The use of global navigation satellite system (GNSS) antenna arrays for applications such as interference counter-measure, attitude determination and signal-to-noise ratio (SNR) enhancement is attracting significant attention. However, precise antenna array calibration remains a major challenge. This paper proposes a new method for calibrating a GNSS antenna array using live signals and an inertial measurement unit (IMU). Moreover, a second method that employs the calibration results for the estimation of steering vectors is also proposed. These two methods are applied to the receiver in two modes, namely calibration and operation. In the calibration mode, a two-stage optimization for precise calibration is used; in the first stage, constant uncertainties are estimated while in the second stage, the dependency of each antenna element gain and phase patterns to the received signal direction of arrival (DOA) is considered for refined calibration. In the operation mode, a low-complexity iterative and fast-converging method is applied to estimate the satellite signal steering vectors using the calibration results. This makes the technique suitable for real-time applications employing a precisely calibrated antenna array. The proposed calibration method is applied to GPS signals to verify its applicability and assess its performance. Furthermore, the data set is used to evaluate the proposed iterative method in the receiver operation mode for two different applications, namely attitude determination and SNR enhancement.