Abstract:
A method and apparatus for eliminating aspect dependence of images generated by a radiative scanner such as a radar, sonar, or the like. Echoes from the scanner are received back and detected at a known and preselected number of aspects. The echo received at each aspect is multiplied by the transform of the point spread function of each of the other preselected aspects. In this manner, the frequency domain version of each echo is multiplied by the frequency domain point spread function of all of the preselected aspects, and the ultimate processed echo will be aspect independent.

Description:
CLAIM OF PRIORITY 
     This application has the priority of U.S. Provisional Patent Application Ser. No. 61/216,566, filed May 18, 2009, which is currently pending. 
    
    
     STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor. 
    
    
     FIELD OF THE INVENTION 
     The Invention pertains to radiative imaging, such as by radar or sonar, and feature based navigation. 
     BACKGROUND OF THE INVENTION 
     A fundamental problem in sonar or radar imaging is that the echoes returned from the same object will differ depending on the aspect at which the sonar or radar radiatively scans the object. This is of special concern to a class of problems collectively named feature based navigation, in which a vessel, such as an ocean going ship, submersible platform, helicopter or airplane, or the like, compares echoes it receives to a pre-existing radar/sonar map to identify or update the vessel&#39;s location. If the aspect at which the map was generated differs from the aspect at which the vessel&#39;s radar/sonar scans, and all things being equal this would be so almost always, the correlation between the vessel&#39;s scan and the pre-existing map will be degraded. Another way to put this is that the point spread function relating radiative scatter from a point, to a detector, varies with aspect, so that, for example, a sonar detector will have a different point spread function at each aspect at which it can scan. Thus even echoes from the same object taken at identical distances from the detector, but at different aspects with respect to the detector, will have different signatures, and their correlation with one another, or with the same object&#39;s echo signature in an extant map, will be degraded. 
     SUMMARY OF THE INVENTION 
     Accordingly, an object of the invention is to reduce or eliminate aspect dependence of radar/sonar echoes returned from the same object, or from highly similar objects. 
     Another object is to reduce or eliminate aspect dependence in feature based navigation. 
     In accordance with these and other objects made apparent hereinafter, the invention concerns a method and apparatus in which a radiative scanning signal, such as from a radiative scanner such as a sonar or radar, produces echoes of the signal, for example from an object one knows is in the vicinity. The echoes are received back and detected at a known and preselected number of aspects with respect to the radiative scanner. The echo received at each aspect is multiplied by the transform of the point spread function of each of the other preselected aspects. In this manner, the frequency domain version of each echo is multiplied by the frequency domain point spread function of all of the preselected aspects, and the ultimate processed echo will be aspect independent. Thus a vessel that processes its echoes in this manner can compare it to a pre-existing map generated in this manner to identify matches, thus determining the position of the vessel. 
     These and other objects are further understood from the following detailed description of particular embodiments of the invention. It is understood, however, that the invention is capable of extended application beyond the precise details of these embodiments. Changes and modifications can be made to the embodiments that do not affect the spirit of the invention, nor exceed its scope, as expressed in the appended claims. The embodiments are described with particular reference to the accompanying drawings, wherein: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a plan view illustrating an embodiment of the invention and its operational environment. 
         FIG. 2   a  is a view in the direction of lines  2   a - 2   a  of  FIG. 1 . 
         FIG. 2   b  is a view like that of  FIG. 2   a , which illustrates the problem of aspect dependence on imaging. 
         FIG. 3  is a view similar to that of  FIGS. 2   a  and  2   b , illustrating operation of an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     With reference to the drawing figures, wherein like numbers indicate like parts throughout the several views,  FIG. 1  shows a ship  10  on surface  20  with a side scanning sonar  12 .  FIG. 1  also shows a set of reference axes marked z, indicating altitude above marine bottom  22 , and x-y, indicating the plane in which marine bottom  22  lies. Sonar  12  acoustically scans marine bottom  22  with a beamwidth illustrated in  FIG. 1  as having azimuthal (z axis) boundary  14 . Within beamwidth  14  on marine bottom  22  is bottom patch  16  which is distinct from the surrounding portion of bottom  22 . Patch  16  could be, for example, areas of sea shells or pebbles, surrounded by an otherwise sandy bottom  22 . 
       FIGS. 2   a  and  2   b  show the same scene as  FIG. 1 , but looking down in the direction of marine bottom  22 , and with the difference between  2   a  and  2   b  being that ship  10  is at a different position with respect to bottom patch  16 . In each of these drawing figures, patch  16  is located within beamwidth  14 , but with aspect  18  in  FIG. 2   a , and aspect  18 ′ in  FIG. 2   b.    
     The effect of varying aspect is seen from the following: For a sonar on ship  10  centered at (x,y), the image I 1 (x,y) of a point at (x 1 , y 1 ) is:
 
 I   1 ( x,y )= p   1 ( x−x   1   ,y−y   1 )
 
Where P 1  is the point spread function of I 1  for sonar  12 . A scene at some distance (x 1 , y 1 ) from sonar  12  can be represented as a collection of sonar point scatterers, which are representable as the sum of impulse functions:
 
               f   ⁡     (     x   ,   y     )       =       ∑     i   =   1     N     ⁢     δ   ⁡     (       x   -     x   1       ,     y   -     y   1         )               
The image I 1  of scene f, as viewed at sonar  12 , is the convolution of scene f(x,y) with a time reversed version of the point spread function, which in the frequency domain is:
 
 I   1 ( k   x   ,k   y )= F ( k   x   ,k   y ) P   1 *( k   x   ,k   y )
 
where k x  and k y  are spatial wavenumbers in the x and y directions, I 1 (k x , k y ) are the two dimensional spatial Fourier transforms of I 1 (x,y) and f(x,y) respectively, and P 1 *(k x , k y ) is the complex conjugate of the two dimensional Fourier Transform of p 1  (x,y). A second image I 2  at a second vantage point (x 2 , y 2 ) would similarly have a frequency domain representation:
 
 I   2 ( k   x   ,k   y )= F ( k   x   ,k   y ) P   2 *( k   x   ,k   y )
 
To recover the images, one must deconvolve them. In principle, one could simply divide I 1  or I 2  by its corresponding point spread function, and, if desired, transform back to the real domain (x and Y). This, however, is computationally problematic, and may on occasions involve division by zero. If, however, one is concerned with only a finite number of vantage points (here, as an example, two:  18  and  18 ′), and one can convolve (or multiply in the frequency domain) an image viewed at one aspect by the point spread functions associated with each of the other aspects of interest, then, in this example, one gets:
 
 I   2 ( k   x   ,k   y ) P   1 *( k   x   ,k   y )= I   1 ( k   x   ,k   y ) P   2 *( k   x   ,k   y )= F ( k   x   ,k   y ) P   1 *( k   x   ,k   y ) P   2 *( k   x   ,k   y )
 
and thus the signature of an image of an object as detected is the same, regardless of the vantage point, i.e. aspect at which one images the object.
 
     The value of this is further illustrated in  FIG. 3 , in which side scanning sonar  12  on ship  10  is illustrated collectively as having plural aspects  18 ″ of interest, which are relatively finely spaced apart, each aspect having its own point spread function with respect to sonar  12 . Sonar  12  is directional, e.g. a linear phased array, and thus one knows a priori the direction corresponding to each one of the aspects  18 ″. As sonar  12  scans, a processor aboard ship  10  associated with sonar  12  records the echo signatures, determines from which direction relative to sonar  12  the echoes arrived, and thus identifies which point spread function that corresponds to which echo. The processor is preferably an onboard process computer, but could be, e.g., a distant computer to which sonar  12  is telimetered. The processor transforms the echoes into the frequency domain, by performing a Fourier Transform on each, preferably by a Fast Fourier Transform, and multiplies each echo by the Fourier Transform of each of the other aspects  18 ″ of interest. If the processor aboard ship  10  has a pre-existing map of marine bottom  22  generated earlier by a survey in which a like sonar produced echo data recorded at the same aspects  18 ″, with the echoes at each aspect multiplied by the frequency domain point spread functions at each of the other aspects, then an echo returned from the same object will have the same signature, regardless of aspect. If, for example, one wishes to establish ship  10 &#39;s position, sonar  12  scans, and compares, preferably by correlation, its echoes to echoes in the above described pre-existing sonar map to establish as a match. Because the echoes in the map, and those generated by sonar  10  are aspect independent, an echo from patch  16  in the map will correlate strongly with an echo from patch  16  detected at sonar  12  whether or not sonar  12  and the survey that generated the map scanned patch  16  from the same aspect. A strong correlation indicates a match, identifying ship  10 &#39;s location with respect to patch  16 , which, presumably, would be a feature of known position, thus identifying ship  10 &#39;s location absolutely. 
     Instead of transforming echoes and point spread functions to and from the frequency domain and multiplying as above described, one could instead convolve the signals&#39; echoes and point spread functions with one another, although this is much more computationally involved and correspondingly less efficient. 
     In practice, a large range of sensors could advantageously use the foregoing scheme, for example nearfield real aperture sonars or radars, synthetic aperture sonars or radars, or coherent near aperture sensors using other modalities. 
     Likewise, a large range of vehicles could advantageously use the foregoing scheme, for example autonomous underwater vehicles (AUVs), or submarines or other submersibles. So too could unmanned aerial vehicles (UAVs), or airplanes, helicopters, or spacecraft with radars like that currently on the Space Shuttle or satellites. 
     The invention has been described in what is considered to be the most practical and preferred embodiments. It is recognized, however, that obvious modifications to the embodiments may occur to those with skill in this art. Accordingly, the scope of the invention is to be discerned from reference to the appended claims, wherein: