  In the classical Kalman filter(KF), the estimated state is a linear
combination of the one-step predicted state and measurement state, their
confidence level change when the prediction mean square error matrix and
covariance matrix of measurement noise vary. The existing student's t based
Kalman filter(TKF) works similarly to the way KF works, they both work well
with impulse noise, but when it comes to Gaussian noise, TKF encounters an
adjustment limit of the confidence level, this can lead to inaccuracies in such
situations. This brief optimizes TKF by using the Gaussian mixture model(GMM),
which generates a reasonable covariance matrix from the measurement noise to
replace the one used in the existing algorithm and breaks the adjustment limit
of the confidence level. At the end of the brief, the performance of the
covariance adaptive student's t based Kalman filter(TGKF) is verified.
