Patent Publication Number: US-2022229173-A1

Title: Complex recurrent neural network for synthetic aperture radar (sar) target recognition

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of the filing date and right of priority under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application No. 63/135,553 filed on Jan. 8, 2021, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The subject disclosure is related to Synthetic Aperture Radar (SAR) systems, and more particularly, for example, to systems and techniques for SAR target recognition. 
     BACKGROUND 
     Synthetic-aperture radar (SAR) Identifying targets from synthetic aperture radar (SAR) data is a widely-used technique, but most existing SAR automatic target recognition (ATR) systems use SAR images for target recognition. To form SAR images from raw SAR data, which is generated from backscattered radio frequency (RF) radar pulses that were reflected from a scene being observed by a SAR system on an ATR system, is a computationally intensive process. Generally, this technique prevents real-time computation for low size, weight and power (SWAP) SAR based ATR systems. 
     Some attempts have been made to process raw SAR data, which are complex radar pulses, instead of using the SAR images but these attempts generally have included using real SAR range profile data from the raw SAR data, which results in the loss of phase information of the SAR range profile data. Unfortunately, the phase information of SAR range profile data may provide helpful information to characterize the surfaces of a target because the depth variation of the surfaces of a target may result in a phase variation in the reflected RF pulses that are part of the raw SAR data. As such, the phase information of the raw SAR data may be helpful for target recognition. 
     Therefore, in relation to low SWaP SAR based ATR systems, contemporary SAR-based target identification techniques require extensive processing and data resources for SAR image reconstruction and feature detection which can present several challenges for low SWaP SAR based ATR systems, such as for example for systems with limited computational power and resources. 
     SUMMARY 
     This summary is not an extensive overview of the specification. It is intended to neither identify key or critical elements of the specification nor delineate any scope particular embodiments of the specification, or any scope of the claims. Its sole purpose is to present some concepts of the specification in a simplified form as a prelude to the more detailed description that is presented in this disclosure. 
     Disclosed is a synthetic aperture radar (SAR) system for target recognition with complex range profile. The SAR system comprising a memory, a recurrent neural network (RNN), a multi-layer linear network, and a machine-readable medium on the memory. The machine-readable medium is configured to store instructions that, when executed by the RNN, cause the SAR system to perform various operations. The various operation comprise: receiving raw SAR data associated with observed views of a scene, wherein the raw SAR data comprises information captured via the SAR system; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex range profile data with the RNN having RNN states; and mapping the RNN states to a target class with the multi-layer linear network. 
     In this example, the RNN and multi-layer linear network may be implemented on one or more processors and the RNN may be implemented as a gated recurrent unit (GRU) neural network (GRUNN). 
     In general, as an example of operation, disclosed is method comprising: receiving raw SAR data associated with observed views of a scene, where the raw SAR data comprises information captured via an automatic target recognition (ATR) system having a SAR system; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex range profile data with a RNN having RNN states; and mapping the RNN states to a target class with a multi-layer linear network. 
     Other devices, apparatuses, systems, methods, features, and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional devices, apparatuses, systems, methods, features, and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The invention may be better understood by referring to the following figures. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. In the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1A  is a perspective view of a diagram of an example of an implementation of a Synthetic Aperture Radar (SAR) system in a vehicle flying a course along a flight path over a landmass in accordance with the subject disclosure. 
         FIG. 1B  is a top view of the SAR system in the vehicle shown in  FIG. 1A  in accordance with the subject disclosure. 
         FIG. 1C  is a top view of the SAR system operating in a circular mode in the vehicle shown in  FIG. 1A  in accordance with the subject disclosure. 
         FIG. 1D  is a top view of the SAR system operating in a spotlight mode in the vehicle shown in  FIG. 1A  in accordance with the subject disclosure. 
         FIG. 2  is a system block diagram of an example of an implementation of the SAR system, shown in  FIGS. 1A through 1D , in accordance with the subject disclosure. 
         FIG. 3  is a flowchart of an example of an implementation of a method performed by the SAR system, shown in  FIG. 2 , in accordance with the subject disclosure. 
         FIG. 4A  is a system block diagram of an example of an implementation of a first gated recurrent unit (GRU) neural network (GRUNN) and second GRUNN utilized to compute a target identification (ID) from a complex SAR range profile data in accordance with the subject disclosure. 
         FIG. 4B  is a system block diagram of an example of an implementation of a single GRUNN utilized to compute a target identification (ID) from the complex SAR range profile data in accordance with the subject disclosure. 
         FIG. 5  is a system block diagram of an example of an implementation of GRUNN in accordance with the subject disclosure. 
         FIG. 6  is a system block diagram of an example of an implementation of a GRU processing cell of the GRUNN shown in  FIG. 5  in accordance with the subject disclosure. 
         FIG. 7A  is an example of a sample of range profile data for use with the SAR system, shown in  FIG. 2 , in accordance with the subject disclosure. 
         FIG. 7B  is example of another sample of range profile data for use with the SAR system, shown in  FIG. 2 , in accordance with the subject disclosure. 
         FIG. 7C  is example of yet another sample of range profile data for use with the SAR system, shown in  FIG. 2 , in accordance with the subject disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Disclosed is a synthetic aperture radar (SAR) system for target recognition with complex range profile. The SAR system comprising a memory, a recurrent neural network (RNN), a multi-layer linear network, and a machine-readable medium on the memory. The machine-readable medium is configured to store instructions that, when executed by the RNN, cause the SAR system to perform various operations. The various operation comprise: receiving raw SAR data associated with observed views of a scene, wherein the raw SAR data comprises information captured via the SAR system; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex range profile data with the RNN having RNN states; and mapping the RNN states to a target class with the multi-layer linear network. 
     In this example, the RNN and multi-layer linear network may be implemented on one or more processors and the RNN may be implemented as a gated recurrent unit (GRU) neural network (GRUNN). 
     In general, as an example of operation, disclosed is method comprising: receiving raw SAR data associated with observed views of a scene, where the raw SAR data comprises information captured via an automatic target recognition (ATR) system having a SAR system; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex range profile data with a RNN having RNN states; and mapping the RNN states to a target class with a multi-layer linear network. 
     SAR System 
     Turning to  FIG. 1A , a perspective view of a diagram of an example of an implementation of a SAR system in a vehicle  100  in a stripmap mode flying along a straight flight path (i.e., travel path  102 ) with a constant velocity  104  and at a constant altitude  106  over a landmass  108  in accordance with the subject disclosure. The vehicle  100  (also known as a platform) can be, for example, a manned or unmanned aircraft such as an airplane, a drone, a spacecraft, a rotorcraft, or other type of unmanned or manned vehicle. The vehicle  100  flies along the travel path  102  at the constant altitude  106  such that a SAR system  110  (on the vehicle  100 ) is directly above a nadir  112 . In this example, the nadir  112  is a locus of points on the surface of the Earth (e.g., the landmass  108 ) directly below an antenna  114  of the SAR system  110 . It is appreciated by those of ordinary skill in the art that in radar systems the nadir  112  is the beginning of the range parameter of a SAR radar. 
     In an example of operation, the SAR system  110  radiates (e.g., transmits) SAR radar signal pulses  116  obliquely at an approximate normal (e.g., a right angle) direction to a direction  118  of the flight along the travel path  102 . The SAR radar signal pulses  116  are electromagnetic waves that are sequentially transmitted from the antenna  114 , which is a “real” physical antenna located on the vehicle  100 . As an example, the SAR radar signal pulses  116  can be linear frequency modulated chip signals. 
     The antenna  114  is fixed and directed (e.g., aimed) outward from a side of the vehicle  100  at an obliquely and approximately normal direction to the side of the vehicle  100 . The antenna  114  has a relatively small aperture size with a correspondingly small antenna length. As the vehicle  100  moves along the travel path  102 , the SAR system  110  synthesizes a SAR synthetic antenna  120  that has a synthesized length  122  that is much longer than the length of the real antenna  114 . It is appreciated by those of ordinary skill in the art that the antenna  114  can optionally be directed in a non-normal direction from the side of the vehicle  100 . In this example, the angle at which the fixed antenna  114  is aimed away from the side of the vehicle  100  (and resultingly the travel path  102 ) will be geometrically compensated in the computations of the SAR system  110 . 
     As the SAR radar signal pulses  116  hit the landmass  108  they illuminate an observed scene  124  (also referred to as a “footprint,” “parch,” or “area”) of the landmass  108  and scatter (e.g., reflect off the landmass  108 ). In this example, the scene  124  can include one or more ROIs within the scene  124  such as, for example, first ROI  125  and second ROI  127 . The illuminated scene  124  corresponds to a width  126  and  128  of the main beam of the real antenna  114  in an along-track direction  130  and across-track direction  132  as the main beam intercepts the landmass  108 . In this example, the along-track direction  130  is parallel to the direction  118  of the travel path  102  of the vehicle  100  and it represents the azimuth dimension for the SAR system  110 . Similarly, the across-track direction  132  is perpendicular (e.g., normal) to the travel path  102  of the vehicle  100  and it represents the range dimension of the SAR system  110 . As the vehicle  100  travels along the travel path  102 , the illuminated scene  124  defines a stripmap swath  134 , having a swath width  136 , which is a strip along the surface of the landmass  108  that has been illuminated by the illuminated scene  124  produced by the main beam of the antenna  114 . In general, the length  122  of the SAR synthetic antenna  120  is directly proportional to the range in that as the range increases, the length  122  of the SAR synthetic antenna  120  increases. 
     In  FIG. 1B , a top view of the SAR system  110  in the vehicle  100  is shown in accordance with the subject disclosure. Again, the vehicle  100  is shown flying along the straight travel path  102  with a constant velocity  104 . In operation, as the vehicle  100  flies along the travel path  102 , the SAR system  110 , through the antenna  114 , radiates, within a SAR beam  115 , the SAR radar signal pulses  116  at the ground (e.g., landmass  108 ) at an approximately normal direction from the travel path  102  (and the along-track direction  130 ) where the SAR radar signal pulses  116  illuminate the scene  124  of the landmass  108  and scatter. The scatter off the scene  124  produces at least backscatter waves that are radar return signals  138  (i.e., backscattered return signals) that have reflected off the landmass  108  and reflected back towards the antenna  114 . The antenna  114  receives the radar return signals  138  and passes them to the SAR system  110  that processes the radar return signals  138 . In this example, the processing can include recording and storing the radar return signals  138  in a storage (not shown) in a data grid structure. The SAR system  110  utilizes consecutive time intervals of radar transmission and reception to receive radar phase history data of the illuminated and observed scene (e.g., scene  124 ) at different positions along the travel path  102 . Normally, the processing the combination of raw radar data (e.g., radar phase history data of illuminated scene) enables the construction of a SAR image (e.g., a high-resolution SAR image) of the captured scene (e.g., scene  124 ). However, the disclosed SAR system  110  obviates the need for the construction of SAR images in order to perform a target recognition task, instead, the SAR system  110  computes the spatial-temporal features of targets with a RCNN network directly from the complex range profiles of the received phase history data for recognition of the targets. 
     In this example, the widths  126  and  128  of the main beam of the antenna  114  are related to the antenna beamwidth ϕ  140  of the main beam produced by the antenna  114 . Additionally, in this example, the vehicle  100  is shown to have traveled along the travel path  102  scanning the stripmap swath  134  at different positions along the travel path  102 , where, as an example, the SAR system  110  is shown to have scanned two earlier scenes  142  and  144  the stripmap swath  134  at two earlier positions  146  and  148  ( FIG. 1B  doesn&#39;t have positions  146  and  148 ) along the travel path  102 . 
     It is appreciated by those of ordinary skill in the art that while the example vehicle  100  shown in  FIGS. 1A and 1B  is a manned aircraft, this is for illustrative purpose only and the vehicle  100  can also be an unmanned aircraft such as an unmanned aerial vehicle (UAV) or drone. 
     In  FIG. 1C , a top view of the SAR system  110  operating in a circular mode in the vehicle  100  is shown in accordance with the subject disclosure. In this example, the travel path  102  is a circular path and the SAR system  110  illuminates a circular scene  170 . Turning to  FIG. 1D , a top view of the SAR system  110  operating in a spotlight mode in the vehicle  100  is shown in accordance with the subject disclosure. In this example, the travel path  102  is straight similar to the example shown in  FIG. 1A  and the SAR system  110  illuminates another circular scene  175 . It is appreciated by those of ordinary skill in the art that the scene  170  in  FIG. 1C  and scene  175  in  FIG. 1D  can each include one or more ROI, however, for the purpose of ease of illustration the one or more ROIs are not shown in these figures. 
     In  FIG. 2 , a system block diagram of an example of an implementation of the SAR system  200  is shown in accordance with the subject disclosure. The SAR system  200  is substantially similar to SAR system  110  and can include functionality as more fully described herein, for example, as described above with regard to SAR system  110 . The SAR system  200  can be part of a SAR automatic target recognition (ATR) system on the vehicle  100 . In this example, the SAR system includes a memory  202 , an RNN  204 , a multi-layer linear network  206  in signal communication the RNN  204 , and a machine-readable medium  208  on the memory  202 . 
     Moreover, in this example, the memory  202 , RNN  204 , a multi-layer linear network  206  can be part of a computing device  210  that can also include one or more processors  212  and one or more communication interfaces  214 . In this example, the RNN  204  and multi-layer linear network  206  can be implemented in hardware or software in the computing device  210  and can be controlled and/or implemented on the one or more processors  212  based on a predetermined design preference. The SAR system  200  can also include a SAR sensor  218  and storage  220 . 
     The machine-readable medium  208  is configured to store instructions  216  that, when executed by the RNN, cause the SAR system to perform various operations. The various operations comprise: receiving with the combination of the antenna  114  and SAR sensor  218  raw SAR data associated with observed views of a scene (e.g., scene  124 ,  170 , or  175 ), where the raw SAR data comprises information captured via the SAR system  110 ; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex range profile data with the RNN  204  having RNN states; and mapping the RNN states to a target class with the multi-layer linear network  206 . 
     In general, the SAR system  200  is utilized to capture and process phase history data from observation views, of the scene  124 ,  170 , or  175  in the swath  134 , in accordance with various techniques. The SAR system  200  is generally a SAR ATR or navigation guidance system that comprises a SAR radar device that transmits and receives electromagnetic radiation as RF signals and provides representative data in the form of raw SAR data such as SAR phase history data. As an example, the SAR system  200  is implemented to transmit and receive radar energy pulses in one or more frequency ranges from less than one gigahertz to greater than sixteen gigahertz based on a given application for the SAR system  200 . 
     In this example, the computing device  210  includes the one or more processing units  212  that include, for example, a microprocessor, a single-core processor, a multi-core processor, a microcontroller, an application-specific integrated circuit (ASIC), a logic device (e.g., a programmable logic device configured to perform processing operations), a digital signal processing (DSP) device, one or more memories for storing executable instructions (e.g., software, firmware, or other instructions), and/or any other appropriate combination of processing device and/or memory  202  to execute instructions to perform any of the various operations described in the subject disclosure. The one or more processing units  212  are adapted to interface and communicate with the memory  202  and SAR sensor  218  via the one or more communication interfaces  214  to perform method and processing steps as described herein. The one or more communication interfaces  214  include wired or wireless communication buses within the vehicle  100 . 
     In various examples, it is appreciated by those of ordinary skill in the art that the processing operations and/or instructions are integrated in software and/or hardware as part of the one or more processing units  212 , or code (e.g., software or configuration data), which is stored in the memory  202 . The examples of processing operations and/or instructions disclosed in the subject disclosure are stored by the machine-readable medium  208  in a non-transitory manner (e.g., a memory  202 , a hard drive, a compact disk, a digital video disk, or a flash memory) to be executed by the one or more processing units  212  (e.g., a computer such as a logic or processor-based system) to perform various methods disclosed herein. In this example, the machine-readable medium  208  is shown as residing in memory  202  within the computing devices  210  but it is appreciated by those of ordinary skill that the machine-readable medium  208  can be located on other memory external to the computing device  210 , such as for example, the storage  220 . As another example, the machine-readable medium  208  can be included as part of the one or more processing units  212 . It is also appreciated by those of ordinary skill in the art that the RNN  204  and multi-layer linear network  206  can be implemented by the one or more processors  212  running the instructions  216 . 
     In this example, the memory  202  can include one or more memory devices (e.g., one or more memories) to store data and information. The one or more memory devices can include various types of memory including volatile and non-volatile memory devices, such as RAM (Random Access Memory), ROM (Read-Only Memory), EEPROM (Electrically-Erasable Read-Only Memory), flash memory, or other types of memory. The memory  202  can include one or more memory devices within the computing device  210  and/or one or more memory devices located external to the computing device  210 . The one or more processing units  212  are adapted to execute software stored in the memory  202  to perform various methods, processes, and operations in a manner as described herein. 
     The SAR sensor  218  is utilized to transmit electromagnetic waves (e.g., SAR radar signal pulses  116 ) and receive backscattered waves (e.g., received phase history data from the radar return signals  138 ) of scene  124 ,  170 , or  175 . In this example, the SAR sensor  218  includes a radar transmitter to produce the SAR radar signal pulses  116  that are provided to the antenna  114  and radiated in space toward scene  124 ,  170 , or  175  by antenna  114  as RF electromagnetic waves. The SAR sensor  218  further includes a radar receiver to receive backscattered waves (e.g., radar return signals  138 ) from antenna  114 . The radar return signals  138  are received by SAR sensor  218  as raw SAR data of the received phase history data of the scene  124 ,  170 , or  175 . The SAR sensor  218  communicates the received phase history data to the one or more processing units  212  and/or memory  202  via the one or more communication interfaces  214 . 
     The antenna  114  is implemented to both transmit the SAR radar signal pulses  116  and receive backscattered waves (e.g., radar return signals  138 ). In this example, the antenna  114  is in a fixed position on the vehicle  100  and is directed outward from the side of the vehicle  100  since the SAR system  200  is operating as a side-looking radar system. The antenna  114  can be implemented as phased-array antenna, horn type of antenna, parabolic antenna, or other type of antenna with high directivity. 
     The storage  220  can be a memory such as, for example, volatile and non-volatile memory devices, such as RAM, ROM, EEPROM, flash memory, or other types of memory, or a removable storage device such as, for example, hard drive, a compact disk, a digital video disk. The storage  220  can be utilized to store template range profile data of the scenes. 
     In  FIG. 3 , a flowchart is shown of an example of an implementation of the method  300  performed by the SAR system  200  in accordance with the subject disclosure. The method  300  begins by receiving  302  the raw SAR data associated with the observed views of the scene  124 ,  170 , or  175 . The raw SAR data includes information captured via an ATR system having the SAR system  200 . As discussed earlier, in operation, as the vehicle  100  flies along the travel path  102 , the SAR system  200 , through the antenna  114 , radiates the SAR radar signal pulses  116  at the landmass  108  at an approximately normal direction from the travel path  102  and the along-track direction  130  where the SAR radar signal pulses  116  illuminate the scene  124 ,  170 , or  175  of the landmass  108  and scatter. The scatter off the scene  124 ,  170 , or  175  produces at least backscatter waves that are radar return signals  138  (i.e., backscattered return signals) that have reflected off the landmass  108  and reflected back towards the antenna  114 . The antenna  114  receives the radar return signals  138  and passes them to the SAR system  200  that processes the radar return signals  138 . In this example, the radar return signal  138  are the raw SAR data that is two-dimensional data that includes frequency band data and pulse domain data. 
     The method  300  then includes RF preprocessing  304  the received raw SAR data to produce a processed raw SAR data. It is appreciated by those of ordinary skill in the art that, in general, RF preprocessing  304  includes producing an in-phase component and a quadrature-phase component of the received raw SAR data that represent the real and imaginary parts of the processed raw SAR data, where the processed raw SAR data includes two-dimensional data that includes frequency band data and pulse domain data 
     The method  300  then converts  306  the processed raw SAR data into a complex SAR range profile data. The processed raw SAR data can be converted into the complex SAR range profile data by applying a window function to the processed raw SAR data and then applying a Fourier transform to the pulse domain data within the processed raw SAR data. In this example, the window function can be, for example, Hanning window function and/or Hamming window function. Moreover, the Fourier transform can be performed by a fast Fourier transform. 
     The method  300  then processes  308  the complex range profile data with the RNN  204  having RNN states and mapping  310  the RNN states to a target class with the multi-layer linear network  206 . The SAR system  200  produces  312  a target identification (ID) and the method  300  then ends. 
     Determine the Complex Range Profile 
     As described earlier, prior to determining the complex range profile—i.e., converting  306  the processed raw SAR data into the complex SAR range profile data, the received raw SAR data, which are RF pulses, need to be preprocessed for phase and/or frequency compensation in order to make the RF pulses of the raw SAR data useful. Once processed, the SAR system  200  then computes the complex range profile of the raw SAR data to produce the processed raw SAR data. Again, the input processed raw SAR data (i.e., RF phase history) is data that is organized as a two-dimensional array where one dimension is representative of the frequency bands and the other one dimension is representative of the RF pulses. The range profile of raw SAR data can be computed by applying one-dimensional Fourier transformation to the input RF pulses. For example, let PH(m, n) be a two-dimensional RF phase history array and the column represents the radar pulse domain, which means each column vector represents radar pulses collected at a specific time step. The SAR radar pulses can be extracted from the column vectors of PH(m, n), utilizing the relationship (1) P r =PH(:, r). In this example, m represents frequency band values of a row vector P f  of the frequency band data and n represents pulse domain values of the column vector P r  of the pulse domain data. 
     A window function, such as Hanning or Hamming window, can be applied to the pulse vectors for reducing the boundary effect of the Fourier transformation. In this example, a windowed pulse vector is determined by the relationship (2) P w (i)=P r  (i)*w(i), where the vector w(i) is a window function vector, * is the Hadamard product operation, and i is the integer index representing a range bin from 0 to M, where M is a constant value that represents the maximal range bin that is determined by the number of sampling frequencies in the frequency band data. It is appreciated by those of ordinary skill in the art that a Hadamard product is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimension as the operands, where each element i, j is the product of elements i, j of the original two matrices. Utilizing this approach, a range profile vector rp r (m) is determined by the relationship (3) 
     
       
         
           
             
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     In this example, after all of the column vectors P r  in PH(m, n) are processed with relationships (1) to (3), a two-dimensional range profile, RP(m, n) is determined from the relationship (4) RP(m, n)=RP[rp r (m)] r=0   T-1  where one dimension (i.e., m) represents range bins and the other dimension (i.e., n) represents time-steps. In this example, the range-profile RP(m, n) is a complex value matrix and there are two ways to represent a complex value that include to utilize the real part and imaginary part or to use the amplitude and phase of the number. In this disclosure, the real and imaginary parts are utilized. In this example, it is appreciated that the complex matrix RP(m, n), m=0 to M−1; n=0 to T−1 representing M range bins=M sampling frequencies in the frequency band domain and T time-steps=T pulses in the pulse domain. 
     Process the Complex Range-Profile Data with a Gru Neural Network 
     In the fourth processing step  308 , an RNN is utilized to process the complex SAR range profile data. It is appreciated by those of ordinary skill in the art that an RNN is a class of artificial neural networks having a plurality of nodes that are interconnected. The connections between the nodes form a directed graph along a temporal sequence. This allows an RNN to exhibit temporal dynamic behavior. Derived from feedforward neural networks. RNNs can use their internal state (memory) to process variable length sequences of inputs. Generally, these properties have allowed RNNs to be utilized fir tasks such as unsegmented, connected handwriting recognition or speech recognition. In general, RNNs include recurrent long-short term memory (LSTM) neural networks and the GRUNN. The GRUNN is computationally simpler than a LSTM neural network but has comparable classification capability. As such, for these examples, a GRUNN will be utilized as the RNN even though it is appreciated that LSTM neural network can also be utilized. 
     In  FIG. 4A , a system block diagram of an example of an implementation of a first GRUNN  400  and second GRUNN  402  utilized to compute a target identification (ID)  404  from a complex SAR range profile data is shown in accordance with the subject disclosure. In this example, the complex SAR range profile data has been separated into a real part  406  of the SAR range profile data and an imaginary part  408  of the SAR range profile data. Similarly, in  FIG. 4B , a system block diagram of an example of an implementation of a single GRUNN  410  utilized to compute the target ID  412  from the complex SAR range profile data  414  in accordance with the subject disclosure. 
     In this example, to process the complex SAR range profile data  414 , the two approaches shown in  FIGS. 4A and 4B  can be utilized (e.g., by the SAR system  200 ). The first approach is shown in  FIG. 4A  where the real part  406  and imaginary part  408  of complex SAR range-profile data are separately processed by the first GRUNN  400  and second GRUNN  402  and the second approach is to process the real and imaginary parts of the complex SAR range profile data  414  jointly in the single GRUNN  410  with complex operation as shown in  FIG. 4B . In the separate processing scheme shown in  FIG. 4A , the two GRUNNs (i.e., first GRUNN  400  and second GRUNN  402 ) each act as separate channels. 
     In the first example, the first GRUNN  400  receives the real part  406  of the SAR range profile data and process it produce a plurality of first GRUNN states with the first GUNN  400  that are mapped to a target class for the real part  406  of the SAR range profile data with a first multi-layer linear network  416 . The second GRUNN  402  receives the imaginary part  408  of the SAR range profile data and process it produce a plurality of second GRUNN states with the second GUNN  402  that are mapped to a target class for the imaginary part  408  of the SAR range profile data with a second multi-layer linear network  418 . The mapped first target class and second target class are combined to compute  420  the target ID  404 . 
     In the second example, the single GRUNN  410  receives the complex SAR range profile data  414  and jointly processes the real and imagery parts of the complex SAR range profile data  414  to produce a plurality of GRUNN states that are mapped to a target class for the both the real and imaginary parts of the complex SAR range profile data  414  with a joint multi-layer linear network  422 . The mapped joint real and imaginary target classes are utilized to compute  424  the target ID  412 . 
     In operation, the process of training the GRUNNs shown in  FIG. 4A , both the first GRUNN  400  and second GRUNN  402  are controlled by a single objective function; therefore, both the first GRUNN  400  and second GRUNN  402  are trained by one optimization process that includes the single objective function. In the joint processing method shown in  FIG. 4B , both the real part and imaginary part of the complex SAR range profile data  414  are processed by the single GRUNN  410 , which uses complex operations in its GRU processing cells. 
     In  FIG. 5 , a system block diagram of an example of an implementation of GRUNN  500  is shown in accordance with the subject disclosure. In this example, the GRUNN  500  is shown including a set of GRU processing cells that include n GRU processing cells that for purposes of illustration are a first GRU processing cell  502 , second GRU processing cell  504 , and n th  first GRU processing cell  506 . The inputs to each of the GRU processing cells  502 ,  504 , and  506  include a temporal sequence x t  and the outputs of the GRU processing cells are the states of GRU processing cells (i.e., the GRUNN states) h 0 , h 1 , h 2 , etc. 
     Since each GRU processing cell  502 ,  504 , and  506  obtains input information from the previous state variable (past time GRUNN states) of the GRUNN  500  and the current input sequence (current input values x t ), the GRU network has the capability to learn the temporal patterns from input temporal sequences x t . For the SAR range-profile data, at a specific time, a range-profile vector represents the range-distribution in the spatial domain. Therefore, the GRUNN can learn the spatial-temporal patterns from SAR range-profile data. 
       FIG. 6  is a system block diagram of an example of an implementation of a GRU processing cell  600  of the GRUNN  500  is shown in accordance with the subject disclosure. In this example, the GRU processing cell  600  includes a first adder  602 , second adder  604 , third adder  606 , a fourth adder  608 , a first Hadamard product operator  610 , second Hadamard product operator  612 , third Hadamard product operator  614 , a first gate function  616 , second gate function  618 , and a hyperbolic tangent function  620 . The operation of the GRU processing cell  600  can be mathematically described by a set of equations given as follows: 
         z   t =σ( W   z   x   t   +U   z   h   t-1   +b   z );  (4)
 
         r   t =σ( W   r   x   t   +U   r   h   t-1   +b   r ); and  (5)
 
         h   t =(1− z   t )* h   t-1   +z   t *tan  h [ W   h   x   t   +U   h ( r   t   *h   t-1 )+ b   h ],  (6)
 
     where the gate function σ(x) is a logistic sigmoid function defined by the relationship 
     
       
         
           
             
               
                 
                   
                     σ 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         1 
                         + 
                         
                           e 
                           
                             - 
                             x 
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The gate function tan h(x) is a hyperbolic tangent function defined by the relationship 
     
       
         
           
             
               
                 
                   
                     tanh 
                     ⁡ 
                     
                       ( 
                       g 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           e 
                           x 
                         
                         - 
                         
                           e 
                           
                             - 
                             x 
                           
                         
                       
                       
                         
                           e 
                           x 
                         
                         + 
                         
                           e 
                           
                             - 
                             x 
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In these relationships, z t  is the updated gate variable of the GRU processing cell, r t  is the reset gate variable, and h t  is the state variable. The network parameters, W z , U z , b z , W r , U r , b r , U h , and b h  are learned from a learning process performed by the GRU processing cell. Again, the state variable, h t , is the output variable of the GRU processing cell and the notation * is the Hadamard product operation. In a complex GRU processing cell, if implemented as shown in  FIG. 4B , all the operations, multiplication, addition and the Hadamard product are complex operations and the gate functions are applied to the real part and imaginary part of the complex variables separately. 
     The states of the GRUNN  500  are high-dimensional vectors, which contain the spatial-temporal correlations of the input temporal sequences x t . In general, a readout neural network is needed to map the high-dimensional network state variables into the vectors in the application domain. In this example, the GRUNN  500  utilizes the multi-layer linear network  416 ,  418 , or  422  to map the high-dimensional network state variables into target class vectors. 
     Mapping GRUNN States to Target Class 
     In the fifth processing step  310 ,  FIG. 3 , a two-layer feed-forward neural network is used to map the GRUNN  500  states into class vectors Y C . In this example, H is defined as a GRUNN state vector and Y C  is defined by the relationship (9) 
         Y   C =σ( V   2 σ( V   1   H+b   1 )+ b   2 ),
 
     where the parameters, V 1 , V 2 , b 1 , and b 2 , are determined by a network training process and the magnitude Y C  is used for representing a class ID vector, which is a real value vector. The class ID vector is defined by the relationship (10) 
         Y   cm =[∥ y   c   1   ∥, . . . ∥y   c   m ∥],
 
     where the variable y c   i  is a complex component of Y C . The objective function (Obj) for training the GRUNN  500  is a real valued function defined by the relationship (11) 
     
       
         
           
             
               
                 
                   
                     Obj 
                     = 
                     
                       
                         1 
                         N 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           i 
                         
                         ⁢ 
                         
                            
                           
                             
                               
                                 Y 
                                 
                                   c 
                                   ⁢ 
                                   m 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                             - 
                             
                               
                                 Y 
                                 th 
                               
                               ⁡ 
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                           
                            
                         
                       
                     
                   
                   , 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     where the constant N is equal to the number of training data and the vector Y th (i) is the labeled data. 
     In this example, the training process includes initially setting all of the parameters of the GRUNN  500  to a random value uniformly distributed in the range of −1.0 to 1.0. The parameters or the GRUNN  500  are then updated by a gradient descent technique that is defined by the relationships 
     
       
         
           
             
               
                 
                   
                     
                       
                         W 
                         z 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           W 
                           z 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               W 
                               z 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         U 
                         z 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           U 
                           z 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               U 
                               z 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         W 
                         r 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           W 
                           r 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               W 
                               r 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         U 
                         r 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           U 
                           r 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               U 
                               r 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         W 
                         h 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           W 
                           h 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               W 
                               h 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         U 
                         h 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           U 
                           h 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               U 
                               h 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         V 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           V 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               V 
                               1 
                             
                           
                         
                       
                     
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         V 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           V 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         α 
                         ⁢ 
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               V 
                               2 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     where α is a learning rate. In this example, all of the derivatives from the relationships are calculated by an algorithm of back-propagation through time (BPTT) described in Paul J. Webos, “Backpropagation Through Time: What is does and How to do it,” Proceedings of the IEEE, Vol. 78, No. 10, pp. 1550-1560, 1990, which is herein incorporated by reference in its entirety. Moreover, in this example, for a complex variable, W=W r +jW i , the partial derivative of the complex variable is given by the relationship 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       W 
                     
                   
                   = 
                   
                     
                       
                         ∂ 
                         Obj 
                       
                       
                         ∂ 
                         
                           W 
                           r 
                         
                       
                     
                     + 
                     
                       j 
                       ⁢ 
                       
                         
                           
                             ∂ 
                             Obj 
                           
                           
                             ∂ 
                             
                               W 
                               i 
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     As an example of operation, the SAR system  200  was implemented and complex images test images from the Moving and Stationary Target Acquisition and Recognition (MSTAR) public data provided by DARPA/U.S. Air Force Research Laboratory where utilized to produce pseudo phase-history data and complex SAR range profile data that was processed by the SAR system  200 . 
     Turning to  FIGS. 7A-7C , examples of three samples of amplitudes of complex range-profile data produced from the MSTAR public data are shown in accordance with the subject disclosure. These samples are from three targets referred to as BMP2, M2, and T72 that are respectively shown in  FIGS. 7A, 7B, and 7C . In this example, each complex SAR range-profile data sequence converts one degree of target view and  FIGS. 7A-7C  presents some samples of the resulting SAR range profile data. Each range-profile data was scaled to a two-dimensional array with a size of 40 range bins by 60 time-steps. In this example, the SAR system  200  has 2400 SAR complex range-profile data sequences in the training data set and 450 complex range-profile data sequences in the testing data set. 
     To evaluate the benefits of utilizing the complex SAR range profile data for ATR, the SAR system  200  is implemented to test three processing methods that include: 1) processing only real SAR range-profile data (i.e., one GRUNN with real operations); 2) processing the real part and imaginary part of complex SAR range-profile data separately (i.e., utilizing the two GRUNN  400  and  402  with real operations); and 3) processing the real part and imaginary part jointly of complex SAR range-profile data (i.e., the single GRUNN  422  with complex operations). 
     In this example, in implementing the GRUNN, each GRUNN uses 60 GRU processing cells and each GRU processing cell uses 80 internal states. For the two-layer mapping network described by the relationship defining the class vector Y C , the first layer uses 80 neurons and the second layer uses 3 neurons, which are for the three-target tanks. In the training process, all testing networks are trained with 25 epochs and a learning rate of 0.0001. In the first processing method, a GRUNN with real operations is used to process the real SAR range-profile of our test data. The classification result on the testing data is shown in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Classification Result of Processing Real Range Profile Data 
               
            
           
           
               
               
               
            
               
                   
                 True Class 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 BMP2 
                 M2 
                 T72 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Computed Class 
                 BMP2 
                 0.8417 
                 0.0863 
                 0.0720 
               
               
                   
                   
                 M2 
                 0.1212 
                 0.7758 
                 0.1030 
               
               
                   
                   
                 T72 
                 0.0890 
                 0.0685 
                 0.8425 
               
            
           
           
               
               
               
               
            
               
                   
                 Average Rate 
                 82% 
               
               
                   
                   
               
            
           
         
       
     
     In this example, the GRUNN produces a reasonably good result with an average classification rate that is greater than 82%. This means the amplitude of SAR range-profile data carries the most information about the targets. 
     In the second processing method, the real part and imaginary part of the complex range-profile data are processed separately in the first GRUNN  400  and the second GRUNN  402  as shown in  FIG. 4A . Since only one objective function (as defined in relationship 11) is used for training the network, both the first GRUNN  400  and the second GRUNN  402  in  FIG. 4A  are jointly optimized to learn the weights of the network. Each GRU network (i.e., first GRUNN  400  and the second GRUNN  402 ) in  FIG. 4A  uses real value operations to process the real part and imaginary part of the complex range-profile data. The classification result from separately processing the real part and imaginary part of the complex SAR range-profile data is shown in Table 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Classification Result of Separate 
               
               
                 Processing Real and Imaginary Data 
               
            
           
           
               
               
               
            
               
                   
                 True Class 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 BMP2 
                 M2 
                 T72 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Computed Class 
                 BMP2 
                 0.9286 
                 0.0454 
                 0.0260 
               
               
                   
                   
                 M2 
                 0.0288 
                 0.9424 
                 0.0288 
               
               
                   
                   
                 T72 
                 0.0191 
                 0.0764 
                 0.9045 
               
            
           
           
               
               
               
               
            
               
                   
                 Average Rate 
                 93.18% 
               
               
                   
                   
               
            
           
         
       
     
     From these results it is appreciated that the separate GRUNN  400  and GRUNN  402  produces a better result with an average classification rate of greater than 90% compared to the GRUNN that only processes real range-profile data shown in Table 1. This result shows that the phase information of complex SAR range-profile data is helpful for target recognition. In the last processing method, the single complex GRUNN  422  in  FIG. 4B  is used to process the complex SAR range profile data. The classification result produced by the single complex GRUNN  422  is shown in Table 3. In this example, the single complex GRUNN  422  produces a slightly better result than the one produced by the separate GRUNN  400  and GRUNN  402 . However, the separate processing network utilizing GRUNN  400  and GRUNN  402  is computationally simpler than the single complex GRUNN  422  since the separate processing network (utilizing GRUNN  400  and GRUNN  402 ) uses real number operations. To complete a complex multiplication in the single complex GRUNN  422  requires completing four real-number multiplications. The separate processing network utilizing GRUNN  400  and GRUNN  402  only needs to perform two real-number multiplications for processing a multiplication of two complex numbers due to its two-channel real-number operations. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Classification Result of Separate 
               
               
                 Processing Real and Imaginary Data 
               
            
           
           
               
               
               
            
               
                   
                 True Class 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 BMP2 
                 M2 
                 T72 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Computed Class 
                 BMP2 
                 0.8916 
                 0.0602 
                 0.0482 
               
               
                   
                   
                 M2 
                 0.0 
                 0.9710 
                 0.0290 
               
               
                   
                   
                 T72 
                 0.0137 
                 0.0411 
                 0.9452 
               
            
           
           
               
               
               
               
            
               
                   
                 Average Rate 
                 93.60% 
               
               
                   
                   
               
            
           
         
       
     
     In this example, three different processing methods were testes with predetermined training and testing data sets. The average classification accuracy of the three different processing methods on the same testing data set is summarized as follows: the processing of only real data had an average classification rate of 82.00%; the processing of the real and imaginary data separately had an average classification rate of 93.16%; and the processing of real and imaginary data jointly has an average classification rate of 93.60%. 
     These results show that the method of processing the real amplitude data produces the poorest result and the method of using the complex GRUNN to process the complex data generates the best result. Moreover, the results also show that the phase information of complex SAR range profile data is helpful for target recognition and both the joint processing (complex GRUNN) and separate processing complex SAR range profile data via GRUNN  400  and GRUNN  402  can achieve comparable classification results. 
     In summary, the SAR system  200  is a SAR target recognition system that can identify different targets/objects without the use of SAR images. The SAR system  200  uses SAR range profile data to identify targets, which is computationally efficient and can enable real-time SAR target recognition from streaming raw SAR data. The proposed system is an extension of a previous invention of range profile SAR based ATR. In this example, the SAR system  200  utilizes complex SAR range profile data and a complex GRUNN to achieve ATR capability. The SAR system  200  is effective to improve target classification with complex SAR range profile data and a complex GRUNN. 
     Further, the disclosure comprises embodiments according to the following clauses. 
     Clause 1. A method, comprising: receiving raw synthetic aperture radar (SAR) data associated with observed views of a scene, wherein the raw SAR data comprises information captured via an automatic target recognition (ATR) system having a SAR system; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex SAR range profile data with a recurrent neural network (RNN) having RNN states; and mapping the RNN states to a target class with a multi-layer linear network. 
     Clause 2. The method of clause 1, wherein the RF preprocessing the received raw SAR data includes producing an in-phase component of the received raw SAR data and a quadrature-phase component of the received raw SAR data. 
     Clause 3. The method of clause 1 or 2, wherein the processed raw SAR data includes two-dimensional data that includes frequency band data and pulse domain data, and converting the processed raw SAR data comprises applying a Fourier transform to the pulse domain data to produce the complex SAR range profile data. 
     Clause 4. The method of clause 3, wherein the Fourier transform is a fast Fourier transform. 
     Clause 5. The method of clause 3, 4, or 5, wherein converting the processed raw SAR data further comprises applying a window function prior to applying the Fourier transform to the pulse domain data, and wherein the window function includes a Hanning window function and a Hamming window function. 
     Clause 6. The method of clause 3, 4, or 5, wherein the processed raw SAR data is represented by a two-dimensional array represented by PH(m, n), wherein m represents frequency band values of a row vector P f  of the frequency band data and n represents pulse domain values of a column vector P r  of the pulse domain data, and applying the window function includes determining a windowed pulse vector P w  using a relationship P w (i) equals P r (i) combined with w(i) via a Hadamard product operation, wherein w(i) is window function vector and i represents a range from zero to M, wherein M is a constant value that represents a number of sampling frequencies in the frequency band data, determining a range profile vector rp r (m) defined by a relationship defined as 
     
       
         
           
             
               
                 r 
                 ⁢ 
                 
                   
                     p 
                     r 
                   
                   ⁡ 
                   
                     ( 
                     m 
                     ) 
                   
                 
               
               = 
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     M 
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     
                       P 
                       w 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   ⁢ 
                   
                     e 
                     
                       
                         - 
                         j 
                       
                       ⁢ 
                       
                         
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           m 
                           ⁢ 
                           k 
                         
                         M 
                       
                     
                   
                 
               
             
             , 
           
         
       
     
     and determining a two-dimensional range profile RP(o, p) that is equal to RP[rp r (o)] r=0   T-1 , wherein o represents one-dimensional range bins of the two-dimensional range profile RP(o, p) and p represents one-dimensional time-steps of the two-dimensional range profile. 
     Clause 7. The method of clause 1, 2, 3, 4, 5, or 6, wherein the complex SAR range profile data includes an in-phase component of the complex SAR range profile data and a quadrature-phase component of the complex SAR range profile data, wherein the processing the complex SAR range profile data with the RNN includes processing the in-phase component of the complex SAR range profile data with a first gated recurrent unit (GRU) neural network (GRUNN) having first GRUNN states and processing the quadrature-phase component of the complex SAR range profile data with a second GRUNN having second GRUNN states, and wherein the mapping the RNN states to the target class includes mapping the first GRUNN states to a first target sub-class and mapping the second GRUNN states to a second target sub-class and determining a target identification from the mapped first target sub-class and the mapped second target sub-class. 
     Clause 8. The method of clause 6, wherein the complex SAR range profile data includes an in-phase component of the complex SAR range profile data and a quadrature component of the complex range profile data, the processing the complex SAR range profile data with the RNN includes processing both the in-phase component of the complex SAR range profile data and quadrature component of the complex SAR range profile data with a gated recurrent unit (GRU) neural network (GRUNN) having GRUNN states, and the mapping the RNN states to the target class includes mapping the GRUNN states to the target class, and the method further comprises determining a target identification from the mapped target class. 
     Clause 9. The method of clause 8, wherein the processing both the in-phase component of the complex SAR range profile data and quadrature-phase component of the complex SAR range profile data with the GRUNN includes processing the in-phase component of the complex SAR range profile data and quadrature-phase component of the complex SAR range profile data with a plurality of GRU processing cells within the GRUNN utilizing complex operations within each of the plurality of GRU processing cells, wherein the plurality of GRU processing cells are sequentially connected to each other and each of the plurality of GRU processing cells has a GRU processing cell input that is a temporal sequence x t  and a GRU processing cell output h t  that is a GRUNN state of the GRUNN states. 
     Clause 10. The method of clause 9, wherein each of the plurality of GRU processing cells performs a sub-method that includes receiving x t  and a previous GRU processing cell output h t-1 , and producing an updated gate variable z t  and a reset gate variable r t , wherein the GRU processing cell output h t  is a state variable, wherein z t  is produced by a first gate function of a first combination of a first product of a first network parameter W z  and x t , a second product of a second network variable U z  and h t-1 , and a third network parameter b z , r t  is produced by the first gate function of a second combination of a third product of a fourth network parameter W r  and x t , a fourth product of a fifth network variable U r  and h t-1 , and a sixth network parameter b r , and h t  is produced by a relationship defined as h t =(1−z t )*h t-1 +z t *tan h[W h x t +U h (r t *h t-1 )+b h ], wherein W h  is a seventh network parameter, U n  is an eighth network parameter, and b h  is a ninth network parameter, wherein the first gate function is a logistic sigmoid function as a function of d defined by 
     
       
         
           
             1 
             
               1 
               + 
               
                 e 
                 
                   - 
                   d 
                 
               
             
           
         
       
     
     and tan h is a second gate function that is a hyperbolic tangent function as a function of g defined as 
     
       
         
           
             
               
                 tanh 
                 ⁡ 
                 
                   ( 
                   g 
                   ) 
                 
               
               = 
               
                 
                   
                     e 
                     g 
                   
                   - 
                   
                     e 
                     
                       - 
                       g 
                     
                   
                 
                 
                   
                     e 
                     g 
                   
                   + 
                   
                     e 
                     
                       - 
                       g 
                     
                   
                 
               
             
             , 
           
         
       
     
     and wherein * is the Hadamard product operation. 
     Clause 11. The method of clause 10, wherein the W z , U z , b z , W r , U r , b r , W h , U h , and b n  are learned from a learn process performed by the GRU processing cell. 
     Clause 12. The method of clause 11, wherein the first gate function and the second gate function are applied to the in-phase component of the complex SAR range profile data separately from the quadrature component of the complex range profile data. 
     Clause 13. The method of clause 10, wherein the mapping the RNN states to the target class with the multi-layer linear network includes utilizing a two-layer feed-forward neural network, as the multi-layer linear network, to map the GRUNN states to a plurality of class vectors, wherein a class vector Y c , of the plurality of class vectors, is related to a GRUNN vector H, a tenth network parameter V 1 , eleventh network parameter V 2 , a twelfth network parameter b 1 , and a thirteenth network parameter b 2 , wherein Y c  is defined utilizing a relationship defined as Y C =σ(V 2 σ(V 1 H+b 1 )+b 2 ), wherein σ(d) is the first gate function and is a logistic sigmoid function as a function of d, and wherein V 1 , V 2 , b 1 , and b 2  are determined by a network training process. 
     Clause 14. The method of clause 13, wherein the determining the target identification from the mapped target class includes determining a magnitude of Y c  to represent a class identification vector Y cm  that is defined as Y cm =[∥y c   1 ∥, . . . ∥y c   m ∥], where y c   i  is a complex component of Y c . 
     Clause 15. The method of clause 14, wherein an objective function Obj for training the GRUNN is defined as 
     
       
         
           
             
               Obj 
               = 
               
                 
                   1 
                   N 
                 
                 ⁢ 
                 
                   Σ 
                   i 
                 
                 ⁢ 
                 
                    
                   
                     
                       
                         Y 
                         
                           c 
                           ⁢ 
                           m 
                         
                       
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                     - 
                     
                       
                         Y 
                         th 
                       
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                   
                    
                 
               
             
             , 
           
         
       
     
     wherein N is a constant that is equal to a total quantity of training data and Y th (i) is a labeled data, wherein mapping the RNN states to the target class further includes randomly initializing each network parameter W z , U z , b z , W r , U r , b r , W h , U h , b n , V 1 , V 2 , b 1 , and b 2  to an initialization value that is uniformly distributed between a range of −1.0 to 1.0, and wherein the network parameters are updated by relationships 
     
       
         
           
             
               
                 
                   W 
                   z 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     W 
                     z 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         W 
                         z 
                       
                     
                   
                 
               
             
             , 
             
               
                 
                   U 
                   z 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     U 
                     z 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         U 
                         z 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   W 
                   r 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     W 
                     r 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         W 
                         r 
                       
                     
                   
                 
               
             
             , 
             
               
                 
                   U 
                   r 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     U 
                     r 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         U 
                         r 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   W 
                   h 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     W 
                     h 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         W 
                         h 
                       
                     
                   
                 
               
             
             , 
             
               
                 
                   U 
                   h 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     U 
                     h 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         U 
                         h 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   V 
                   1 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     V 
                     1 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         V 
                         1 
                       
                     
                   
                 
               
             
             , 
             
               
                 and 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     V 
                     2 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
               
               = 
               
                 
                   
                     V 
                     2 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       - 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   α 
                   ⁢ 
                   
                     
                       ∂ 
                       Obj 
                     
                     
                       ∂ 
                       
                         V 
                         2 
                       
                     
                   
                 
               
             
             , 
           
         
       
     
     where α is a learning rate. 
     Clause 16. An automatic target recognition (ATR) system having a synthetic aperture radar (SAR) configured to perform the method of claim  1 , the ATR system comprising: a memory comprising a plurality of executable instructions and adapted to store template range profile data; the SAR system; and one or more processors configured as the RNN and the multi-layer linear network for executing the plurality of instructions to perform the method of clause 1. 
     Clause 17. A synthetic aperture radar (SAR) system for target recognition with complex range profile, the SAR system comprising: a memory; a recurrent neural network (RNN); a multi-layer linear network in signal communication the recurrent neural network; a machine-readable medium on the memory, the machine-readable medium storing instructions that, when executed by the RNN, cause the SAR system to perform operations comprising: receiving raw SAR data associated with observed views of a scene, wherein the raw SAR data comprises information captured via the SAR system; radio frequency (RF) preprocessing the received raw SAR data to produce a processed raw SAR data; converting the processed raw SAR data to a complex SAR range profile data; processing the complex SAR range profile data with the RNN having RNN states; and mapping the RNN states to a target class with the multi-layer linear network. 
     Clause 18. The SAR system of clause 17, wherein the RNN and the multi-layer linear network are configured on one or more processors. 
     Clause 19. The SAR system of clause 17, wherein the complex SAR range profile data includes an in-phase component of the complex SAR range profile data and a quadrature component of the complex range profile data, the processing the complex SAR range profile data with the RNN includes processing the complex SAR range profile data with gated recurrent unit (GRU) neural network (GRUNN) having GRUNN states that includes processing both the in-phase component of the complex SAR range profile data and quadrature component of the complex SAR range profile data with a plurality of GRU processing cells within the GRUNN utilizing complex operations within each of the plurality of GRU processing cells, and the plurality of GRU processing cells are sequentially connected to each other and each of the plurality of GRU processing cells has a GRU processing cell input that is a temporal sequence x t  and a GRU processing cell output h t  that is a GRUNN state of the GRUNN states. 
     Clause 20. The SAR system of clause 19, wherein each of the plurality of GRU processing cells performs a sub-method that includes receiving x t  and a previous GRU processing cell output h t-1  and producing an updated gate variable z t  and a reset gate variable r t , wherein the GRU processing cell output h t  is a state variable, wherein z t  is produced by a first gate function of a first combination of a first product of a first network parameter W z  and x t , a second product of a second network variable U z  and h t-1 , and a third network parameter b z , r t  is produced by the first gate function of a second combination of a third product of a fourth network parameter W r  and x t , a fourth product of a fifth network variable U r  and h t-1 , and a sixth network parameter b r , and h t  is produced by a relationship defined as 
         h   t =(1− z   t )* h   t-1   +z   t *tan  h [ W   h   x   t   +U   h ( r   t   *h   t-1 )+ b   h ],
 
     wherein W h  is a seventh network parameter, U n  is an eighth network parameter, and b h  is a ninth network parameter, wherein the first gate function is a logistic sigmoid function as a function of d defined by 
     
       
         
           
             1 
             
               1 
               + 
               
                 e 
                 
                   - 
                   d 
                 
               
             
           
         
       
     
     and tan h is a second gate function that is a hyperbolic tangent function as a function of g defined as 
     
       
         
           
             
               
                 tanh 
                 ⁡ 
                 
                   ( 
                   g 
                   ) 
                 
               
               = 
               
                 
                   
                     e 
                     g 
                   
                   - 
                   
                     e 
                     
                       - 
                       g 
                     
                   
                 
                 
                   
                     e 
                     g 
                   
                   + 
                   
                     e 
                     
                       - 
                       g 
                     
                   
                 
               
             
             , 
           
         
       
     
     and wherein * is a Hadamard product operation. 
     Clause 21. The SAR system of clause 20, wherein the W z , U z , b z , W r , U r , b r , W h , U h , and b n  are learned from a learn process performed by the GRU processing cell. 
     It will be understood that various aspects or details of the disclosure can be changed without departing from the scope of the disclosure. It is not exhaustive and does not limit the claimed disclosures to the precise form disclosed. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation. Modifications and variations are possible in light of the above description or can be acquired from practicing the disclosure. The claims and their equivalents define the scope of the disclosure. Moreover, although the techniques have been described in language specific to structural features and/or methodological acts, it is to be understood that the appended claims are not necessarily limited to the features or acts described. Rather, the features and acts are described as example implementations of such techniques. 
     To the extent that terms “includes,” “including,” “has,” “contains,” and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition word without precluding any additional or other elements. Moreover, conditional language such as, among others, “can,” “could,” “might” or “may,” unless specifically stated otherwise, are understood within the context to present that certain examples include, while other examples do not include, certain features, elements and/or steps. Thus, such conditional language is not generally intended to imply that certain features, elements and/or steps are in any way required for one or more examples or that one or more examples necessarily include logic for deciding, with or without user input or prompting, whether certain features, elements and/or steps are included or are to be performed in any particular example. Conjunctive language such as the phrase “at least one of X, Y or Z,” unless specifically stated otherwise, is to be understood to present that an item, term, etc. may be either X, Y, or Z, or a combination thereof. 
     In some alternative examples of implementations, the function or functions noted in the blocks may occur out of the order noted in the figures. For example, in some cases, two blocks shown in succession may be executed substantially concurrently, or the blocks may sometimes be performed in the reverse order, depending upon the functionality involved. Also, other blocks may be added in addition to the illustrated blocks in a flowchart or block diagram. Moreover, the operations of the example processes are illustrated in individual blocks and summarized with reference to those blocks. The processes are illustrated as logical flows of blocks, each block of which can represent one or more operations that can be implemented in hardware, software, or a combination thereof. In the context of software, the operations represent computer-executable instructions stored on one or more computer-readable medium that, when executed by one or more processing units, enable the one or more processing units to perform the recited operations. Generally, computer-executable instructions include routines, programs, objects, modules, components, data structures, and the like that perform particular functions or implement particular abstract data types. The order in which the operations are described is not intended to be construed as a limitation, and any number of the described operations can be executed in any order, combined in any order, subdivided into multiple sub-operations, and/or executed in parallel to implement the described processes. The described processes can be performed by resources associated with one or more device(s) such as one or more internal or external CPUs or GPUs, and/or one or more pieces of hardware logic such as FPGAs, DSPs, or other types of accelerators. 
     All of the methods and processes described above may be embodied in, and fully automated via, software code modules executed by one or more general purpose computers or processors. The code modules may be stored in any type of computer-readable storage medium or other computer storage device. Some or all of the methods may alternatively be embodied in specialized computer hardware.