An accurate and efficient approximation to the normal gravity

Accelerometer measurements include the vehicular acceleration as well as the gravity contribution. In order for the Inertial Navigation System (INS) to compute the position and velocity of the vehicle correctly, the gravity portion from the measurements must be removed. Currently, the normal gravity model is widely used as a mathematical model for this purpose. The normal gravity model is described in this paper. Starting with the geodetic coordinates of a point, the normal gravity can be computed via complex coordinate transformations. Although the J₂ gravity model (an approximation to true gravity) provides a simple, straightforward computation, it has been found that the difference in the vertical component can reach 12 μg and the difference in the NS-component can be as much as 6.3 μg, compared to the normal gravity model. Hence it is not acceptable for high accuracy applications. Another way to obtain the gravity approximation is to generate the gravity vector g&oarr; via the normal gravity model at various grid points (φ_i, h_j), then fit them with some reasonable model and determine the model coefficients in the least square sense. The proposed approximation formulas in this article make use of the geodetic latitude and the eccentric latitude, together with the geodetic altitude, to obtain the gravity vector via a straightforward, accurate method. The results found through MATLAB for this study are valid for all latitudes and geodetic heights up to 100000 ft, with an RMS residual error of less than 0.0077 μg and 0.0090 μg, for the North-South and Vertical components of the gravity vector, respectively. The method call be extended to higher altitudes with the inclusion of higher degree terms in the polynomial function