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This paper applies the second order Taylor approximation to model the nonlinear uncertainty of acceleration rotation for MEMS based strapdown integration. Filtering solutions for tracking comprising inertial sensors require a good statistical modeling of the inertial measurements. The nonlinearity results in an umbrella-shape probability density distribution, and causes net downward vertical acceleration bias, which can not be estimated by traditional methods using only the first order approximation. This in turn leads to increasing vertical velocity and position errors after double integration which is significant for MEMS grade inertial sensors. Moreover, the analytical second order nonlinear term is applied in an extended Kalman filter (EKF) framework and compared with a normal EKF. The benefits of the method are demonstrated using a 3D MEMS IMU.