Binaural speech enhancement in hearing aids requires accurate estimates of the acoustic transfer functions (ATFs) of the active sources and the noise covariance matrix to drive spatial filters that simultaneously suppress interference and preserve binaural cues. Existing methods estimate these quantities sequentially, introducing error propagation and a dependency on noise-only intervals that limits robustness in adverse acoustic conditions. This thesis proposes a covariance-domain extension of Simultaneous Orthogonal Matching Pursuit that jointly estimates the active head-related transfer function (HRTF) subspace, source signal energies, and noise covariance from the observed cross-power spectral density matrix within a single iterative procedure. Controlled simulation experiments against a GEVD-based baseline demonstrate consistently lower HRTF estimation error across a wide range of SNR levels, time block sizes, and source azimuth configurations, with particular advantage at low SNR and short block lengths. When used to drive a joint binaural LCMV beamformer, the framework yields near-zero and stable target interaural time difference errors across the full SNR range, confirming that the joint estimation strategy produces internally consistent beamformer inputs that support robust binaural cue preservation. ... Read more