Unknown Noise-MUSIC (UN-MUSIC) is a promising method of direction of arrival (DOA) estimation in unknown spatially correlated noise using sparse arrays composed of two widely separated sub-arrays. The conventional UN-MUSIC estimator only utilizes information from one calibrated sub-array. If two sub-arrays are calibrated, a joint estimator that equally weights two sub-arrays’ conventional estimators has been found in literature. But no theoretical study has been reported. To compare and improve performance of different UN-MUSIC estimators, this paper proposes a unified framework of sub-array weighting to investigate the UN-MUSIC estimators, including the conventional one and the joint ones. The closed-form expression of the sub-array weighting estimator’s variance is derived which has not been done before. With the asymptotic results, different weighting strategies are compared and optimal weighting strategy to minimize estimation variance is proposed. Numerical simulations demonstrate the theoretical analysis and the validity of optimal weighting estimator.