Ambiguity Resolution in Direction of Arrival Estimation with Linear Antenna Arrays Using Differential Geometry

Linear antenna arrays (LAs) can be used to accurately predict the direction of arrival (DOAs) of various targets of interest in a given area. However, under certain conditions, LA suffers from the problem of ambiguities among the angles of targets, which may result in misinterpretation of such targets. In order to cope up with such ambiguities, various techniques have been proposed. Unfortunately, none of them fully resolved such a problem because of rank deficiency and high computational cost. We aimed to resolve such a problem by proposing an algorithm using differential geometry. The proposed algorithm uses a specially designed doublet antenna array, which is made up of two individual linear arrays. Two angle observation models, ambiguous observation model (AOM) and estimated observation model (EOM), are derived for each individual array. The ambiguous set of angles is contained in the AOM, which is obtained from the corresponding array elements using differential geometry. The EOM for each array, on the other hand, contains estimated angles of all sources impinging signals on each array, as calculated by a direction-finding algorithm such as the genetic algorithm. The algorithm then contrasts the EOM of each array with its AOM, selecting the output of that array whose EOM has the minimum correlation with its corresponding AOM. In comparison to existing techniques, the proposed algorithm improves estimation accuracy and has greater precision in antenna aperture selection, resulting in improved resolution capabilities and the potential to be used more widely in practical scenarios. The simulation results using MATLAB authenticates the effectiveness of the proposed algorithm.