Linear array lateral motion compensation method

Abstract: A method for compensating for lateral distortion (30) in a moving linear array (20) using a frequency domain beamformer, comprising the steps of measuring the instantaneous lateral distortion (30) of the linear array (20) at discrete points (40) along the array (20), corresponding to array element locations, calculating a shading weight for each of the discrete points (40) along the array (20), corresponding to array element locations based on the instantaneous lateral distortion (30) at each said point (40) and calculating the compensated beam magnitude by multiplying said shading weight into the frequency domain beamformer equation.

Description: This invention relates to a method for compensating for lateral distortion in a moving linear array using a frequency domain beamformer. US-A-4,454,597 discloses a narrow-band compensating beamformer for a receiving array that conforms to some surface other than a plane and thus is, in general, three-dimensional. The array comprises a number of sensing elements arranged in a non-planar pattern. Each sensing element has its output signal delayed or phase-shifted as a function of the receiving angle by the beamformer in such a way as to produce an equivalent "projected planar array" in a particular direction. The problem of this compensating beamformer is that it does not properly compensate signals of a moving linear array, the sensing elements of which are changing their position permanently. This compensating beamformer only works when the sensing elements are arranged in a fixed manner. In general, a linear arrary is a linear distribution of sensors, or other type of emitting/receiving device, in which there are a multitude of receiving/radiating elements, each arranged in a straight line. When the received or emitted signal is represented in frequency domain and properly phased or time delayed for arrivals from or emissions to a particular direction, the resulting interference produces a maximum response in that direction. This maximum response is called a beam in that direction. Beams may be formed in multiple directions simultaneously by a process known as a beamformer. The linear array can be designed to operate either actively or passively. The direction and intensity of the beams is determined by the beamformer which controls the output of the beams in either the time domain or the frequency domain. A time domain beamformer inserts a time delay into the signal from/to each radiating element. A frequency domain beamformer shifts the phase of the signal from/to each radiating element. Frequency domain beamformers are gaining in acceptance in the art due to the increased abundance and speed of Fast Fourier Transform (FFT) electronic devices. An interference pattern is created by the intersection of the modulated signal from each of the radiating elements, and these lines of interference are the antenna beams. A fixed linear array can achieve a high degree of beam pointing accuracy, because there is no lateral distortion of the array. However, when the array is in motion, the linear symmetry or shape of the array is distorted and the beam pointing accuracy significantly diminishes. A towed SONAR array is an example of a moving linear array. In a towed SONAR array, receiving elements are strung linearly along the length of a cable, which is towed behind a ship. An array can generate a very high number of beams, each projecting outward from the array. A towed linear array operating passively is extremely useful, as the beams can simultaneously identify and localize numerous ocean targets, such as enemy ships or submarines, in various positions relative to the tow ship, without giving away the tow ship location. A significant problem with towed arrays is the difficulty in maintaining the linear symmetry of the array. As the cable moves through the water, the ocean currents and the even velocity and steering of the tow ship causes distortions in the shape of the array. These distortions diminish the accuracy and utility of the towed array, because the actual beam pointing direction is different from the calculated direction. There currently exists no method of compensating for this distortion, and the reduction in accuracy is generally accepted as a condition of the device. However, U.S. patent No. 4,301,523 discloses a method for compensating for position deviations of the sensing elements in a linear array. The sensor elements are attached along a flexible member in spaced-aparat relationship, a lead element out of the number of elements being closer to a first end than the other elements. A motion measuring device is coupled to the lead element to generate signals which indicate the velocity of the lead sensor element in the environment. A processor, having an input which is limited to lead element velocity signals, generates estimates of the positions of respective sensor elements. Based upon these estimations time delay elements are adjusted for proper beam steering. A comparable method and system is known from the article my Michel Bouvet "Beamforming of a distorted line array in the presence of uncertainties on the sensor positions", in Journal of the Acoustical Society of America, Vol. 81, June 1987, No. 6, pp. 1833-1840. A mechanical device is provided for measuring the angles inside the array, whereupon the total time delay between the first sensor and any of the remaining sensors in the array is calculated using all of the angle information. Then, the beam steering vector is calculated using all of the calculated time delays. In view of the above it is an object of the present invention to provide a method for compensating for the lateral motion of a linear array using a frequency domain beamformer. According to the invention this object is achieved by a method for compensating for lateral distortions in a moving linear array using a frequency domain beamformer, comprising the steps of: measuring the instantaneous lateral distortion of the linear array at discrete points along the array, corresponding to array element locations; calculating a shading weight for each of the discrete points along the array, corresponding to array element locations based on the instantaneous lateral distortion at each said point; calculating the compensated beam magnitude by multiplying said shading weight into the frequency domain beamformer equation; calculating the shading weight (b n ) according to the algorithm b n ( m ) = a n e -2π j Y n (f/c)cos m where a n is the element shading constant, f is the frequency of the propagated signal, c is the speed of the propagated signal, and  is the beam pointing direction relative to broadside; and calculating the compensated beam magnitude (X m ) according to the algorithm where N is the total number of elements in the array, S n (t) is the signal on the n th element of the array, n is the element number, and m is the beam number. A linear array is a sensing device in which multiple receiving or transmitting elements are arranged in a straight line. Multiple beams are formed by the linear array and each beam focusses in a predetermined direction. Lateral motion of the array distorts the array shape and consequently alters the beam pointing direction. This method results in improved beam pointing accuracy in linear arrays over uncompensated arrays. The invention is advantageously used in linear arrays such as used in towed SONAR arrays. Towed SONAR arrays are commonly used by Navy ships to localize distant enemy targets. A significant problem with towed SONAR arrays is that the wave motion and uneven tow ship steering and velocity distorts the shape of the towed linear array, thus reducing the accuracy of the array. By use of the invention, the instantaneous variations in array shape are compensated for, significantly improving the utility of the arrays. Briefly, and in general terms, the method for distortion compensation according to the present invention includes a means for measuring the magnitude of the instantaneous distortion in the array; the calculation of element shading weights based on the distortion magnitudes by the use of an algorithm; and the compensation of individual beam magnitudes by using the shading weights in the control of the arrays. In common usage within the art, linear arrays are controlled by frequency domain beamformers. These frequency domain beamformers utilize algorithmic methods to control beam magnitude and direction. A major advantage of the invention is that the shading weights calculated are simply multiplied into the frequency domain beamformer equation. Therefore, the array distortion can be compensated for without a significant deviation in current linear array design. From the above, it may be seen that the present invention has important advantages related to linear array lateral motion compensation, and particularly to towed SONAR array motion compensation. Other aspects and advantages of the invention will become apparent from the following detailed description and the accompanying drawings, which illustrate by way of example the features of the invention. As shown in the drawings, which are included for the purpose of illustration, the invention is embodied in a method to compensate a linear array for the effects of lateral distortion. A linear array is an antenna, or other type of receiving device, in which there are multitude of receiving elements arranged in a straight line. The array can generate a multitude of beams for the purpose of localizing distant targets. Lateral distortion occurs when the linear symmetry of the array is altered by outside forces and results in an overall reduction in array pointing accuracy. A common use of a linear array is in the field of towed SONAR arrays. In a towed SONAR array, a Navy ship drags a lengthy cable through the water. The cable has a multitude of receiving elements or transponders positioned at even increments along its length. A frequency domain beamformer is used to convert all the transponder signals into coherent localization information. The phase of the signal information from each transponder is shifted by varying degrees, and all the signal information is summed by Fast Fourier Transform (FFT). This summation results in individual beams of signal energy in a known angle relative to the direction of the array. The precise localization of the target can be determined from the intersection of the beams. A significant problem with towed SONAR arrays is the distortion of the shape of the array, which decreases its pointing accuracy. As the cable moves through the water, ocean currents and tow ship steering and velocity variations cause ripples in the array; instead of remaining in a perfectly straight line, the cable bends and curves. Figure 1 shows a distorted array. The tow ship 10 pulls a linear array cable 20, which has been substantially distorted 30. With the array distorted, the actual pointing direction varies by several degrees from the expected direction and incorrect target localization would be obtained. The invention utilizes an algorithmic method to determine a shading weight to be applied to the signal from each transducer. The shading weight attenuates the magnitude of the beams, thus correcting for distortion. To further describe the details of the invention, the mathematical derivation of the algorithm will be illustrated. In an embodiment of the invention (Fig. 2), an array would be equipped with N transducers, each spaced a distance d apart. The ship travels in the X-axis direction, such that the linear coordinate of a specific transducer n is X n . The array displacement direction is perpendicular to the array, and in the Y-axis such that the magnitude of transponder displacement is Y n . In perfect conditions, with no lateral displacement, Y n is equal to zero. The array forms m beams, and each beam points in the direction  m , relative to broadside. Therefore, the magnitude of the m th beam for a steering direction  m is described by the equation where S n (t) is the signal on the n th element at time t; a n is a shading constant for calibration of the transducers; f is the frequency of the signal S n (t); and c is the speed of the propagated signal. In a towed SONAR array, c is the speed of sound in water. In an undistorted array, the Y n coordinate is zero and the magnitude of the m th beam for a steering direction  m is described as Equation (2) is the Frequency Domain Beamformer equation as commonly used in the art. The equation can be solved using a Fast Fourier Transform (FFT) to determine array beam magnitude. From equation (1), the missing component for the Y-displacement can be recalculated as the new shading weight b n , such that (3) b n ( m )=a n e -2πjY n (f/c)cos m and Equation (4) replaces equation (2) as the Frequency Domain Beamformer equation. It too can be readily solved using an FFT. Therefore, by multiplying the shading weight in the frequency Domain Beamformer equation, the resulting beam magnitude values will be compensated for lateral distortion. The values for the lateral distortion, Y n can be measured directly from the array. Heading sensors mounted adjacent to the transponders will track array movement through the water, and provide instantaneous position information by sampling the set of of heading sensors. These array distortion figures are then input into the shading weight calculated in equation (3). The invention comprises three discrete steps. The first step is the sampling of the heading sensors to obtain array distortion data, Y n . Next, the shading weight, b n , is calculated for each transducer position. Lastly, the shading weight is combined in the Frequency Domain Beamformer equation to correct the resulting phase value to compensate for the distortion. The resulting calibrated beam magnitude values yield more accurate results when used to localize distant targets. Computer simulation of distorted linear arrays has been performed to characterize the improvements in accuracy by use of the invention. The simulation involved a half-cycle cosine shaped array with twenty displacement measurements. An uncompensated array was compared to one compensated by the invention. The test results revealed significant improvement in localization accuracy of simulated distant targets over the uncompensated array. Those skilled in the art will appreciate from the foregoing description that the present invention for compensation of a linear array for lateral distortion can achieve a significant improvement in pointing accuracy over uncompensated linear arrays. A significant advantage of the invention is that accurate array information can be obtained despite substantial distortion in array shape, while undertaking only modest changes to current design.

Claims: A method for compensating for lateral distortion (Y n ) in a moving linear array (20) using a frequency domain beamformer, comprising the steps of: measuring the instantaneous lateral distortion (Y n ) of the linear array (20) at discrete points (40) along the array (20), corresponding to array element locations; calculating a shading weight (b n ) for each of the discrete points (40) along the array (20), corresponding to array element locations based on the instantaneous lateral distortion (Y n ) at each said point (40); calculating the compensated beam magnitude (X m ) by multiplying said shading weight (b n ) into the frequency domain beamformer equation; calculating the shading weight (b n ) according to the algorithm b n ( m ) = a n e -2π j Y n (f/c)cos m where a n is the element shading constant, f is the frequency of the propagated signal, c is the speed of the propagated signal, and  m is the beam pointing direction relative to broadside; and calculating the compensated beam magnitude (X m ) according to the algorithm where N is the total number of elements in the array, S n (t) is the signal on the n th element of the array, n is the element number, and m is the beam number.

Inventors: BREED BEN R, POSCH THEODORE E, REPASKY BERNHARD J, BREED, BEN R., POSCH, THEODORE E., REPASKY, BERNHARD J.
Applicants: RAYTHEON CO, RAYTHEON COMPANY
Application year: 1993
Main classification: G01S7
IPC codes: G01S15, G06F17, G01V1, G01S7, H04B1