Strapdown inertial navigation systems (INS) often employ aiding sensors to increase accuracy. Nonlinear filtering algorithms are then needed to fuse the collected data from these aiding sensors with measurements of strapdown rate gyros. Aiding sensors usually have slower dynamics compared to gyros and therefore collect data at lower rates. Thus the system will be unobservable between aiding sensors' sampling instants, and the error covariance, which shows the uncertainty in the estimation, grows during the sampling period. This paper presents a divided difference filter (DDF)-based data fusion algorithm, which utilizes the complementary noise profile of rate gyros and gravimetric inclinometers to extend their limits and achieve more accurate attitude estimates. It is confirmed experimentally that DDF achieves better covariance estimates compared to the extended Kalman filter (EKF) because the uncertainty in the state estimate is taken care of in the DDF polynomial approximation formulation.