Efficient source positioning method based on two stations using GROA and AOA measurements

By utilising the gain ratio of arrival (GROA) and angles of arrival (AOAs), three-dimensional source localisation with only two stations is studied. The weighted least squares (WLS) algorithm yields the typical closed-form solution, which is obtained by first establishing a set of linear equations and then determining the source position. However, the WLS solution exhibits poor performance at high noise levels. Hence, an efficient parameter augmented constraint method is proposed by extending the parameter space. The proposed method minimises the cost function by imposing a quadratic constraint such that the expectation of the cost function will attain its minimum value at the true solution. In addition, the proposed method yields an explicit algebraic solution and does not depend on a good initial guess; thus, there is no convergence problem. Theoretical analysis and simulation results verify the effectiveness of the proposed method.