Distributed algorithms, particularly Diffusion LMS (DLMS), are widely favored for their reliability, robustness, and fast convergence in various industries. However, limited observability of the target can compromise the integrity of the algorithm. To address this issue, this paper proposes a framework for analyzing combination strategies by drawing inspiration from signal flow analysis. A thresholding-based algorithm is also presented to identify and utilize the support vector in scenarios with missing information about the target vector's support. The proposed approach is demonstrated in two combination scenarios, showcasing the effectiveness of the algorithm in situations characterized by sparse observations in the time and transform domains. The paper concludes with a discussion of the results obtained and avenues for further exploration.

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