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In order to solve the problem of poor robustness in the case of inaccurate system models and abrupt state transitions for square root cubature kalman filter (SCKF), a multiple fading factors strong tracking SCKF (MSTSCKF) is proposed. Combining with strong tracking filter idea, MSTSCKF adjusts the gain matrix in real-time through multiple fading factors, establishes a multiple fading factors numerical solution method and overcomes the dependent on prior knowledge. Meanwhile, MSTSCKF uses hypothesis testing theory to detect system anomalies, reduces the probability of misjudgment and improves filter stability. At last, SCKF、single strong tracking SCKF(STSCKF) and MSTSCKF is compared in numerical simulation experiments under different conditions. The simulation results declare that MSTSCKF has better performance on tracking accuracy and robustness.