Hybrid array is able to leverage array gains, transceiver sizes, and costs for massive multiple-input-multiple-output systems in millimeter-wave frequencies. Challenges arise from the estimation of angle-of-arrival (AoA) in localized hybrid arrays, due to the array structure and the resultant estimation ambiguities and susceptibility to noises. This paper eliminates the ambiguities and enhances the tolerance to the noises based on our new discoveries. Particularly, by designing new subarray-specific time-varying phase shifts, we discover that the cross-correlations between the gains of consecutive subarrays have consistent signs except the strongest. This enables the cross-correlations to be deterministically calibrated and constructively combined for the noise-tolerant estimation of the propagation phase offset between adjacent subarrays. Given the phase offset, the AoA can be estimated unambiguously with few training symbols. We also derive a closed-form lower bound for the mean square error of AoA estimation. Corroborated by simulations, our approach is able to dramatically improve estimation accuracy by orders of magnitude while reducing complexity and training symbols, as compared to the state of the art. With the ambiguities eliminated, the estimation errors of our method asymptotically approach the lower bound, as training symbols increase.