Fast　power　system　state　estimation　(SE)　solution　is　indispensable　to　achieve　real-time　decision　making　in　power　grid　management.　Semidefinite　programming　(SDP)　reformulation　has　shown　powerful　to　approach　the　global　optimum　of　the　nonlinear　SE　problem,　while　suffering　from　high　computational　complexity.　Thus,　we　leverage　the　recent　advances　in　nonconvex　SDP　reformulation　that　can　allow　first-order　updates　to　potentially　solve　the　original　SDP　problem.　We　further　adopt　the　accelerated　gradient　descent　(AGD)　method　for　the　resultant　unconstrained　problem　for　improved　convergence　speed.　Numerical　tests　have　demonstrated　that　AGD　can　achieve　comparable　SE　performance　as　the　globally　optimal　SDP　solution　at　improved　computational　efficiency.