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State estimation (SE) is an important energy management system application for power system operations. Linear state estimation (LSE) is a variant of SE based on linear relationships between state variables and measurements. LSE estimates system state variables, including bus voltage magnitudes and angles in an electric power transmission network, using a network model derived from the topology processor and measurements. Phasor measurement units (PMUs) enable the implementation of LSE by providing synchronized high-speed measurements. However, as the size of the power system increases, the computational overhead of the state-of-the-art (SOTA) LSE grows exponentially, where the practical implementation of LSE is challenged. This paper presents a distributed linear state estimation (D-LSE) at the substation and area levels using a hierarchical transmission network topology processor (H-TNTP). The proposed substation-level and area-level D-LSE can efficiently and accurately estimate system state variables at the PMU rate, thus enhancing the estimation reliability and efficiency of modern power systems. Network-level LSE has been integrated with H-TNTP based on PMU measurements, thus enhancing the SOTA LSE and providing redundancy to substation-level and area-level D-LSE. The implementations of D-LSE and enhanced LSE have been investigated for two benchmark power systems, a modified two-area four-machine power system and the IEEE 68 bus power system, on a real-time digital simulator. The typical results indicate that the proposed multilevel D-LSE is efficient, resilient, and robust for topology changes, bad data, and noisy measurements compared to the SOTA LSE.