Space shuttle guidance, navigation and control equation document no. 4: Precision state and filter weighting matrix extrapolation

The Precision State and Filter Weighting Matrix Extrapolation Routine is described which provides the capability to extrapolate any spacecraft geocentric state vector either backwards or forwards in time through a force field consisting of the earth's primary central-force gravitational attraction and a superimposed perturbing acceleration. The routine also provides the capability of extrapolating the filter-weighting matrix along the precision trajectory. This matrix is a square root form of the error covariance matrix and contains statistical information relative to the accuracies of the state vectors and certain other optionally estimated quantities. The routine is a cooled algorithm for the numerical solution of modified forms of the basic differential equations which are satisfied by the geocentric state vector of the spacecraft's center of mass and by the filter-weighting matrix.