Acoustic Emission (AE) techniques are used for the structural health monitoring of civil, aeronautic and aerospace structures. Recently, these structures are made of composite materials due to their advantages over traditional materials, but this increases the interpretation complexity of the failure modes present. Therefore, in order to make AE a trustworthy technique, reliable source location and damage mechanism characterization must be accomplished. On that account, this work proposes a novel approach based on a chirplet atomic decomposition, time-frequency energy distribution and dispersion analysis, where the failure-emitted signals are separated from extraneous noise and the detected modes are analyzed according to their dispersive behaviour and angular dependence characteristics. Dispersion relations are obtained by the use of a higher order plate theory on a non-absorbing anisotropic plate model, and then used in conjunction with the previous methodologies for mode identification and localization. The proposed methodology and model are validated, and the capability of the method to overcome practical issues encountered in AE testing is demonstrated experimentally.