In view of the abnormal situation in the measurement, an Adaptive Robust Squareroot ContinuousDiscrete Cubature Kalman Filter algorithm is proposed based on the Mestimated. The algorithm is that the target tracking problem is modeled as a continuousdiscrete time model, the idea of improved M estimation is integrated into the continuousdiscrete cubature Kalman filter algorithm, threshold abnormal measurements are made by using Mahalanobis distance, a correction factor is introduced, and the size of the observed noise covariance matrix is adaptively adjusted in accordance with the observation residuals to further improve the robustness of the filtering algorithm. And by combining the continuousdiscrete model with the correction factor, the filtering accuracy and the antiabnormal measurement value are unified. The simulation results show that compared with the traditional robust algorithm, MARSRCDCKF can track targets more accurately and the robustness is more strong under conditions of singlepoint measurement abnormality and multipoint measurement abnormality.