A hearing aid configured to be worn at, and/or in, an ear of a user, comprises a forward path for processing sound from the environment of the user. The forward path comprises a) at least one first microphone providing at least one first electric input signal representing said sound as received at the respective at least one first microphones, said at least one first microphone being located away from a first ear canal of the user, b) an audio signal processor for processing said at least one first electric input signal, or a signal or signals originating therefrom, and for providing a processed signal, c) an output transducer for providing stimuli perceivable as sound to the user in dependence of said processed signal, and d) at least one second microphone connected to said audio signal processor, the at least one second microphone being configured to provide at least one second electric input signal representing said sound as received at the at least one second microphone, the at least one second microphone being located at or in said first ear canal of the user, and e) a feature extractor for extracting acoustic characteristics of said ear of the user from said at least one second electric input signal, or a signal originating therefrom. The hearing aid is configured to include said acoustic characteristics in the processed signal. The invention may e.g. provide improved sound localization in hearing aids.