Abstract: A simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) can simultaneously assist wireless communication for users located on both sides of the STAR-RIS. The uplink channel estimation problem of a dual-user millimeter wave communication system assisted by STAR-RIS is studied, and the joint sparse characteristic of the two users in the angle domain is explored. Based on the joint sparse characteristic of cascaded channels and compressed sensing theory, the cascaded channel estimation problem is transformed into a sparse signal recovery problem , and a Position-Judgment Orthogonal Matching Purity (PJ-OMP) algorithm is proposed to reduce pilot overhead. Simulation results show that compared with the traditional Orthogonal Matching Pursuit (OMP) algorithm, the proposed method can reduce pilot overhead in the channel estimation process, and can accurately estimate the channel even when the energy allocated to the user on one side is less.