Abstract: To address the degradation of Direction of Arrival (DOA) estimation accuracy in coprime arrays due to gain and phase errors, this paper proposes a calibration method for hole-free coprime arrays using a minimal number of auxiliary sensors. First, three pre-calibrated auxiliary sensors are appended to the original array. By leveraging the concept of subarray decomposition, the received array data is decomposed into two subarray datasets. The covariance matrix-based R-instrumental sensor method (R-ISM) is then applied to independently estimate the gain and phase errors for each subarray. These error estimates are sorted and recombined to derive the full-array error vector, which is used to calibrate the received data covariance matrix. Finally, DOA estimation is performed via the MUSIC algorithm. Theoretical analysis and simulation results demonstrate that the proposed method effectively calibrates coprime array gain and phase errors using only three auxiliary sensors. Compared with the traditional method requiring four auxiliary sensors, the proposed approach reduces the Root Mean Square Error (RMSE) by 0.3° under conditions of 0 dB SNR and 300 snapshots. Additionally, it eliminates the need for optimization procedures, thereby reducing computational complexity.