A binaural hearing aid system comprising a first hearing aid, a second hearing aid, and a first wireless link configured for establishing a wireless connection between the two hearing aids of the binaural hearing aid system, wherein each of the hearing aids comprises: - a primary signal path comprising an acoustical-electrical input transducer, a digital signal processor configured to amplify an electrical input signal, representing an acoustic input to the acoustical-electrical transducer, in order to alleviate a hearing loss of an individual hearing aid system user, hereby providing a processed electrical input signal, and an electrical-acoustical output transducer; - a sound generator configured to provide an electrical training signal, representing the acoustic output from a virtual object; - a Head-Related-Transfer-Function filter, configured to receive the electrical training signal as input and providing as output a filtered electrical training signal; - a summing unit adapted for adding the filtered electrical training signal to a signal in the primary signal path; - a synchronization unit adapted for synchronizing the operation of the two hearing aids of the binaural hearing aid system at least with respect to the output from the sound generators and the setting of the Head-Related-Transfer-Function filters; wherein at least one of the hearing aids comprises: - a randomization unit adapted to provide an at least partly and in time varying, random position for said virtual object relative to the binaural hearing aid system, - a user input adapted to provide a change of the random position for said virtual object by the user intending to move the position for said virtual object to a desired position and wherein the user input is configured to provide a relative change of the position for said virtual object, - a position determination unit adapted to determine the position for said virtual object based on the input from the randomization unit and from the user input; and - a look-up table holding Head-Related-Transfer-Functions for a number of discrete positions for said virtual object, whereby the Head-Related-Transfer-Function filters of the two hearing aids can be set such that a selected one of said discrete positions of the virtual object relative to the binaural hearing aid system is simulated for a user of the binaural hearing aid system. - a primary signal path comprising an acoustical-electrical input transducer, a digital signal processor configured to amplify an electrical input signal, representing an acoustic input to the acoustical-electrical transducer, in order to alleviate a hearing loss of an individual hearing aid system user, hereby providing a processed electrical input signal, and an electrical-acoustical output transducer; - a sound generator configured to provide an electrical training signal, representing the acoustic output from a virtual object; - a Head-Related-Transfer-Function filter, configured to receive the electrical training signal as input and providing as output a filtered electrical training signal; - a summing unit adapted for adding the filtered electrical training signal to a signal in the primary signal path; - a synchronization unit adapted for synchronizing the operation of the two hearing aids of the binaural hearing aid system at least with respect to the output from the sound generators and the setting of the Head-Related-Transfer-Function filters; - a randomization unit adapted to provide an at least partly and in time varying, random position for said virtual object relative to the binaural hearing aid system, - a user input adapted to provide a change of the random position for said virtual object by the user intending to move the position for said virtual object to a desired position and wherein the user input is configured to provide a relative change of the position for said virtual object, - a position determination unit adapted to determine the position for said virtual object based on the input from the randomization unit and from the user input; and - a look-up table holding Head-Related-Transfer-Functions for a number of discrete positions for said virtual object, whereby the Head-Related-Transfer-Function filters of the two hearing aids can be set such that a selected one of said discrete positions of the virtual object relative to the binaural hearing aid system is simulated for a user of the binaural hearing aid system.