In order to estimate the long-distance relative state of space non-cooperative spacecraft，a nonlinear relative motion model for the long-distance tracking of non-cooperative space spacecraft is established.The linear and nonlinear states are separated and discretized，by which the discretization accuracy is improved while the local nonlinear characteristics of the model are preserved.In view of the features that the state equation of this model is only partially nonlinear and the linear and nonlinear parts are decoupled from each other while interacting with each other，a local nonlinear Kalman filter （LNKF） is proposed based on matrix partitioning，and a simplified setting method of quadrature points without information loss is designed.This filter combines both linear and nonlinear operations，which reduces the computational complexity of the algorithm on the basis of avoiding the loss of state information.The proposed algorithm is applied to the long-distance relative state estimation for non-cooperative spacecraft，and the simulation results show that the calculation efficiency of the LNKF is significantly higher than that of the extended Kalman filter （EKF） and cubature Kalman filter （CKF） on the premise of ensuring the calculation accuracy.