This paper aims to enhance the array Beamforming (BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming (CMBB). To achieve this, we introduce a novel approach that incorporates an L1-regularizer term in BF weight state estimation. We start by explaining the CMBB formation mechanism under conditions where there is a mismatch in the far-field signal model. Subsequently, we reformulate the BF weight state estimation challenge using a method known as variable-splitting, turning it into a noise minimization problem. This problem combines both linear and nonlinear quadratic terms with an L1-regularizer that promotes the sparsity. The optimization strategy is based on a variable-splitting method, implemented using the Alternating Direction Method of Multipliers (ADMM). Furthermore, a variable-splitting framework is developed to enhance BF weight state estimation, employing a Kalman Smoother (KS) optimization algorithm. The approach integrates the Rauch-Tung-Striebel smoother to perform posterior-smoothing state estimation by leveraging prior data. We provide proof of convergence for both linear and nonlinear CMBB state estimation technology using the variable-splitting KS and the iterated extended Kalman smoother. Simulations corroborate our theoretical analysis, showing that the proposed method achieves robust stability and effective convergence, even when faced with signal model mismatches.