Generalised algorithm for DOA estimation in a passive sonar

A new method is proposed for DOA estimation in the presence of correlated sources and unknown correlated noise fields when the receiving array is linear with equispaced sensors. This method makes use of the fact that the autocovariance matrix R of the received sensor signals is the sum of the two matrices, one of which is Toeplitz and the other nonToeplitz. The Toeplitz part consists of the signal-alone autocovariance matrix (corresponding to uncorrelated sources) plus the noise covariance matrix whereas the nonToeplitz part is the source cross-covariance matrix. It is known that any Toeplitz matrix T will satisfy the property, ET ^TE=T where E is the exchange matrix and superscript `T´ represents matrix transpose. This property is used to cancel out the Toeplitz part of the autocovariance matrix R. It is shown that the resultant difference matrix has a column space which is the same as the `signal subspace´ and a nullspace equal to the `noise subspace´. Hence, any null eigenvector of the difference matrix can be utilised for computing the pseudospatial spectrum and then DOAs can be estimated. Computer simulation results are presented to support the theory