This paper introduces a decentralized estimator-based safety-critical controller designed for formation control of non-holonomic mobile robots operating in communication-constrained environments. The proposed framework integrates a robust state estimator capable of accurately reconstructing neighboring agents' velocity vectors and orientations under varying dynamic conditions, with a decentralized formation tracking controller that leverages Control Barrier Functions (CBFs) to guarantee collision avoidance and inter-agent safety. We present a closed-form control law that ensures both stability and string stability, effectively attenuating disturbances propagating from leader to followers. The theoretical foundations of the estimator and controller are established using Lyapunov stability analysis, which confirms global asymptotic stability under constant velocities and global uniformly ultimate boundedness under time-varying conditions. Extensive numerical simulations and realistic Gazebo-based experiments validate the effectiveness, robustness, and practical applicability of the proposed method, demonstrating precise formation tracking, stringent safety maintenance, and disturbance resilience without relying on inter-robot communication.