Abstract:
A method is taught to extract more information about the motion of an acoustic wave emitter moving relative to a line array of hydrophones that are part of a sonar system by determining the variation in Doppler shift across the entire line array of hydrophones together with the a range measurement of the emitter to calculate the emitter&#39;s velocity.

Description:
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 therefore. 
    
    
     CROSS REFERENCE TO OTHER RELATED APPLICATIONS 
     Not applicable. 
     BACKGROUND OF THE INVENTION 
     (1) Field of the Invention 
     The present invention relates to active sonar systems, and more specifically to a novel method of processing the Doppler shift from a line array of acoustic sensors to determine the speed of an acoustic wave emitter moving parallel to the line array. 
     (2) Description of the Prior Art 
     Certain sonar applications utilize the properties of Doppler effects to analyze the data obtained from acoustic wave receivers. The Doppler effect or Doppler shift expresses the apparent change in the frequency and wavelength of an acoustic wave perceived by an acoustic receiver that is moving relative to the source of the acoustic wave. This relative motion can be caused by the movement of the emitter, the receiver or both the emitter and the receiver. For example, a receiver having velocity ν r  relative to a source having velocity ν s  introduces a Doppler shift as follows: 
     
       
         
           
             
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                 . 
               
             
           
         
       
     
     The Doppler shift can be derived for a plane wave from a stationary source having a pressure field of the form p(x,t)=P 0 e i(ωt-kx) . A stationary receiver at x=0 measures the field p(x,0)=P 0 e iωt , while a receiver moving according to x=−νt, i.e., opposite to the propagation direction of the plane wave, measures the field p(x,t)=P 0 e i(ω+ων/c)t =P 0 e iωt(1+ν/c) . 
     The Doppler effect produces a frequency shift when an object emitting acoustic waves is moving relative to an acoustic receiver such as a hydrophone. In the context of a sonar system, the Doppler effect is typically used only to determine the speed of the emitter along the line connecting the emitter and the receiver. When a line array of multiple receivers is used, however, there is the potential for extracting more information about the velocity of the emitter. 
     SUMMARY OF THE INVENTION 
     It is a general purpose and object of the present invention to determine the actual velocity of a moving acoustic wave emitter as detected by a line array of hydrophones. 
     This object is accomplished by a method of determining the Doppler shift across the entire line array of hydrophones through the use of a narrow band continuous wave pulse at a known frequency directed at a moving acoustic wave emitter, and then using the variation in the Doppler shifts across the multiple hydrophones in the array together with the a range measurement of the emitter to calculate the emitter&#39;s velocity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete understanding of the invention and many of the attendant advantages thereto will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein: 
         FIG. 1  is an illustration of a line array of hydrophones with an acoustic wave emitter aligned with the line array and moving parallel to the line array; 
         FIG. 2  is an illustration of a line array of hydrophones with an acoustic wave emitter that is not aligned at all with any part of the line array and moving parallel to the line array; 
         FIG. 3  is an illustration of a linear least squares fit plot of multiple frequency shifts versus individual hydrophone array elements in a line array of N hydrophones. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to  FIG. 1  there is illustrated an implementation of the method of the present invention, which makes use of a long line array  10  of N hydrophones that is part of a sonar system  14  (not shown) to determine the velocity v of a moving object  12  that is emitting acoustic waves and that is located parallel to the line array  10 . The sonar system  14  will have as part of the system components signal processors and data processors capable of receiving signals from the hydrophones in line array  10  and performing calculations on these received signals and plotting data. In the ideal situation, when the moving object  12  is aligned with the center of the line array  10  at point x 0 , the Doppler Shift measured at x 0  is zero. However, the Doppler shift at the two ends (x 1  and x 2 ) is not zero. Measurement of the frequency shift is initiated with a narrowband non-continuous wave pulse of a known frequency f 0 . The frequency shift at the two ends (x 1  and x 2 ) are as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
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                   ( 
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                     ∴           Δ   ⁢           ⁢     f   2       -     Δ   ⁢           ⁢     f   2           f   0       ≅       2   ⁢           ⁢   v   ⁢           ⁢   θ     c         =         v   ⁢           ⁢   Δ   ⁢           ⁢   θ     c     .             (   3   )               
where c is the speed of sound in water, f 1  is the frequency received at x 1  and f 2  is the frequency received at x 2 , so that Δf 1 =(f 1 −f 0 ) and Δf 2 =(f 2 −f 0 ). The above equations (1)-(3) can be calculated by the sonar system  14 .
 
     The Doppler shift varies linearly across the individual hydrophones (1 to N) of the line array  10 . This is also true for the general case in which the moving object  12  is not aligned at all with any part of the array as illustrated in  FIG. 2 . The frequency shift in this case is given as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
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                   ; 
                 
               
               
                 
                   ( 
                   4 
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                           ( 
                           
                               
                           
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                   ( 
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                   ∴           Δ   ⁢           ⁢     f   2       -     Δ   ⁢           ⁢     f   2           f   0       ≅         v   ⁢           ⁢   Δ   ⁢           ⁢   θ     c     .               (   6   )               
where Δθ=θ 1 −θ 1 . The above equations (4)-(6) can be calculated by the sonar system  14 .
 
     In active sonar, f 0  is known. The distance or range R from the object  12  to the line array  10  can be determined with a short non-continuous wave pulse. In the situation where R is much larger than the length of the line array  10 , (x 1 −x 2 ), then the value of De can be calculated according to the following: 
                     Δ   ⁢           ⁢   θ     =         (       x   1     -     x   2       )     R     .             Eq   .           ⁢     (   7   )                 
The equation (7) can be calculated by the sonar system  14 .
 
     Note that the range R of the object  12  is approximately the same for each element (1 to N), since as stated above the aperture length of the line array  10  is small compared to R. A line array has N hydrophones spaced λ/2 apart. Each hydrophone experiences a different frequency shift Δf z  that varies linearly, based on its position on the line array  10 . This results in the measurement of N different Doppler frequency shifts which is a significant data sample size. Since all of the frequency shifts must fit to a line in a plot of frequency shifts versus individual hydrophone array elements as illustrated in  FIG. 3 , then the data can be fit using a least squares fit to a line of frequency shifts versus hydrophones. The large data sample size increases signal data over noise thereby reducing error. 
     In the situation where the line array  10  is not long enough to get a measurable difference in Doppler shifts, a synthetic aperture can be formed as the line array  10  moves to get enough length to obtain a reliable measurement. 
     If there is any motion of the object  12  normal to the line array  10 , this will lead to a competing effect involving the variation of the Doppler shift due to that motion. However, this effect is much smaller. For the same velocity v, the Doppler shifts at the left and right most elements of the array are respectively: 
     
       
         
           
             
               
                 
                   
                     
                       
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                   ; 
                 
               
               
                 
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                   ( 
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                       . 
                     
                   
                 
               
               
                 
                   ( 
                   10 
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     Since θ&lt;&lt;1, then θ 2 &lt;&lt;θ, so the difference in Doppler shift from the left or right most elements compared to the center element is much smaller due to the motion normal to the line array. However, this can also be accounted for with a least squares fit. 
     In active sonar, both the range, R, and the Doppler shift, Δf x =(f x −f 0 ), are directly measureable by the sonar system  14 . This enables the measurement of the velocity parallel to the line array  10 , assuming that the variation in Doppler shifts, Δf 2 −Δf 1 /f 0 , along the line array  10  is measurable (either using the aperture length itself, or forming a synthetic aperture). For active sonar, the procedure involves first making contact with an object  12  with the line array  10  by pinging on it with a narrowband continuous wave pulse at a frequency f 0 . A shorter pulse is used to estimate the distance R. A sufficient amount of data is acquired to estimate the Doppler shift. For example, if the Doppler shift is 1 Hz, approximately 1 second of continuous wave time series data is needed for resolution of the Doppler shift. The Doppler shift is then determined at the two end elements x 1  and x 2  of the line array  10 . Measured Doppler shifts at the interior elements allow for confirmation of the estimate of any difference in frequency (by fitting them to a line, e.g., with a least-squares fit), leading to improved accuracy. 
     The advantage of the present invention over the prior art is that in sonar, normally, the motion of an object parallel to a line array can only be detected when the object moves from one beam to another. The present invention provides a much faster and more accurate way to measure the velocity of an object parallel to the line array. 
     In light of the above, it is therefore understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.