Research On The Calculation Methods Of Non-concentric Multi-beam Beam Footprint Coordinates

The multi-beam system is the mainly-used equipment for measuring underwater topography,and the method of calculating beam footprint coordinates directly affects the accuracy of multi-beam data post-processing.At present,the multi-beam beam footprint coordinate calculation mainly includes three models: traditional concentric array,virtual concentric array and non-concentric array.The former two do not solve the problem of disagreement between the transmitter and the receiver.Although the latter takes into account the problem of non-concentricity,the calculation efficiency and reliability of the existing algorithms are low.Therefore,this paper proposes a high-precision and high-efficiency iterative calculation method based on the propagation surface for the beam footprint position of the transmitting and receiving transducers under non-concentric conditions,which solves the problem of accurately and quickly determining the beam footprint position.The main work and contributions in the paper are as follows:(1)Propagation surface model and high-precision calculation method of non-concentric multi-beam beam footprint coordinates.According to the principle of multi-beam measurement,the propagation surface model is deduced;and this paper proposes a high-precision calculation method based on the propagation surface for the beam footprint position of the transmitting and receiving transducers under non-concentric conditions.(2)Analyze the impact of non-concentric arrays on existing algorithms.Under constant sound velocity,the beam footprint coordinates of the existing algorithm and the propagation surface model are derived;the simulation data is used to analyze the errors of each algorithm when the transmitting and receiving transducers are not concentric,and the factors that affect the size of the error.(3)Based on the high-precision algorithm of the propagation surface,a high-precision and efficient calculation method for multi-beam beam footprint coordinates is proposed.First,optimize the iterative process of a single beam footprint to reduce the number of iterations;secondly,use the correlation of adjacent beam footprints for interpolation to reduce the number of sound ray tracking;finally,use the constant gradient template interpolation algorithm to improve the efficiency of sound ray tracking.A comprehensive calculation method of beam footprint coordinates with both efficiency and accuracy is given;and based on the measured data,it is proved that the internal coincidence accuracy of the algorithm is higher than that of the traditional concentric and virtual concentric algorithms,and the calculation efficiency is similar.