Irreducible form of maximum likelihood criterion for bearing estimation using a uniform linear array

摘要

This paper presents an improvement of the Alternating Projection (AP) algorithm for the Maximum Likelihood bearing estimation using a uniform linear array of sensors. Solutions by the AP algorithm may oscillate because of numerical instability which occurs due to indefiniteness of the AP criterion, when estimated bearings more than one approach to the identical value. The oscillation makes the condition for terminating iterations complex. This paper derives an irreducible form of the AP criterion which never get indefinite. The irreducible form has the advantage of not only suppressing the oscillation but also being efficient since the order of the amount of arithmetic operations in each step of iteration decreases. Furthermore FFT and gradient methods, such as the Newton method, can be applied to recuce the operations.