Extension local representation of gravity anomaly along glide trajectory

Abstract

An extension local representation and its corresponding fast approximation scheme for the computation of the gravity anomaly along glide trajectories of a hypersonic vehicle are initially proposed, involving field model reconstruction, channel model reconstruction, and onboard approximation. To meet the needs of temporary mission changes, the mathematic model for the tridimensional envelope of glide trajectories is deduced, and thus developing a universal field model by dividing the domain and assigning values to the nodes. To lighten the computational burden, a local channel model is reconstructed by the acquisition of the data of nodes for the three-level extension cells which the planned trajectory flies through. The multi-gridded scheme restrains the actual glide trajectory from flying beyond the channel while the extension approximation achieves a high-fidelity computation of the gravity anomaly. To simplify the partitioning process, a “transposed-pole” coordinate system is employed. Simulations indicate that the approximation accuracy of the extension method is over an order of magnitude higher than that of the nonextension method. The terminal positional deviations of glide trajectories due to approximation errors are beneath 1 m and 100 m on the partitioning schemes of $10\text{km}/1.2^{\circ }/1.2^{\circ }$ and $10\text{km}/{20}^{\circ }/{20}^{\circ }$ , respectively. By using the scheme of $10\text{km}/{20}^{\circ }/{20}^{\circ }$ , it just needs 816 memorized data and 76.781 s to achieve the computation of a glide trajectory containing 10,000 calculation points, with a 100-times enhanced trajectory accuracy. The onboard computational time for the proposed method is only 6000th of that for 1080-order spherical harmonics. The high-adaptability for temporary mission changes and the virtues of exactness, rapidity, and applicability make this method attractive for both of onboard computations and offline analysis of gravity anomaly along glide trajectories.