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Clock synchronization is crucial in time-sensitive networks (TSN) to ensure the normal operation of devices. However, traditional synchronization techniques face challenges such as the accumulation of synchronization errors over multiple hops and slow synchronization speed, which hinder the development of large-scale and multi-hop TSN. In this paper, we propose a cooperative synchronization scheme based on two-way timestamp exchange to reduce error accumulation and enable synchronization information exchange between any node in the network and the reference node. Moreover, we develop a fast Kalman filter (FKF) algorithm to estimate clock offset and clock skew. To reduce time complexity, we replace the calculation of gain matrices with extremely high dimension with a small matrix based on the randomization matrix approximation in the updating phase of the Kalman Filter. Simulation results show that the proposed method significantly reduces synchronization complexity without sacrificing clock synchronization accuracy, making it highly promising for future TSN deployments. [ABSTRACT FROM AUTHOR]