s: In the GNSS/SINS integrated navigation system, due to the interference from internal and external environments, the measurement noise often appears as colored noise. The maximum correlation entropy Kalman filter (MCCKF) based on the Gaussian kernel function is an effective filtering method for dealing with this situation. The kernel bandwidth is a key parameter of the kernel function, and the filtering accuracy of MCCKF is very sensitive to the change of the kernel bandwidth. A small change in the kernel bandwidth will lead to a significant change in the filtering accuracy of MCCKF, thus resulting in poor filtering stability of MCCKF. To solve this problem, this paper proposes a maximum correlation entropy Kalman filtering algorithm based on the Cauchy kernel function (CkMCCKF). Firstly, a maximum correlation entropy criterion was established based on the Cauchy kernel function, which is insensitive to the kernel bandwidth; then, the fixed-point iterative algorithm of CkMCCKF was derived and established; finally, CkMCCKF was applied to the GNSS/SINS integrated navigation system and experimental verification was conducted. The experimental results have verified the excellent performance of CkMCCKF. Compared with MCCKF, the filtering stability of CkMCCKF has been significantly improved, that is, the filtering accuracy of CkMCCKF is less sensitive to the kernel bandwidth.