implicit guidance

The complexity and cost of solid fuel engines cut-off demands a comprehensive method for guiding these missiles so current required velocity methods can not solve this problem. This paper presents an implicit cut-off insensitive guidance scheme for ballistic missiles. The main idea behind this scheme is to correct the nominal flight path angle, at arbitrary time with respect to value of disturbances and uncertainties such as wind, thrust misalignment, thrust value, aerodynamic coefficients, to satisfy the nominal burnout time conditions. Compared with preset scheme, the proposed scheme is more robust to motor performance uncertainty. The circular error probability of proposed method is calculated about 1.242 km which is 61% less than preset method's circular error probability. It is also simpler and has a lighter calculation load. It is shown that the proposed algorithm has good performance through the computer simulation.The circular error probability of proposed method is calculated about 1.242 km which is 61% less than preset method's circular error probability. It is also simpler and has a lighter calculation load. It is shown that the proposed algorithm has good performance through the computer simulation.

In this paper, implicit guidance equations are derived in polar coordinates. Depending on applications, implicit guidance equations in polar coordinates may be preferred over cartesian coordinates. Moreover, depending on the type of guidance problem, analytical solutions for sensitivity matrices may be simplified using polar coordinates. Therefore, transformation of implicit guidance equation into polar coordinates can be useful in guidance problems. In addition, the resulting equations are extended to cylindrical coordinates.

In this research, an approximate solution of the required velocity with final velocity constraint is derived using linear gravity assumption along the path of current position to the final position vectors. Moreover, an approximate solution for sensitivity matrix of the required velocity with respect to the position vector is obtained. The presented solutions are given for a predetermined final time. In this case, for the free final position, the analytical solution is rather more difficult than its fixed final position counterpart. Therefore, three approaches are utilized for approximation of the final position vector. Finally, the obtained solutions are compared to exact numerical one for the spherical- Earth model.