms may be calculated as follows: 
                     Δ   ⁢           ⁢       ϕ   ^     ⁡     (   m   )         =     ∠   ⁢       ∑     k   =   1     N     ⁢         f   *     ⁡     (     k   ,     m   -   1       )       ⁢     f   ⁡     (     k   ,   m     )       ⁢           ⁢   and                 (   1   )                     ϕ   ^     ⁡     (   m   )       =       ∑     l   =   1     m     ⁢     Δ   ⁢           ⁢       ϕ   ^     ⁡     (   l   )             ,           (   2   )               
where ∠(ƒ) denotes “phase angle,” ƒ(k,m) is the radar measurement for the m th  pulse at the k th  range gate (i.e., the range gate k, “decompressed”—or Fourier-transformed—in the cross-range dimension), ƒ*(m) is the complex conjugate of ƒ(m), and N is the number of range gates used to estimate the phase correction—typically equal to the number of range gates in the image. The “corrected” measurement then becomes:
 
 {tilde over (F)} ( k,u )=IFFT m {ƒ( k,m ) e   −i{circumflex over (φ)}(m) }.  (3)
 
     From equations 1, 2, and 3, it was recognized that the phase gradient correction attempts to adjust the phase at each pulse to approximate the phase of the first pulse. This should achieve, as closely as possible, the constant phase desired prior to cross-range integration via the FFT. 
     An Autofocus-based Compensation (ABC) algorithm according to embodiments of the invention was derived from the PGA algorithm as applied to MTI datasets by the inventors. 
     For the ABC algorithm processing, the MTI image domain corresponds to the range-Doppler plane, a space versus frequency plane, as opposed to the SAR image domain, which corresponds to a purely spatial plane. As recognized by the inventors, a fundamental problem in both cases centers about the detection and elimination of phase distortions impacting the summation that determines the final image pixel value. 
     The methodology outlined in the block diagram of  FIG. 6  was modified from a known PGA algorithm by the inventors. In particular, the SAR data of PGA algorithm was replaced with the Doppler range data, and the SAR&#39;s cross-range dimension for SAR data was replaced with the MTI&#39;s Doppler dimension. After incorporation of these modifications, the other MTI steps may proceed similarly as per the SAR PGA algorithm. Other differences may relate to the number of range gates, N, used to calculate the correction term, the number of iterations performed prior to algorithm termination, and the procedure used to implement the “circular shift.” In an effort to limit the amount of computation required for MOCOMP, the number of background gates was limited. For instance, N may represent 400 background gates. This approach also has the added benefit of retaining a more localized estimate of the phase correction function. Similarly, after observing that a single iteration yields almost all of the improvement, the number of calculations required was reduced by evaluating only a single iteration of the algorithm (i.e., by calculating the phase correction function only once). Finally, since the amount of circular shift is small and consistent throughout all of the range gates (recall that the “target” in this case is the main clutter ridge at zero Doppler), it was incorporated into the overall phase correction function. 
     While this brief description touches upon the elements of the processing chain of  FIG. 6  that were altered, it is useful to discuss in detail how the processing steps in  FIG. 6  are adapted for MTI processing. Each of the steps is addressed below. 
     In step  610 , where SAR image is ordinarily input, range data (e.g., Doppler range data) is now the input to the system. As mentioned previously, the FORESTER data cube comprises measurements from 16 channels, 1024 CPI pulses, and 2048 range gates. Thus, the 3D data cube that includes FORESTER measurements must be reduced to a 2D data cube suitable for autofocus processing. For instance, the 16 channels of data may be collapsed by coherently summing them (i.e., forming a beam at 0° relative to a line perpendicular to the antenna array) to create a 2048×1024 matrix of range and CPI values. Collapsing refers to a data dimensionality reduction process, which here is from 2048×1024×16 to 2048×1024. The collapsing process may be described as follows: 
     
       
         
           
             
               
                 
                   
                     
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     where d(i,j,k) denotes the original data cube, and Nc denotes the number of receive channels. 
     Next, an unweighted FFT is calculated across CPI pulses for each of the range gates as follows: 
                       G   ⁡     (     m   ,   n     )       =     K   ⁢       ∑     k   =   0         N   ⁢           ⁢   p     -   1       ⁢       g   ⁡     (     m   ,   k     )       ⁢     ⅇ       -   j     ⁢           ⁢   2   ⁢   π   ⁢           ⁢     kn   /   N                 ,     where   ⁢           ⁢   K   ⁢           ⁢   is   ⁢           ⁢   a   ⁢           ⁢   scale   ⁢           ⁢     factor   .               (   5   )               
In the example here, there are 2048 range gates.
 
     And, the result is circularly shifted such that the zero-Doppler bin appears in the center column as follows:
 
 G   circular shift ( i )= G (( i+N/ 2)mod  N ),for  i= 0,1,2  . . . ,N− 1.  (6)
 
     This version of the range-Doppler matrix serves as an input to the main processing loop. The relationship between the range-Doppler domain and the range-CPI domain is preserved. As a result, an inverse fast Fourier transform (IFFT) may be used instead of the FFT. 
     To illustrate applying a shift to input data further reference is made to  FIG. 19 . Here, R is the range to the target area and L is the array length. Since R may be much larger than L, the phase correction calculated to the center of the array can effectively be applied to each channel. The antennas in the array are spaced apart by a distance δ. Finally, since the phase correction Δφ is calculated for a broadside antenna beam (i.e. a beam that is directed along a ray perpendicular to the axis of the antenna array), it sharpens the response from targets located at angles near 0° relative to a line perpendicular to the array axis. To optimally process targets at other angles, the proper phase shifts Δφ would be applied to the data in each channel to steer the beam in that direction based on the L R  and the wavelength λ corresponding to the center frequency as follows:
 
Δφ=2 πL   R /λ  (7)
 
     Referring back to  FIG. 6 , in step  620 , the target (e.g., brightest) pixel is circularly shifted to the center of the image. In one implementation, the brightest pixel may be calculated as follows: 
     
       
         
           
             
               
                 
                   
                     
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     Following the FFT, the complex magnitude is calculated for each Doppler signature, by applying a moving average filter to the magnitude of each signature, and then locating the brightest pixel and verifying that this pixel is located near the center of the signature. That is, the main clutter ridge produces the maximum pixel value. No additional modifications may be further required since a correction for the Doppler offset can be incorporated into the final phase correction function. 
     In step  630 , an appropriate window width (i.e., width of the target response) is determined and applied. Typically, this width represents the distance between the first pixels more than M dB below the peak, where M is a number such as 10, for instance. After determining the location of the main clutter lobe, its width may be estimated by finding the two Doppler bins, e.g., in the filtered “magnitude” signature—one on either side of the peak, that are closest to being a predetermined threshold below the maximum pixel. The main clutter lobe is the set of pixels within a given range gate with values that are less than M dB below the peak. The main clutter ridge denotes the surface created by the main clutter lobes from multiple, contiguous range gates. For example, the predetermined threshold may be 10 dB in some instances. Since these two bins lie on either side of the peak, the separation between them becomes the estimate of the width. This process may be repeated for each range gate; thus, obtaining  2048  estimates of the mainlobe width, for instance. Only a smaller, more suitable subset of the complete collection to estimate the phase correction may be employed in some instances. The rectangular window may be applied corresponding to the estimated width to the Doppler signatures in each range gate. 
     In step  640 , a Fourier Transform is applied in the range dimension. As noted earlier, the cross-range dimension for SAR image in the conventional PGA algorithm has been replaced by the range dimension, which here is the Doppler dimension. Hence, the IFFT of the complex Doppler signature is calculated. 
     In step  650 , a phase error function is estimated. In one embodiment, a value of N=400 in (1) may be selected in order to allow the estimator to be somewhat localized in range while still obtaining good integration gain. The samples used by the estimator may include, for example, N/2 contiguous samples abutting either side of the range cell under consideration. For the nearest and farthest range gates (i.e., those less than N/2 from the edges), it may use either the initial N samples or the final N samples. 
     In step  660 , a determination is made whether the phase error is less than a predetermined threshold. If the root-mean-square (RMS) of the phase error is less than the threshold, the method proceeds to step  670  or otherwise commences in step  690 . 
     Once the phase correction function for each range gate is determined, it may be applied in step  670 , producing the compensated range-Doppler image given as follows:
 
 {tilde over (G)} ( k,u )=FFT m   {g ( k,m ) e   i{circumflex over (φ)}(m) },  (9)
 
where g(k,m) denotes the raw data samples collected at range gate k and CPI pulse m, FFT m  denotes the FFT taken with respect to the variable m, and {tilde over (G)}(k,u) denotes the motion-compensated range-Doppler image.
 
     The final phase correction function, {circumflex over (φ)}(m), in equation 9 may be used to correct both for clutter mainlobe shifts and smearing due to non-linear components of the platform&#39;s trajectory. It requires no detailed information about the aircraft&#39;s position, hence it could function as either a replacement for faulty INS/GPS measurements or an enhancement to INS/GPS motion compensated range-Doppler imagery. While the above methodology assumed targets at a bearing angle of nearly 0° (relative to a line of sight perpendicular to the antenna array axis), there is nothing to prohibit the beamformer from steering to any arbitrary bearing angle. Such a step should occur naturally as part of the scanning operation of the FORESTER system. 
     In step  680 , an inverse Fourier Transform is applied to transform the image data back to image domain. For instance, one representative inverse Fourier Transform equation which may be used is as follows: 
     
       
         
           
             
               
                 
                   
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     In order to quantify the ABC algorithm&#39;s effectiveness, several metrics which typically are associated with SAR data processing were evaluated by the inventors for the ABC algorithm. 
     The first metric considered was the average distance between points that are 6.5 dB down on either side of a MTS peak location. This quantity provided an indication of the mainlobe width of a point target, and it illustrated how effectively the algorithm eliminated “smear” in the imagery due to nonlinear aircraft motion. A comparison of the MTS mainlobe widths before and after ABC processing also indicated the degree to which the original range-Doppler image had been corrupted. 
       FIG. 7  shows a plot of the mean difference between compensated and uncompensated MTS mainlobe widths for each of the data cubes. Here, mainlobe width is defined by the 6.5 dB points. The difference is expressed in terms of Doppler bins. These plots show that certain cubes experienced a great deal of “smearing” (e.g., cube  11 ), while others did not (e.g., cube  10 ). 
       FIG. 8  illustrates plots showing distorted and corrected responses from MTSs. In particular,  FIGS. 8(   a ) and ( b ) illustrate the effectiveness of applying the ABC algorithm to data cube  11 . Here, data is interpolated in the Doppler dimension, producing an image that contains four times as many Doppler samples as the original image. This provides a degree of “smoothing” and made the effects of uncompensated motion more apparent in both the imagery and the plots. The “smearing,” clearly evident in the MTS images of  FIG. 8(   a ), was eliminated by ABC as evident in  FIG. 8(   b ). In  FIGS. 8(   a ) and  8 ( b ), the Doppler bins have been interpolated by a factor of 4. 
       FIG. 8(   c ) shows a log plot of the main clutter lobe and several MTS signatures as a function of Doppler frequency bin. Here, the smooth (outer) line represents the original, uncompensated Doppler profile, while the dotted (inside) line represents the ABC-processed Doppler profile. The amount of MTS smearing is clearly evident in the plot of  FIG. 8(   c ), as is the improvement realized via the ABC algorithm processing. 
     The next metric considered was target location accuracy. This metric quantifies the accuracy of the MTS Doppler location estimates by: (1) calculating the variance between target location estimates from different data cubes, and (2) determining the offset between MTS responses that were symmetric relative to zero Doppler. The inventors believed that these were important considerations, since the adaptive procedure also calculated a Doppler shift as part of the overall phase correction function. Hence, symmetric positive- and negative-MTS response locations, together with a low variance in the final MTS position estimates, combined to indicate that the procedure successfully incorporated this portion of the compensation. 
       FIG. 9  is a plot showing the standard deviation (σ=√{square root over (variance)}) calculated for each of the several MTS responses in the scene. These plots demonstrate that the 2-sigma point of the deviations from estimated MTS response locations is still less than one Doppler bin. 
       FIG. 10  illustrates the mean difference between positive and negative Doppler frequency estimates as a function of positive Doppler bin index. The MTS produced symmetric positive and negative Doppler signals. 
     More particularly, the plot in  FIG. 10  shows that the location estimates following ABC processing preserved the high degree of symmetry inherent in the MTS responses. In this plot, the difference between the corresponding positive and negative frequency estimates are plotted as a function, ƒ(i), of the data cube index, where calculated ƒ(i) using 
                       f   ⁡     (   i   )       =         1     N   targ       ⁢         ∑     x   &lt;   0                   positive   ⁢           ⁢   _   ⁢           ⁢   freg   ⁢           ⁢   _   ⁢           ⁢   bin   ⁢           ⁢   _   ⁢           ⁢     index   ⁡     (   x   )         ≠   ∅       ⁢       (     x   +     positive_freq   ⁢   _bin   ⁢   _index   ⁢     (   x   )         )     2             ,           (   11   )               
where x indicates the estimated negative frequency bin (index) of an MTS response, positive_freq_bin_index(x) represents the corresponding, estimated positive frequency bin, the summation is taken over all negative frequency bin estimates with a corresponding positive frequency bin estimate, and N tarq  represents the number of targets available for the summation.
 
     Negative frequency bins exist because the indices are adjusted so that zero Doppler occurs at bin number 513. For instance, the global Doppler bin  520  may correspond to Doppler bin  7  in equation 11, while the global Doppler bin  506  would correspond to Doppler bin −7 in equation 11. A negative frequency bin, x&lt;0, may correspond to a positive frequency bin, y&gt;0, if (x+y)&lt;3. 
     Examination of  FIG. 10  reveals that, on average, almost all of the data cubes yielded estimates of the MTS target locations (in Doppler space) that were symmetric about zero Doppler (i.e., fell within one Doppler bin of zero). The two notable exceptions were cubes  4  and  28 , indicating a bias in the ABC estimate of the DC offset. 
     Another metric consider was the mainlobe width of MTS and MOCOMP outputs. This metric quantified the cost of applying the ABC algorithm to previously motion-compensated MTI data.  FIG. 11  presents the mean difference (i.e., ABC estimated mainlobe width versus MOCOMP calculated mainlobe width) for several target responses. From the plot, it is apparent the maximum difference is a small fraction of one Doppler bin. The plot of  FIG. 11  suggests that the ABC processing could be applied in addition to or as a “backup” to standard motion compensation, without introducing any adverse effects. Such an approach would add additional robustness and security to the overall system. 
     An autofocus algorithm for an MTI mode on a hovering platform was developed and tested it using FORESTER data. As part of this development, the motion compensation concepts employed by the SAR community were leveraged by the inventors and who further extended them for use by the hovering platform performing MTI. The newly formulated ABC algorithm was found to effectively reduce Doppler-domain distortions introduced by errors in the estimated aircraft motion, and it has shown promise as a supplement for existing MOCOMP algorithms. With it, both Doppler frequency target shifts and Doppler frequency target “smearing” due to errors in the estimated aircraft motion may be corrected. In addition, it is believed that the ABC algorithm introduces no adverse effects on the MTS mainlobe width when it is applied. 
     Results indicate that ABC algorithm processing may be incorporated as an effective complement for measurement-based MOCOMP procedures. For example, the experimental results indicate that the ABC algorithm could replace INS/GPS MOCOMP procedures when precise measurements of aircraft position are not available. The ABC processing may enable significant contributions to the overall effectiveness and reliability of a hovering MTI system. 
     The ABC algorithm processing first estimates distortions of a received radar signal due to undesired motion of a hovering aircraft, and subsequently removes these distortions. It may be used for either enhancing or replacing an existing MOCOMP system that requires precise, real-time estimates of the aircraft position, provided that the radar system under consideration satisfies certain requirements. 
       FIG. 12  illustrates a block diagram of the ABC algorithm processing method  1200  according to an embodiment of the present invention. A detailed explanation of the various steps is provided below. 
     In step  1205 , range-Doppler MTI data is provided from an array-based system. The array-based system may be the DARPA FORESTER system, for example. In some embodiments, the radar system under consideration includes an array of L receive antennas, providing L coherent channels that support the implementation of standard beam-steering algorithms. Beam-steering may be implemented via hardware, digitally, or a combination thereof. In addition to the L receive channels, the radar system also measures M coherent pulses within one coherent processing interval (CPI), and this coherent data is suitable for standard frequency-domain analysis (such as via a fast Fourier transform (FFT)). A coherent processing interval (CPI) of many seconds may be used to produce high-resolution for instance. The radar measures all of this coherent data at each of N specific ranges, providing the GMTI algorithm access to an N×L×M data cube. 
     System architecture of this type has long been used within the GMTI community (e.g. for space-time adaptive processing (STAP)) as discussed, for example, by Brennan, L. et al., “Adaptive arrays in airborne MTI”, IEEE Trans., 1976, AP-24, (5), pp. 607-615, &amp; Ward, J., “Space-time adaptive processing for airborne radar” Technical Report No. 1015, Lincoln Laboratory, MIT, December 1994, herein incorporated by reference. This architecture can similarly be applied to a single-channel system, provided that the system beamwidth is narrow enough to provide adequate angular resolution. 
     In step  1210 , beam steering is performed. Beam steering involves changing the direction of the main lobe of a radiation pattern. This may be accomplished by switching antenna elements or by changing the relative phases of the RF signals driving the elements. In one embodiment, the beam steering includes steering the receive beam in a desired direction by applying an appropriate phase adjustment at each receive (Rx) element, and summing across the dimension of the N×L×M data cube corresponding to the antenna array elements. This step reduces the three-dimensional N×L×M data cube to a two-dimensional N×M data cube. If single-channel range-Doppler data is used, then this step may be eliminated. 
     In step  1215 , the width of the main clutter lobe is determined. This may be performed by identifying the Doppler cells that are: (a) at least x dB below the peak value, and (b) closest to the Doppler cell containing the peak value. This operation may be repeated for each of the N range gates. In some instances, x may be 10 dB. The closest cell represents the cell offset by the smallest number of pixels from the peak. 
     In step  1220 , data that is not part of the main-lobe clutter response is excluded or eliminated. To illustrate elimination of the non-main-lobe clutter response further reference is made to  FIG. 20 . For example,  FIG. 20A  shows the nominal Doppler profile (signature) magnitude including the Main lobe  2010  and non-Main lobe clutter  2020 . And  FIG. 20B  shows the nominal Doppler profile (signature) magnitude with the non-Main-lobe-clutter  2020  removed. It is noted that the full profiles for both signatures here are complex. 
     Referring back to  FIG. 12 , in step  1225 , an inverse FFT is executed along the Doppler dimension. This operation transforms range Doppler data into the Range pulse domain. In step  1230 , the range gate counter i is initially set to a 1. 
     In step  1235 , the phase correction term is calculated similar to a synthetic aperture radar (SAR) autofocus technique. For example, this correction could be calculated according to the following equations: 
                       Δ   ⁢           ⁢       ϕ   ^     ⁡     (   m   )         =     ∠   ⁢       ∑     i   =   1         2   ⁢   k     +   1       ⁢         f   *     ⁡     (     i   ,     m   -   1       )       ⁢     f   ⁡     (     i   ,   m     )               ,   and           (   12   )                     ϕ   ^     ⁡     (   m   )       =       ∑     l   =   1     m     ⁢     Δ   ⁢           ⁢     ϕ   ⁡     (   l   )             ,           (   13   )               
where ƒ(i,j) represents the (complex) radar measurement at range gate i for pulse m, ƒ*(i,j) denotes the complex conjugate of ƒ(i,j), ∠ƒ(i,j) denotes the phase angle of the complex quantity ƒ(i,j), and {circumflex over (φ)}(m) represents the final phase correction term. Equations 12 and 13 are essentially the same as Equations 1 and 2, except for the underlying variables.
 
     In step  1240 , the phase correction term is then applied according to the equation.
 
{tilde over (ƒ)}( k,m )=ƒ( k,m ) e   −i{circumflex over (φ)}(m)   (14)
 
Previously, in Equation 3, there was a 2-D spatial domain (x vs. y). Now, in Equation 14, there is a space vs. frequency domain. And the initial image which is to be to “sharpened” or “focused” is the range-Doppler image.
 
     In step  1245 , the range gate counter i is increased in value by 1. A determination is made in step  1250  whether the range gate counter value i is greater than N. If the determination here is “yes,” the process proceeds to step  1255 . Otherwise, if the determination is “no,” the process returns to step  1235  for the next range gate. 
     In step  1255 , the motion-compensated, beam-steered data is converted to the range-CPI domain. Since the targets may be assumed to be at extremely far ranges, the phase correction term, {circumflex over (φ)}(m), can also be applied separately to each of the L channels. This yields the motion-compensated data cube suitable for down-stream GMTI (e.g. STAP) processing. 
       FIG. 13  illustrates block diagrams of GMTI system showing incorporation of the ABC processing step according to embodiments of the present invention. In step  1310 , range-CPI MTI data is collected by an array-based system may be provided. In step  1320 , compensation for effects of aircraft motion using measurement of aircraft position may be made. In step  1330 , transformation from Range-CPI domain to Range Doppler Domain takes place. In step  1340 , ABC processing according to embodiments of the present invention commences. In step  1350 , downstream GMTI processing may be performed. In step  1360 , moving target detection list occurs. 
     In the method  1300   a  shown in  FIG. 13(   a ), the ABC processing has been incorporated into an existing MOCOMP system based on aircraft position measurements. In the method  1300   b  shown in  FIG. 13(   b ), the ABC processing replaces an existing MOCOMP system based on aircraft position measurements. Step  1320  thus is not present in this process. This enables use of in situ clutter measurements to compensate for unmeasured aircraft motion in hovering GMTI systems. Reliance on measured aircraft position as part of MOCOMP calculation need no longer be solely considered. 
       FIGS. 14 and 15  illustrate examples of range-Doppler data before and after ABC processing. The improvements due to motion compensation are clearly evident. Before ABC processing, no artificial aircraft motion has been introduced. Evidence of “smearing” is clearly visible on the point targets in  FIG. 14 .  FIG. 15  illustrates a plot of point target responses before and after the ABC correction for the clutter main lobe and a subset of point target responses. After ABC processing, the increased width of the point target responses (i.e. smearing) is evident in  FIG. 15 . 
       FIG. 16  illustrates the distortion of a point-target response produced by an artificially introduced slant-range motion component. Smearing across multiple Doppler bins is evident in the point-target responses.  FIG. 17  shows the relative uncompensated aircraft offset in the slant-plane as a function of CPI pulse number.  FIG. 18  illustrates the relative aircraft position as a function of CPI pulse number. The uncompensated motion depicted by this plot produced the image distortions in  FIG. 16 . Offsets are all in the slant plane. It is evident from  FIGS. 16-18  that a failure in the motion compensation algorithm would have serious repercussions for downstream GMTI processing. This represents a problem in the current paradigm. 
     Measurement-based MOCOMP systems require high-precision position estimates to successfully eliminate the GMTI signal distortions in hovering aircraft due to aircraft motion. If the position measurement system fails or provides inaccurate estimates, then the motion-induced distortions cannot be reliably corrected. In fact, if the position estimates are severely erroneous and the aircraft motion is extreme, then the “compensated” GMTI signal may be more distorted than the “uncompensated” signal. 
     Embodiments of the present invention solves this problem by formulating a MOCOMP solution adaptively, using clutter samples from the observed scene. Earlier imagery demonstrated the effects of aircraft motion on GMTI canonical target signatures. The ABC algorithm effectively sharpens the point target response when motion-induced “smearing” has occurred. It also produces no adverse effects when applied to data that has already been successfully corrected using a measurement-based MOCOMP procedure. Moreover, the ABC algorithm need not rely upon measured positional information of the moving platform. 
     The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the present disclosure and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as may be suited to the particular use contemplated. 
     Various elements, devices, modules and circuits are described above in associated with their respective functions. These elements, devices, modules and circuits are considered means for performing their respective functions as described herein. 
     While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.