A Method for Active Three-Dimensional Array Calibration

The array steering vector plays a crucial role in direction of arrival (DOA) estimation. However, in practice, various errors such as array position errors, channel gain and phase errors, and element coupling errors lead to inaccurate knowledge of the array steering vector. Therefore, considering multiple errors to calibrate the array for obtaining accurate array steering vector is of great significance. This paper proposes a two-dimensional (2D) array calibration algorithm considering array position errors and channel gain and phase errors based on least squares (LS) and eigen-decomposition methods, and extends it to a three-dimensional (3D) calibration algorithm. The proposed 2D calibration algorithm and the improved 3D calibration algorithm are both validated through numerical simulations, demonstrating the accuracy of the algorithms and providing theoretical basis for practical array calibration methods. By employing the proposed 3D calibration algorithm, the average deviation of the estimated arrival angles of the array after calibration in a anechoic tank is reduced from 1.125° to 0.837°.