A computational scheme for an INS which utilizes micro-electro mechanical systems (MEMS) sensors resolves issues of unnecessarily large computational burden and numerical instability which happen in using conventional methods using high-end inertial sensors. The first aspect is to omit computing Earth radii of curvatures that were used in a high-frequency application. The second aspect is to ignore the Earth rotation and the rotation of the local tangent plane with respect to Earth which are much smaller than noise and bias in the MEMS sensor output. The last aspect is to assume that the absolute amount of the platform pitch and roll angles is less than 90 degrees. According to the aspects noted above, the computational load will be one-fourth of the conventional method without degradation of accuracy.