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A fast MUltiple SIgnal Classification(MUSIC) spectrum peak search algorithms is devised, which reduces the two-dimensional search for azimuth and elevation angles pair into two separate one-dimensional searches. This algorithm first regards elevation angle as a nuisance parameter and explores generalized Rayleigh ratio theory to obtain the azimuth estimates by one-dimensional search. Then the elevation angle is easily determined by another one-dimensional search with known azimuth. Theoretical analysis and simulations show that the proposed method reduces computational and storage costs in conventional MUSIC techniques greatly with comparable performance.