DOA estimation with unknown noise fields: a matrix decomposition method

A new method is presented for direction-of-arrival (DOA) estimation in a passive sonar in the presence of unknown correlated noise fields. It is shown that the autocovariance matrix R of received sensor signals can be uniquely decomposed into the sum of two Hermitian matrices. One of these matrices will have column space equal to the signal subspace and the other will have column space orthogonal to the signal subspace. Essential properties of these matrices are identified. These properties are utilised in the matrix decomposition method. Here, the data vector is transformed to another random vector in such a way that the autocovariance matrix R˜ of the transformed vector can be split into the sum of two Hermitian matrices E and F that satisfy the properties identified earlier. It is shown that the noise subspace vectors are then obtained by solving the generalised eigenvalue problem Fx=λR ˜x corresponding to λ=1. Simulation results are also presented to support the theory