Underwater acoustic array shape estimation and tracking using Kalman filters

Beamforming and DOA (direction of arrival) finding are two well-known methods that use the received signals from sensors of arrays for processing. Determination of location of array sensors is a fundamental condition for proper performance of these methods, but it is not always practicable. In the underwater array, because of water flow and the mechanics of the media, there is a rough deviation and vibration for sensor locations. Estimation of sensor deviations are of the calibration´s section duty. The method presented in this paper uses the phase difference of the received array signals and implements them to a KF (Kalman filter) and predicts fixed and variable sensor deviations. The advantages of the proposed method are as follows: no need to mechanical equipment; possibility of finding multidimensional deviations; predicting, and smoothing the fluctuations; and using time and space correlations and movement of sources for improving the results of estimation. A simple and proper model for vibration of a non-cable array is presented and based on it a state equation is extracted. The procedure for calculation of the observation vector from the Fourier transformed signals is explained. The quality of the method with respect to change in direction of the source radiation, change in SNR (signal to noise ratio) and change in the amount of saved data is examined. Also the results are compared with the CRLB (Cramer-Rao lower bound) as a criterion for the evaluation of results