Distributed state estimation is crucial for multi-agent and sensor network applications, especially when measurements are sporadic and computational resources are limited. We introduce a novel distributed moving horizon estimation (DMHE) framework which integrates Luenberger pre-estimation observers, an L-hop information diffusion mechanism, and environmental convex constraints. The pre-estimation step eliminates the need to estimate the complete disturbance sequence, thereby reducing online computation, while the L-hop diffusion enables sensors to leverage measurements beyond their immediate neighborhood to enhance local observability. Moreover, incorporating convex constraints improves estimation accuracy in scenarios with intermittent sensor observations. Experiments in a multi-robot localization scenario using a sensor camera network confirm that the proposed DMHE approach achieves faster convergence and higher accuracy than existing methods.