Conditional performance error covariance analyses for commercial Titan launch vehicles

Abstract

An important part of space launch vehicle mission planning is the analysis of performance dispersions at various trajectory events such as park orbit injection and payload separation. Performance dispersions produce position, velocity and time errors at these events. The variances and covariances of the performance errors are usually specified by a 7x7 space-time error covariance matrix. At a predetermined mission time, the position and velocity errors are viewed as being conditional upon the predefined time, and there exists a need to comput,e a conditional 6x6 space covariance matrix. A numerical approach is usually used to compute the conditional matrix. In this paper, a comprehensive theoretical method is developed to transform a 7x7 (or higher order) space-time covariance matrix into a 6x6 space covariance matrix for a Commercial Titan launch vehicle. The method is based on the statistical theory of conditional multivariate normal distributions. Using chi-square based equality of variance hypothesis tests, the theoretical matrix is compared to the numerically computed matrix. The hypothesis test results establish that there are no significant differences between the theoretically and numerically computed 6x6 conditional space covariance matrices.