Coherent Acoustic source DOA estimation by nested array based on sparse solution

Direction finding of acoustic sources has special importance in military and industrial applications. Lots of algorithms are proposed for solving this problem but, as the complicated conditions of environment enter the problem, a common method with arbitrary precision does not exist for all situations. One of these cases is finding the direction of acoustic sources in multi reflection media such as shallow waters. In this case, many virtual sources are born which are copies of independent sources and are neither detectable nor removable. When the number of these reflections are more than the number of array sensors, the assumptions of customary direction-finding methods are not satisfied and therefore these methods are no longer applicable. In this case, we are facing a problem that the number of signal sources are more than the number of sensors. An important idea for handling this multipath phenomenon, is to increase the degree of freedom of the sonar array which can be solved based on the sparse arrays. Actually, employing the MRA array, will increase the number of real array sensors virtually so that the problem will return to the ordinary conditions. In this idea, the array manifold matrix is modified to be proportional to the sparse non-uniform array. Simulations confirm the function of the proposed algorithm in the presence of correlated sources that have low error and high angular resolution so that, by 6 real array sensors, this algorithm could find the direction of 12 sources whether independent or correlated. This algorithm is very close to CRLB limit and is better than all compared methods.