High-resolution bearing estimation via unitary decomposition artificial neural network (UNIDANN)

Abstract

A novel artificial neural network (ANN) called the unitary decomposition ANN (UNIDANN), which can perform the unitary (Schur) decomposition of the synaptic weight matrix, is presented. It is shown both analytically and quantitatively that if the synaptic weight matrix is positive definite and normal, the dynamic equation involved will converge to a unitary matrix which can transform the weight matrix into an upper triangular one via the Schur decomposition. In particular, if the synaptic weight matrix is also Hermitian (symmetric for real case), the UNIDANN will perform the eigendecomposition. Compared with other existing ANNs, the proposed one possesses several attractive features such as being more versatile in the sense that it is capable of performing the Schur decomposition, has a low computation time and there is no synchronization problem due to the application of an of analog circuit structure, and a faster convergence speed. Some simulations with particular emphasis at the MUSIC bearing estimation algorithm are provided to justify the validity of the proposed ANN.