Wireless networks are incorporating higher frequency bands and higher bandwidths by exploiting MIMO technology with large arrays. These large arrays and bandwidths enable high resolution estimates of the angles and delays associated to the different multipath components of the MIMO channel. Given the sparse nature of the millimeter wave (mmWave) channel, sparse recovery algorithms can extract the path parameters with reasonable accuracy. Moreover, channel sparsity also facilitates the association of these multipath components to the geometry of the environment, providing sufficient information to determine the user position. In this paper, we address the problem of designing the set of training precoders and combiners that, while providing a high accuracy channel and position estimate, also result in a reduced training overhead with respect to standardized beam training strategies. As performance metric, we consider the mutual coherence between the training hybrid precoders/combiners and the overcomplete dictionary used to represent the channel. The proposed scheme significantly reduces overhead and outperforms previous designs in terms of the accuracy of the channel estimate, which results in a higher localization accuracy and a higher spectral efficiency.