Better method for computing air-to-air missile trajectory

Polynomial fitting method has been generally employed for computing the trajectory of air-to-air missile. It suffers from the following three shortcomings: air-borne computer must store a large number of polynomial coefficients; under certain conditions, its precision is not sufficiently high; under certain conditions, the calculated results are not continuous. We now present a better method that can suppress these three shortcomings. In the paper, we explain our method in detail. The polynomial fitting model of our algorithm and our fast algorithm for calculating the trajectory of air-to-air missile are presented. We give 11 steps for implementing our fast algorithm, in which step 2 is particularly important because it enables our algorithm to start with an approximate initial value based on polynomial fitting that requires only a limited storage of polynomial fitting coefficients and is the basic reason why our algorithm is fast. We give eq. (4) needed by 3rd order Runge-Kutta numerical method. Finally we take as example the firing control system of the air-to-air missile of a certain fighter aircraft. The numerical results obtained with our method as compared with those obtained with traditional polynomial method are given. These results indicate preliminarily that the probability of success is 96.03% for our method and only 74.56% by the traditional polynomial fitting method.