A low cost MEMS based Inertial sensor measurement Unit (IMU) is a key device in Attitude Heading Reference System (AHRS). AHRS has been widely used to provide the position and orientation of an object. The performance of an AHRS system can degrade due to IMU sensor errors, that could be deterministic and stochastic. To improve the AHRS system performance, there is a need to develop; (i) stochastic error models and (ii) minimize the random drift using de-noising techniques. In this paper, the Sage-Husa Adaptive Robust Kalman Filter (SHARKF) is modified based on robust estimation and a time varying statistical noise estimator. In the proposed algorithm, an adaptive scale factor (α) is developed based on a three segment approach. In the MSHARKF, the adaptive factor is updated in each iteration step. The MSHARKF algorithm is applied to minimize the bias drift and random noise of the MEMS IMUs signals. From the Allan variance analysis, the noise coefficients such as bias instability (Bs), angle random walk (N) and drift are evaluated before and after minimizing. Simulation results reveal that the proposed algorithm performs better than other algorithms for similar tasks. © 2018 IEEE.