This paper presents an accelerated distributed receding horizon controller for cooperative network estimation problems using multiple autonomous agents. Our approach accelerates decision-making by integrating a novel heuristic-based ranking system, significantly reducing the dependency on computationally expensive Nonlinear Programs (NLPs). The reduction of computational complexity enables real-time responses and scalability to large systems while maintaining high levels of estimation accuracy. To mitigate the small loss of performance, we further introduce a method that aims at generating the best solution within a given computational time constraint by leveraging both the newly introduced ranking scheme and the traditional NLP solutions. Numerical simulations demonstrate competitive performance when benchmarked against data-driven offline policies (e.g., RL), showing that our methods achieve good results while having enhanced flexibility and robustness properties due to their online nature.