A Study On Fast Computation Of Trajectory Disturbing Gravity

As the flying long-range ballistic missile can be affected by the earth's gravity field, and the space disturbing gravity can affect it's guidance and control accuracy, the trajectory disturbing gravity need to be real-time calculated to correct the inertia guidance system and actual trajectory. It's the important guarantee of improving the long-range ballistic missile's rapid reaction and precision strike capability.On the basis of depth studying the basic theory and method of the earth's gravity field, around the real-time computing needs of engineering, research the fast approximation algorithm of trajectory disturbing gravity and the accuracy of impact point.1. Research the basic theory of computing trajectory disturbing gravity by using the earth's gravity field model. In view of the gravity field model truncation error, calculate the suitable model order for computing in different height. Put three fast computing algorithm: spherical harmonic function improved recursive algorithm, spherical harmonic function coordinate conversion algorithm, spherical cap harmonic analysis. Experiment with the calculated results, the new calculation models' structures are simple and can improve the calculation speed.2. Research the basic theory of computing trajectory disturbing gravity by using point-mass model, and establish the frequency point-mass model of test region. By calculating trajectory disturbing gravity, analysis it's numerical and spectrum characteristics. Put three frequency numerical approximation algorithm: polynomial fitting algorithm, cubic spline interpolation algorithm, the three-parameter nonlinear fitting algorithm. The results of test computing and analysis show that the new frequency numerical approximation algorithms will improve computing speed more than 100 times in calculation precision suitable situation.3. Research the initiative and passive standard trajectory equations and the theory and method of computing landing error under the influence of disturbing gravity. Analyse and calculate the influence of the horizontal and range error of different disturbing gravity, and calculate the trajectory disturbing gravity limit error in different range of height.4. Design and write the corresponding fast approximation algorithms process and code, evaluate their effectiveness on the same computing platform. Guided from the principle of inertia guidance system, explained the importance of real-time computing trajectory disturbing gravity to improve the ballistic missile's combat capabilities. Preliminary design a real-time computing software module structure and calculation process, to provide a theoretical basis for practical application of engineering.