An Efficient Algorithm for Computing the Q-Guidance Matrix
NAVAL SURFACE WEAPONS CENTER DAHLGREN LAB VA
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This paper derives a new method for computing the Q-guidance matrix. This matrix is defined as the derivative with respect to position of the correlated velocity V sub C i.e., the velocity required to reach a given target in a specified time in an inverse-square gravitational field. The method is completely analytic and yields a simple and efficient algorithm. The analytic equation for the partial derivative of the horizontal component of correlated velocity with respect to range angle developed here is also of independent interest. To the authors knowledge, no such expression for this quantity in terms of the given conditions and the components of V sub C has been derived previously. This equation, in conjunction with the others given here, makes it possible to compute virtually any first order derivative of V sub C of interest. The Q-matrix algorithm is of use primarily in the analysis and modeling of guidance systems using some form of V sub G steering.
- Navigation and Guidance