The nonlinear dynamic system has problems of nonlinearity and noise uncertainty, and the cubature Kalman filter has better accuracy for solving such systems. In order to improve the robustness of the navigation system to abnormal observations, the sampled data is average filtered to reduce the impact of the sampled data with greater interference on the filter. The singular value decomposition is used to replace the Cholesky decomposition to avoid the non-positive definite prior covariance reducing the filter stability. Finally, by introducing a robustness factor to adjust the observation covariance matrix, the effect of observation outliers on the filtering results is reduced again. Using simulation experiments for analysis, the improved robust cubature Kalman filter algorithm is effective for reducing the influence of abnormal observations.