Aiming at the problems of large estimation error and poor anti-interference ability in state estimation and parameter learning of time-varying nonlinear systems, a batch state estimation and parameter learning method for accurate sparse Gaussian variational inference for nonlinear systems was proposed. A loss function was proposed based on Gaussian variational reasoning, and the state estimation problem was transformed into an approximation problem to the true posterior, and parameters that need to be learned were introduced. The parameters of the state probability distribution were iteratively updated using the Gauss-Newton op-timizer method, and a complete state estimation iterative scheme was obtained by using Stein"s lemma, the sparsity of the covari-ance matrix and the Gaussian volume method. The noise parameters of the measurement model were learned through expectation maximization, and the inverse Wishart prior was introduced to reduce the influence of measurement noise and outliers on parame-ter learning and state estimation results. The simulation experiment was carried out on the UAV simulation model, and the UAV trajectory can be accurately estimated without adding the UAV movement and the real value of the measurement noise, and the impact of measurement noise and measurement outliers on trajectory estimation accuracy is effectively suppressed.