A beam interpolation algorithm in digital multi-beam sonar

Beamforming is one of the most important part of signal processing in sonar system.Traditionally, in the analogue system the bearing direction is steered by rotating some kind of time-delay compensator, which is usually made by machanic-clectronic components. But,there exists a fixed bias error in target tracking due to the application of discrete tapped delay line. With the development of digital sonar the multi-beamforming technique is extensively used in various sonar systems. In these systems each beam has a fixed bearing direction. The precise DOA (Direction Of Arrival) estimation of the target becomes more important in sonar design. General speaking, if the sampling frequency is high enough, it is possible to get arbitrary number of beams, which steer in any designated direction. But a hardware tradeoff must be taken account for a good designer. In order to obtain higher target spatial resolution and reduce the hardware cost, it is necessary to make some kind of interpolation algorithm in post beamforming. It is proved that in the most interested situation the behavior of directivity function in the neighborhood of main lobe depends on the sinc function and zero order Bessel function. The multi-beam data is actually the spatial sampling to these function. Based on the principle of parabolic interpolation, a simple but high accuracy beam interpolation technique is presented in this paper. The theoretical basis of three-point and five-point interpolation algorithm is described. As an example, the line array and circle array of hydrophones are illustrated to explain this algorithm. The results of system simulation show that the method proposed in this paper has good agreement with the theory. It can be used to improve the behavior of the directivity function and enhance the multi-target resolving ability of digital sonar system. It is also possible to use this technique to implement ATT (Automatic TargetTracking) in real time.