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Two novel L1 estimation methods for multisensor data fusion are developed, respectively in the case of known and unknown scaling coefficients. Two discrete-time cooperative learning (CL) algorithms are proposed to implement the two proposed methods. Compared with the high-order statistical method and the entropy estimation method, the two proposed estimation methods can minimize a convex cost function of the linearly fused information. Furthermore, the proposed estimation method can be effectively used in the blind fusion case. Compared with the minimum variance estimation method and linearly constrained least square estimation method, the two proposed estimation methods are suitable for non-Gaussian noise environments. The two proposed CL algorithms are guaranteed to converge globally to the optimal fusion solution under a fixed step length. Unlike existing CL algorithms, the proposed two CL algorithms can solve a more complex L1 estimation problem and are more suitable for weight learning. Illustrative examples show that the proposed CL algorithms can obtain more accurate solutions than several related algorithms.