Array Element Localisation

Sammanfattning: Abstract—This article have been written in cooperation with The Swedish Defense Research Agency (FOI). The article proposes a method to calibrate hydrophone positions for improved underwater survailence in The Baltic Sea. The idea with the method is to use the sound of a powerboat and a novel beamforming algorithm for array element localisation (AEL). There are strategic military advatages to this method since it is a cost-saving method and do not risk to reveal the array positions to other intelligence agencies. The essence of the algorithm is optimisation over the array output of a delay-and-sum beamformer. Keywords—Beamform, FOI, AEL. I. U NDERWATER SURVAILANCE IN THE BALTIC SEA Ever since World War I the submarine have been an essential piece of naval warfare. With the introduction, the need for underwater surveillance increased dramatically and still occupy the minds of intelligence agencies around the world. The developed surveillance techniques can also be used in nonmilitary applications such as deep-sea pollution monitoring, assessing impacts of offshore infrastructure on local ecosystems and oil leakage control. One primary tool for underwater surveillance is the study of sound propagation under water. The acoustic signals are measured by microphones underwater, so called hydrophones, and the received signal is then treated mathematically to, for example detect passing submarines. In order to accomplish this, several hydrophones are usually placed out together and synchronised into what is called arrays. Some arrays used by FOI to intercept signals, in the Baltic Sea, from different ships, are passive arrays on the sea floor, which, for estimation purposes, are about a hundred meters long and consist of more than fifty hydrophones. A. Sinking the array The hydrophones are all attached to a flexible cord which is connected to a computer, that processes the signal received. When placing the array on the sea floor, it needs to be sunk from a boat. A typical desired array structure, or geometry, on the sea floor is a perfect linear structure. The linear structure simplifies the processing of intercepted signals in the application of submarine detection. Therefore it is important that the array is sunk properly. The computer, or signal transmitter, along with an anchor is sunk from the boat and at the same time the array needs to be stretched. Due to the arrays size, waves and currents, this is problematic and the geometry of the array will shift. Also the topography of the sea floor is problematic since it is likely not to be flat. Rocks and inclination will cause the array to be placed in a sub-optimal position. This sub-optimal position will introduce bias in the array applications and therefore it is needed to calibrate the array by estimating the exact hydrophone positions within the array. Fig. 1. Picture of array cord in laboratory with hydrophones and signal transmitter attached to its end. Source Chen et al. 2013 B. Classified array positions There are several methods to calibrate the array on the sea floor. One method would be to ping the array from several locations nearby, using a boat. The pings appear as spikes in the data transmitted from the array, making them easy to process for array calibration. However this method is very costly because of the need of expensive equipment and also it’s a time consuming task. Another, perhaps more important, aspect of this method is that it might reveal the position of the array. The position of the array is often classified information due to the strategic military advantage it provides. If FOI would be seen by other Intelligence Agencies conducting ping experiments, it is not difficult for them to conclude that they are calibrating arrays. C. Calibrating the array with a powerboat A potentially advantageous method to calibrate an array, would be to, instead of using pings, drive a powerboat nearby for a short period of time. This is a cheap method and it can be done without any risk of revealing the array position. One such method would be a so called Beamforming calibration method. In the case of a powerboat, the data transmitted from the array are no longer nice peaks that are easily identified to compute time differences, instead the signal is messy. The beamforming method builds upon estimating the covariance of the signal intercepted at each hydrophone to understand the time difference for the signal to reach each hydrophone. When this is done, each hydrophone is delayed by its individual time difference, to some reference point, so that the exact same signal is intercepted at each hydrophone at the same time. By then summing over each output signal, the energy of the output will be maximized. To implement this, firstly some basic spectral analysis knowledge is needed. Secondly it requires a lot of data. Since one array usually consists of more than 50 hydrophones, this is a high dimensional nonlinear equation system. D. Implementation tools and performance Several gigabytes of data is needed to positions over 50 hydrophones. To process this large amount of data, and implement the beamforming calibration method, a powerful computer program such as MatLab can be used. Working with large data sets and complex algorithms, it is in general a good idea to break down the problem into smaller parts. This can be done by building a step-by-step simulation of the real world problem in MatLab and understand the parameters of the model. The beamforming calibration method works with high precision in a simulated environment, however the underwater world is very complex and it is hard to encapsulate, for instance, reflections of the propagating sound on the surface that disturb the method. Fig. 2. A simulation of beamforming calibration method in MatLab. The algorithm locates the hydrophone positions very well and suggests that a powerboat might work in practice to calibrate arrays. E. Powerboat results on real data As mentioned earlier, the underwater environment is complex with reflections of the propagating sound and the topography. However the beamform calibration seem to work well