Abstract:
A system and method for mapping a target scene by means of scanning radar utilizing the Doppler effect that arises in the event of movement between radar and target scene, where the movement of a platform upon which the radar&#39;s antenna is mounted is calculated utilizing navigation data obtained for the platform. The system and method can generate high-resolution radar images in an almost forward-looking application. This is achieved by introducing an approach compensation ( 7 ), in which the signal quantity received by the radar which is related to transmitted pulses is transformed pulse by pulse to a corresponding movement-corrected signal quantity by displacement in time and phase, dependent upon the platform&#39;s movement along an imaginary platform movement directed in such a way that the antenna&#39;s momentary direction is essentially 90° to the direction of the movement of the imaginary platform.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This Application claims priority under 35 U.S.C. §119 to European Patent Application 05445017.6 filed on Mar. 29, 2005, the entire contents of which are incorporated herein by reference. 
       BACKGROUND 
       [0002]    The present disclosure relates to a system and method for mapping a target scene using scanning radar utilizing the Doppler effect that arises in the event of movement between the radar and the target scene, in which the movement of a platform on which the radar&#39;s antenna is mounted is calculated utilizing navigation data obtained for the platform. 
         [0003]    As radar is one of the few available sensors for detailed ground mapping, there are continual requirements for further development of the technology. Other commonly used sensors, such as infrared and video sensors, utilize only image processing for image analysis, whereas, using radar technology, it is also possible to take advantage of the signal characteristics that are unique for each specific target. The radar technology has thus the advantage that signal processing and image processing can be combined. 
         [0004]    Viewed historically, radar has been of great significance in association with military applications. At its commencement, the technology made possible the detection of aircraft and vessels. In spite of the limitations of the systems of the time, the enemy could usually be detected in good time, whereby unnecessary losses were avoided. Today, thanks to the developments in technology, detection capabilities have improved considerably. As modern radar technology, in combination with complex signal and image processing, in many cases enables radar images to be of photographic quality, reconnaissance over land and inside archipelagos is nowadays a normal radar application. 
         [0005]    In spite of the developments, problems still remain that restrict the use of radar. One such a problem relates to the ability to generate high-resolution radar images within an adjacent angular interval around the platform motion direction. Phenomena that limit the image generation include Doppler variation and range or distance variation. Both phenomena will be discussed in greater detail below with reference to the figures. A situation as described above with forward-scanning radar is very common in association with military applications, where an approach is expected to take place in the direction of the target. 
         [0006]    Ever since the principles of Doppler resolution became known, radar engineers have tried to utilize in an optimal way the Doppler effect that arises when there is movement between radar and target scene. It will be demonstrated below that the Doppler bandwidth is of decisive importance for the size of the angular resolution. As the illumination angle, that is the angle between movement vector and target, has a large influence on the Doppler characteristics of the illuminated target, the angular resolution is also dependent upon a corresponding angle. Angular resolution, that is given by effective antenna beam width ψ e  divided by a predefined beam sharpening factor R FSAR , is derived below according to 
         [0000]    
       
         
           
             
               
                 
                   
                     ψ 
                     d 
                   
                   = 
                     
                    
                   
                     
                       ψ 
                       e 
                     
                     
                       R 
                       FSAR 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       λ 
                       / 
                       l 
                     
                     
                       
                         
                           2 
                            
                           λ 
                            
                           
                               
                           
                            
                           
                             υ 
                             p 
                           
                         
                         
                           
                             ω 
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                            
                           
                             l 
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                        
                       
                         sin 
                          
                         
                           ( 
                           φ 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ω 
                         s 
                       
                        
                       l 
                     
                     
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                        
                       
                         υ 
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                        
                       
                         sin 
                          
                         
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         [0007]    where λ corresponds to the signal&#39;s wavelength, l is the physical antenna size, υ p  is the platform speed, ω s  is the antenna&#39;s scan rate and φ is the antenna angle. 
         [0008]    At a constant scan rate, all parameters apart from sin(φ) can be assumed to be constant. As the term sin(φ) is found in the denominator in the correlation above, it can be seen that optimal resolution is obtained for the target angle 90°, while small target angles (→0°) do not allow any coherent integration. The angle 0° corresponds here to the platform&#39;s direction of travel, while the angle 90° corresponds to an antenna angle perpendicular to the direction of travel. 
         [0009]    In a target seeker application, an angular interval of approximate size±30° is of particularly great interest, as the approach is assumed to be taking place towards a threatening object. 
         [0010]    Traditionally, radar modes that utilized forward-scanning antenna have been classified within the category DBS (Doppler Beam Sharpening), see Donald R. Wehner, “High-Resolution Radar, Second Edition”, ISBN 0-89006-727-9, Artech House 1995. 
         [0011]    The focusing that traditionally was carried out by filtering, often required extremely complex filter banks to be applied. As each subfilter was optimized for a given spectral area (regarding band width and sidelobe handling), a large number of subfilters were required in order to cover the whole spectral area. 
         [0012]    As modern spectral analysis increasingly utilizes FFT-based (Fast Fourier Transform) tools, these methods have increasingly replaced old technology. Utilizing FFT-related methods, traditional bandpass filtering can be carried out and, in addition, more precisely matched filtering is made possible. The methods differ in execution and also in how the received signal quantity is to be pre-processed. Focusing by bandpass filtering requires a frequency-expanded signal in order for focusing to be achieved. Matched filtering in turn requires a demodulated signal quantity where angle-separated targets are distinguished by frequency. 
         [0013]    Matched filtering integrates all the signal energy belonging to a particular frequency component (a particular target). 
         [0014]    Bandpass filtering suppresses unwanted frequency components. 
       SUMMARY 
       [0015]    The great difference in the focusing techniques, signal integration and signal reduction respectively, has led to the former technology increasingly being classified as SAR (Synthetic Aperture Radar), see Carrara, Goodman, Majewski, “Spotlight Synthetic Aperture Radar, Signal Processing Algorithms”, ISBN 0-89006-728-7, Artech House 1995, instead of DBS. Hence the method developed according to this disclosure has been given the name “Forward-Scanning Synthetic Aperture Radar (FSSAR)”. 
         [0016]    How the collected signal quantity is prepared for coherent integration will be discussed in greater detail below with reference to the attached drawings. 
         [0017]    The object of the present disclosure is to achieve a system and method by means of which high-resolution radar images can be generated in a forward-scanning application. 
         [0018]    The object of the disclosure is achieved by a method characterized in that, for approach compensation, a signal quantity received by the radar related to transmitted pulses is transformed pulse by pulse to a corresponding movement-corrected signal quantity by displacement in time and phase dependent upon the platform&#39;s movement along an imaginary platform movement directed in such a way that the antenna&#39;s momentary direction essentially forms 90° with the movement vector for the movement of the imaginary platform. 
         [0019]    The approach compensation is advantageously carried out in the frequency domain and its size in time T and phase θ is calculated by the correlations: 
         [0000]        T= 2 R/c  and 
         [0000]      θ=(4π/λ c ) R,    
         [0000]    where R is the distance a respective echo is to be displaced, c is the propagation speed and λ c  is the signal&#39;s wavelength. By carrying out the approach compensation in the frequency domain, it can be carried out effectively and in combination with pulse compression. Pulse compression is known in association with radar applications, but not in combination with other steps comprised in our method, which steps interact in a favourable way. 
         [0020]    According to another further development of the system and method according to the disclosure, a reference function is created by: placing a reference target in the platform&#39;s direction of movement; assuming that the reference target is illuminated during the whole of the movement of the platform and across all antenna angles; calculating the phase variation θ ref  that has arisen; creating a reference signal according to S ref =exp(jθ ref ); approach compensating S ref , and by the signal quantity being demodulated by multiplication by the conjugate of the reference function. The demodulated signal quantity can thereby advantageously be angle focused, preferably by a calculation-efficient Fourier transform (FFT). 
         [0021]    According to yet another further development of the system and method according to the disclosure, the angle-focused signal quantity is projected onto a linear frequency scale, whereby a linear correlation is obtained between the target&#39;s initial time position and its final frequency position. 
         [0022]    According to an embodiment of the method according to the disclosure, the scan rate of the scanning radar is kept constant. In this way, radar systems constructed for constant scan rate, which are normally available on the market, can be utilized to realize the method. 
         [0023]    According to an alternative embodiment of the method, the radar&#39;s scan rate can be varied to obtain an essentially constant resolution within the scan area. For this, the radar&#39;s scan rate ω s  is suitably determined by the correlation: 
         [0000]    
       
         
           
             
               ω 
               s 
             
             = 
             
               
                 
                   2 
                    
                   λυ 
                 
                 
                   
                     R 
                     FSAR 
                   
                    
                   
                     l 
                     2 
                   
                 
               
                
               
                 sin 
                  
                 
                   ( 
                   φ 
                   ) 
                 
               
             
           
         
       
     
         [0024]    where λ corresponds to the signal&#39;s wavelength, υ p  is the platform speed, R FSAR  is the beam sharpening factor, l is the physical size of the antenna and φ is the antenna angle. 
         [0025]    The method and system according to the disclosure is particularly advantageous within a limited angular interval in the radar platform&#39;s direction of movement and, according to a suitable embodiment of the method, the mapping of the target scene is carried out within an angular range of approximate size ±30° during the approach towards the target scene. 
         [0026]    According to yet another embodiment of the method, this comprises an IMU-system connected to the radar platform, which continuously measures the movement of the platform. In combination with the IMU-system, there is, in addition, an INS-system which includes a movement calculation filter. The combination of IMU and INS means in this way that the movement of the platform can be kept updated with great precision, which is preferred for the system and method according to the disclosure. 
         [0027]    The basic principles according to the method above can be combined with other radar-based mapping methods and a further development of the method is characterized in that other radar-based mapping methods are utilized in combination with the method, in parts of the angular range to be mapped. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]    The system and method of this disclosure will be described below in greater detail with reference to the attached drawings, in which: 
           [0029]      FIG. 1  shows schematically the functions that constitute the system and method according to the disclosure. 
           [0030]      FIG. 2  shows an example of simulation geometry with target positions, scan interval and platform geometry included. 
           [0031]      FIG. 3  shows an example of platform movement before and after approach correction by enlargement of the platform area according to  FIG. 2 . 
           [0032]      FIG. 4   a  shows an example of the effect of the distance variation on the signal quantity without time correction, for radar with constant scan. 
           [0033]      FIG. 4   b  shows an example of the effect of the distance variation according to  FIG. 4   a  on signal quantity, but with time correction introduced. 
           [0034]      FIG. 5   a  shows an example of the effect of angle-dependent frequency displacement without phase correction. 
           [0035]      FIG. 5   b  shows an example of the effect of angle-dependent frequency displacement according to  FIG. 5   a , but with phase correction. 
           [0036]      FIG. 6   a  shows a proposed reference function together with simulated point targets according to  FIG. 2 . 
           [0037]      FIGS. 6   b  and  7   a  show the reference function conjugated according to  FIG. 6   a  and simulated point targets according to  FIG. 2  after demodulation using the reference function. 
           [0038]      FIG. 7   b  shows an FFT-based angle focusing of the target according to  FIG. 7   a , where  FIG. 7   a  is identical to  FIG. 6   b.    
           [0039]      FIGS. 8   a - 8   c  show the projection of a non-linear spectrum according to  FIG. 7   b  onto a linear spectrum according to  FIG. 8   c , with non-linear and linear frequency scales being illustrated in  FIG. 8   b.    
           [0040]      FIG. 9  shows an example of how the radar&#39;s scan rate can be varied in order to achieve constant angular resolution, where the angle 180° corresponds to the platform&#39;s direction of movement. 
           [0041]      FIG. 10   a  shows an example of the effect of the distance variation on the signal quantity without time correction, for radar with variable scan rate. 
           [0042]      FIG. 10   b  shows an example of the effect of the distance variation according to  FIG. 10   a  on the signal quantity, but with the introduction of time correction. 
           [0043]      FIG. 11  shows an example of the target&#39;s frequency variation with approach compensation. 
           [0044]      FIG. 12   a  shows an example of a proposed reference function for demodulation of illuminated targets together with the targets according to  FIG. 2 . 
           [0045]      FIG. 12   b  shows the conjugate of the reference function in  FIG. 12   a  and the targets after demodulation. 
           [0046]      FIG. 13  shows, for a case with constant angular resolution, the result of demodulated signal quantity after FFT-focusing and projection onto a linear angle scale. 
       
    
    
     DETAILED DESCRIPTION 
       [0047]    The system and method will now be described schematically with reference to  FIG. 1  and will then be discussed in greater detail in the following with reference to the subsequent drawings. 
         [0048]    According to  FIG. 1 , there is a received signal quantity in the form of raw data  1 . The signal quantity comprises reflections of a previously transmitted pulse. The angular range or distance diagram  2  illustrates the signal quantity&#39;s propagation in distance and in angle for a point target  3 . As no signal compression has been carried out, the signal is extended in the respective dimensions. In addition to the signal&#39;s propagation, the effect of distance variation arising due to the radar platform&#39;s approach movement is also shown in the angular distance diagram  2 . 
         [0049]    As a first step, pulse compression of the received signal quantity is carried out according to known principles within the field of radar technology. The function block has been given the reference numeral  4 . The pulse compression that integrates the signal energy in range is suitably carried out in the frequency plane. The angular distance diagram  5  shows the signal&#39;s propagation  6  after pulse compression. 
         [0050]    In association with pulse compression, or as a subsequent element, approach compensation is carried out in a function block  7 . In principle, an imaginary movement of the radar platform is carried out, on the basis of the radar platform&#39;s actual movement and direction of scan in relation to the target scene. The approach compensation compensates for platform motion-dependent time and phase displacement. The angular distance diagram  8  shows how the signal energy for a point target  9  is placed at the same range gate after time compensation has been carried out. An angular frequency diagram  10  shows how the target&#39;s frequency variation is centred around the zero frequency after corresponding phase compensation. The approach compensation is carried out most effectively in the frequency plane, for which reason the embodiment is suitably combined with pulse compression. 
         [0051]    A function block  11  creates a reference function and utilizes this reference function for demodulation of the target&#39;s frequency variation. How the reference function is created is described elsewhere in this description. The frequency variation of the reference function conforms to frequency variation of the illuminated target with the exception of a constant frequency component, using which the demodulated target is placed in a fixed frequency window according to the angular frequency diagram  13 . As the demodulation only adjusts the target&#39;s phase, the target&#39;s distance remains unchanged according to the angular distance diagram  12 . 
         [0052]    After demodulation, the signal is angle focused by means of a calculation-efficient Fourier transform (FFT) in a function block  14 . The Fourier transform that integrates signal energy as a function of frequency generates an almost point-shaped target  16  in the angular distance diagram  15 . However, the focused target is placed in an incorrect angular position as a result of the reference function&#39;s non-linear frequency variation. By re-sampling of the non-linear frequency spectrum to a corresponding linear spectrum in a function block  17 , a point-shaped target  16  is obtained, which, in the angular distance diagram  18 , has assumed a position that conforms well with reality. The relationship between non-linear and linear frequency spectrum is described elsewhere in the description. 
         [0053]    The process involved will now be described below in greater detail with reference to  FIG. 1  and firstly compensation of the approach speed will be discussed with reference to  FIGS. 2 ,  3 ,  4   a ,  4   b ,  5   a  and  5   b.    
         [0054]    In order to clarify the discussion concerning partial elements that constitute the proposed focusing algorithm, a simulation geometry is utilized according to  FIG. 2 . In total, five point targets  19 - 23  are simulated, located at the same distance (4000 metres) and with an angular separation of 5°. The signal characteristics of the respective targets  19 - 23  are studied step by step in order to demonstrate the interaction of the partial elements. The lines  24  and  25  mark the outer limits of the radar&#39;s scan area and the reference numeral  26  marks the position of the platform. 
         [0055]    As for other SAR-algorithms, it is necessary to take into account the approach movement of the platform. Here this is carried out by transforming received signal quantity to a movement-corrected corresponding value. Movement correction is carried out in such a way that all the received signal quantity belonging to a certain transmitted pulse is displaced in time and phase in a suitable way. The size of the displacement depends on the movement of the platform and is calculated using navigation data.  FIG. 3  illustrates how movement correction is carried out in the proposed method. 
         [0056]    Firstly, a distance R is calculated for each platform position where a pulse is transmitted. In  FIG. 3 , a pulse has been sent in the positions  27 - 30 . The distance R extends from the respective position  27 - 30  towards an imaginary movement path  31  for the movement of the platform. The size of R is to be such that a new imaginary platform movement is created, where the momentary antenna direction is 90° relative to the movement of the imaginary platform. In other words, this means that when a corrected movement has been utilized for data collection, a constant antenna direction at right angles to the movement vector would have been required in order to illuminate the same area. The appearance of the corrected movement is of little significance, providing that the above requirement is fulfilled. 
         [0057]    The discussed approach compensation is carried out most effectively in the frequency plane and its size is obtained by: 
         [0000]    
       
         
           
             T 
             = 
             
               2 
                
               
                 R 
                 / 
                 c 
               
             
           
         
       
       
         
           
             θ 
             = 
             
               
                 
                   4 
                    
                   π 
                 
                 
                   λ 
                   c 
                 
               
                
               R 
             
           
         
       
     
         [0000]    where c is the propagation speed of the signal and λ c  is the wavelength of the signal. 
         [0058]    According to the disclosure, the same target areas are illuminated as in the original data collection geometry,  FIG. 1 , but, with signal displacement having been carried out (according to T and θ), unwanted signal characteristics are eliminated, which will be discussed next. In movement according to the original geometry, there is an approach between platform and target area, which gives rise to two negative signal effects. Firstly, there is a certain amount of distance variation (dependent on ω s  &amp; υ p ), which means that the signal energy moves through a plurality of adjacent range or distance gates. This effect, illustrated in  FIG. 4   a , results in a distance spreading of focused targets. The time displacement described above with reference to  FIG. 3  compensates for the distance variation, whereby the signal energy of the respective target ends up in the correct distance gate. The size of the distance variation in  FIG. 4   a  is moderate, as low platform velocity is combined with high scan rate. 
         [0059]    The second effect that arises as a result of approach movement is an angle-dependent phase displacement. This results in unwanted wrapping phenomena, which is illustrated in  FIG. 5   a . Wrapping, which arises when the Nyquist sampling theorem is not fulfilled, involves a frequency shift from π→−π or from −π→π. By phase compensating the signal (according to 0) in proportion to the previous time displacement, an adjusted (zero-centred) signal quantity is obtained according to  FIG. 5   b . The lines  32 - 36  in  FIG. 5   a  and the lines  37 - 41  in  FIG. 5   b  correspond to the normalized frequency variation of the illuminated targets  19 - 23 . The Nyquist sampling theorem is described in the reference Samir S. Soliman, Mandyam D. Srinath, “Continuous and Discrete Signals and Systems”, ISBN 0-13-569112-5, Prentice-Hall. 
         [0060]    In the section above, it has been explained how the movement of the platform is taken into account. In order for this to be able to be realized, precise knowledge of the movement is required. As modern radar systems are increasingly being equipped with IMU-systems (Inertial Measurement Unit), the required platform movement can be measured with great precision. 
         [0061]    According to previous requirements, it is necessary for all the targets to be separated by frequency in order for focusing FFT to be possible. How this is achieved is explained in greater detail here. 
         [0062]    After approach compensation, all the targets are centred around the frequency zero. The target&#39;s frequency variation varies, however, dependent upon its angular position. Small target angles result in limited frequency bandwidth (size of gradient), which results in low resolution. Increasing target angles result in higher bandwidth and thereby improved resolution. In order to obtain the resolution that the bandwidth makes possible, it is necessary for frequency modulation of all the targets to be eliminated. 
         [0063]    In order to make this possible, it is necessary to know the angle-dependent Doppler variation. The method proposed utilizes a reference target against which the phase variation is calculated. A reference function is created according to the following: place an imaginary reference target in the platform&#39;s direction of travel; assume that the reference target is illuminated during the whole of the flight distance and across all antenna angles; calculate the phase variation θ ref  that has arisen; create a reference signal according to S ref =exp(jθ ref ); approach compensate S ref  (only the phase needs to be taken into consideration). 
         [0064]    The proposed reference function can be regarded as a signal created on the basis of the distance difference between the approach-compensated platform movement  31  and the imaginary positioned reference target. The frequency variation calculated in this way corresponds to the Doppler variation that has arisen for the whole target area. Only the difference is a constant frequency component, which makes target separation possible. 
         [0065]      FIG. 6   a  illustrates the normalized frequency variation  42  of the reference function together with the corresponding values  37 - 41  of the illuminated targets. 
         [0066]      FIG. 6   b  shows how the targets  37 - 41  are separated with regard to frequency by demodulation, that is to say by multiplication of signal quantity and the conjugate  43  of the reference function  42 . The ability to separate adjacent targets increases for large antenna angles, as the frequency derivative, the gradient of the curve, increases. This is in agreement with the equation for the angular resolution discussed in the introduction to this description, according to which high resolution is obtained for large target angles. 
         [0067]    It is worth noting that the reference function  43  intersects the respective targets  37 - 41  at their midpoint. This fact, which is of great significance for the final image presentation, is discussed later in this section. 
         [0068]    As target separation by frequency has been fulfilled, angle focusing a calculation-efficient Fourier transform is possible at this stage. In order to optimize the efficiency of the calculation, the FFT length is set to a second power by zero padding. The Fourier transform that integrates signal energy as a function of frequency creates here five well-compressed point targets, according to  FIG. 7   b.    
         [0069]    As the frequency variation  59  of the reference function is non-linear, the demodulated point targets will also be separated in a non-linear way with regard to frequency. The result is thus that, after angle focusing, the original symmetrically-positioned targets are positioned asymmetrically. This fact that is illustrated in  FIG. 7   b  and  FIG. 8   a  means that an angle-related and frequency-related re-sampling must be carried out in order for correct image geometry to be obtained. 
         [0070]    h the method according to the disclosure, this re-sampling is carried out by a transformation of the non-linear angle spectrum to a linear angle scale, according to  FIG. 8   b . The point targets in the simulation model are thus placed in the correct position,  FIG. 8   c , by projecting, see the lines  44 - 46 ,  47 - 49 ,  50 - 52 ,  53 - 55  and  56 - 58 , the non-linear result from  FIG. 8   a  onto a linear frequency scale,  FIG. 8   b . The projection thus involves the original spectrum being displaced as a function of the difference between the linear and non-linear frequency scales. 
         [0071]    The re-sampling results, in addition, in the target&#39;s resolution becoming angle-dependent. A lower resolution is obtained for small target angles, while large target angles result in improved resolution. This conclusion that is in agreement with the equation for angular resolution is illustrated in  FIG. 8   c.    
         [0072]    A result that relates to antenna scan with constant rate has been described above. It can, however, be attractive to vary the antenna&#39;s scan rate so that the angular resolution remains constant. This will be described in greater detail below. 
         [0073]    A radar for reconnaissance has as its main task the location of interesting objects by means of generated radar images. In order that there shall be identical conditions with regard to detection and analysis over the whole of the illuminated area, constant resolution is required. This can be achieved by suitable variation of the scan rate. 
         [0074]    In the equation relating to angular resolution discussed previously, a beam sharpening factor was included, according to: 
         [0000]    
       
         
           
             
               R 
               FSAR 
             
             = 
             
               
                 
                   2 
                    
                   λ 
                    
                   
                       
                   
                    
                   
                     υ 
                     p 
                   
                 
                 
                   
                     ω 
                     
                       s 
                        
                       
                           
                       
                     
                   
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                     2 
                   
                 
               
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                   sin 
                    
                   
                     ( 
                     φ 
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
         [0075]    As there is a correlation between beam sharpening R FSAR  and scan rate ω s , there is also a corresponding correlation between resolution and scan rate. By solving for the scan rate and assuming a constant value for the beam sharpening factor, the necessary scan rate is determined as 
         [0000]    
       
         
           
             
               ω 
               s 
             
             = 
             
               
                 
                   2 
                    
                   λ 
                    
                   
                       
                   
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                     υ 
                     p 
                   
                 
                 
                   
                     R 
                     FSAR 
                   
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                     2 
                   
                 
               
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                     ( 
                     φ 
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                 . 
               
             
           
         
       
     
         [0076]      FIG. 9  illustrates how the scan rate can be varied as a function of the antenna angle. Utilization of the result in  FIG. 9  gives an angle-dependent integration time T int , which is given by effective antenna beam width divided by scan rate. The integration time corresponds to the time when a specific target is within the field of view of the antenna. 
         [0000]    
       
         
           
             
               T 
               int 
             
             = 
             
               
                 
                   λ 
                   / 
                   l 
                 
                 
                   ω 
                   s 
                 
               
               . 
             
           
         
       
     
         [0077]    The equation above combined with the result in  FIG. 9 , shows that targets at small angles, close to the direction of travel, are illuminated for a longer time than targets at large angles. In this way, constant resolution is made possible. 
         [0078]    A strength of the proposed SAR algorithm is that it also handles raw data collected with variable scan rate. As the scan rate is included in the creation of the reference function, no additional adjustment of the focusing method is required. In order to illustrate the above statement, the scene in  FIG. 2  is simulated, but with a variable scan rate. 
         [0079]      FIGS. 10   a ,  10   b  and  FIG. 11  illustrate the effect of approach movement (compare with  FIGS. 4   a ,  4   b  and  5   b ). As the illumination time varies, the size of the distance variation is angle dependent, see  FIG. 10   a . After time displacement, the signal energy comes within the correct distance gate. Corresponding phase displacement results, according to  FIG. 11 , in all the targets being centred around the frequency zero, precisely as before. The approach compensation is thus in agreement with the embodiment discussed previously. 
         [0080]    The creation of the reference function for demodulation/target separation, is carried out according to the method described previously. The result is shown in  FIGS. 12   a  and  12   b , which illustrate the target&#39;s frequency variation  37 - 41 , in addition to the reference function&#39;s normalized frequency  42 .  FIG. 12   b  shows the result after demodulation. The conjugate of the reference function&#39;s normalized frequency is given the reference numeral  43  in  FIG. 12   b . The angle-independent resolution is obtained in this state by the predefined combination between integration time and frequency derivative. 
         [0081]      FIG. 13  illustrates the result after angle focusing of the demodulated signal quantity. The result is plotted here directly on a corrected angular scale in order to obtain the correct angular position. The result illustrates clearly that constant resolution can be also obtained when a scanning radar is utilized. 
         [0082]    The relatively high sidelobe levels are due to no amplitude weighting having been carried out. It is, however, fully possible to introduce amplitude weighting according to known principles within the field of radar technology. 
         [0083]    The disclosure is not intended to be limited to the embodiments described above, but can be modified within the framework of the following patent claims and inventive concept.