Networked microgrids (NMGs) are critical in the accommodation of distributed renewable energy. However, the existing centralized state estimation (SE) cannot meet the demands of NMGs in distributed energy management. The current estimator is also not robust against bad data. This study introduces the concepts of relative error to construct an improved robust SE (IRSE) optimization model with mixed-integer nonlinear programming (MINLP) that overcomes the disadvantage of inaccurate results derived from different measurements when the same tolerance range is considered in the robust SE (RSE). To improve the computation efficiency of the IRSE optimization model, the number of binary variables is reduced based on the projection statistics and normalized residual methods, which effectively avoid the problem of slow convergence or divergence of the algorithm caused by too many integer variables. Finally, an embedded consensus alternating direction of multiplier method (ADMM) distribution algorithm based on outer approximation (OA) is proposed to solve the IRSE optimization model. This algorithm can accurately detect bad data and obtain SE results that communicate only the boundary coupling information with neighbors. Numerical tests show that the proposed algorithm effectively detects bad data, obtains more accurate SE results, and ensures the protection of private information in all microgrids.