A microphone system comprising • a multitude M of microphones, where M is larger than or equal to two, adapted for picking up sound from the environment and to provide M corresponding electric input signals x m (n), m =1,..., M, n representing time, the environment sound at a given microphone comprising a mixture of a target sound signal s m (n) propagated via an acoustic propagation channel from a location of a target sound source, and possible additive noise signals v m (n) as present at the location of the microphone in question; • a signal processor connected to said number of microphones, and being configured to estimate a direction- to and/or a position of the target sound source relative to the microphone system based on ∘ a maximum likelihood methodology; ∘ a database Θ comprising a dictionary of vectors d θ, termed RTF-vectors, whose elements are relative transfer functions d m (k) representing direction-dependent acoustic transfer functions from said target signal source to each of said M microphones ( m =1,..., M) relative to a reference microphone ( m = i) among said multitude of M microphones, k being a frequency index, wherein individual dictionary elements of said database Θ of RTF vectors d θ comprises relative transfer functions for a number of different directions ( θ) and/or positions ( θ, φ, r) relative to the microphone system; and the signal processor is configured to • determine a likelihood function or a log likelihood function of some or all of the elements in the database Θ in dependence of an inter-microphone cross-power spectral density matrix of the noisy signal impinging on said multitude Mof microphones, termed the noisy target signal covariance matrix C x, and an inter-microphone cross-power spectral density matrix of the noise signal impinging on said multitude M of microphones, termed the noise covariance matrix C v, and wherein said noisy target signal covariance matrix C x and said noise covariance matrix C v are represented by smoothed estimates, wherein said smoothed estimates of said noisy target signal covariance matrix Ĉ X and/or said noise covariance matrix Ĉ V are determined by adaptive covariance smoothing with smoothing coefficients determined in dependence of changes in the covariance matrices, and based thereon to • determine an a posterior probability or a log posterior probability of some of or all of said individual dictionary elements, and • determine one or more of the most likely directions to or locations of said target sound source by determining the one or more values among said determined posterior probabilities or said log posterior probabilities having the largest posterior probability or probabilities or log posterior probability or probabilities, respectively. • a multitude M of microphones, where M is larger than or equal to two, adapted for picking up sound from the environment and to provide M corresponding electric input signals x m (n), m =1,..., M, n representing time, the environment sound at a given microphone comprising a mixture of a target sound signal s m (n) propagated via an acoustic propagation channel from a location of a target sound source, and possible additive noise signals v m (n) as present at the location of the microphone in question; • a signal processor connected to said number of microphones, and being configured to estimate a direction- to and/or a position of the target sound source relative to the microphone system based on ∘ a maximum likelihood methodology; ∘ a database Θ comprising a dictionary of vectors d θ, termed RTF-vectors, whose elements are relative transfer functions d m (k) representing direction-dependent acoustic transfer functions from said target signal source to each of said M microphones ( m =1,..., M) relative to a reference microphone ( m = i) among said multitude of M microphones, k being a frequency index, ∘ a maximum likelihood methodology; ∘ a database Θ comprising a dictionary of vectors d θ, termed RTF-vectors, whose elements are relative transfer functions d m (k) representing direction-dependent acoustic transfer functions from said target signal source to each of said M microphones ( m =1,..., M) relative to a reference microphone ( m = i) among said multitude of M microphones, k being a frequency index, • determine a likelihood function or a log likelihood function of some or all of the elements in the database Θ in dependence of an inter-microphone cross-power spectral density matrix of the noisy signal impinging on said multitude Mof microphones, termed the noisy target signal covariance matrix C x, and an inter-microphone cross-power spectral density matrix of the noise signal impinging on said multitude M of microphones, termed the noise covariance matrix C v, and wherein said noisy target signal covariance matrix C x and said noise covariance matrix C v are represented by smoothed estimates, wherein said smoothed estimates of said noisy target signal covariance matrix Ĉ X and/or said noise covariance matrix Ĉ V are determined by adaptive covariance smoothing with smoothing coefficients determined in dependence of changes in the covariance matrices, and based thereon to • determine an a posterior probability or a log posterior probability of some of or all of said individual dictionary elements, and • determine one or more of the most likely directions to or locations of said target sound source by determining the one or more values among said determined posterior probabilities or said log posterior probabilities having the largest posterior probability or probabilities or log posterior probability or probabilities, respectively.