Aiming at the problems that the decline of accuracy appears in traditional CKF under non-Gaussian noise and the slower convergence speed of the traditional MCC algorithm, an improved adaptive correlation entropy high-degree cubature Kalman filter algorithm (ADMCC-HCKF) is proposed. This method adaptively adjusts the kernel width according to the error changes of the MCC iteration process, kernel width can influence the sensitivity of the kernel parameters to the input data, thereby improve the convergence speed of the algorithm and the processing ability of non-Gaussian noise. Under the non-Gaussian noise environment, we build a SINS / CNS / GNSS integrated navigation experiment, the results show that under non-Gaussian noise conditions, the improved adaptive ADMCCHCKF algorithm shows stronger robustness than traditional HCKF and conventional MCC-HCKF, at the same time, it has batter noise reduction performance and resistance to non-Gaussian noise. In terms of filtering accuracy, compared with the HCKF algorithm, an average improvement of 9. 63%.