  Two primary families of methods exist for underdetermined blind
identification (UBI) based on the sparsity of the source matrix: sparse
component analysis (SCA) and $k$-SCA. SCA assumes one active source at each
time instant, while $k$-SCA allows for varying numbers of active sources
represented by $k$. However, existing $k$-SCA methods, which claim to solve UBI
problems by accommodating $k$-sparse sources, predominantly rely on $1$-sparse
sources, limiting their effectiveness in real-world scenarios with high noise
levels.
  In this paper, we propose an effective and computationally less complex
approach for UBI, specifically focusing on the challenging case when the number
of active sources is equal to the number of sensors minus one ($k=m-1$). Our
approach overcomes limitations by using a two-step scenario: (1) estimating the
orthogonal complement subspaces of the overall space and (2) identifying the
mixing vectors. We present an integrated algorithm based on the Gram-Schmidt
process and random sample consensus (RANSAC) method to solve both steps.
Experimental results using simulated data demonstrate the superior
effectiveness of our proposed method compared to existing algorithms.
