Histogram construction via algebraic Monte Carlo method, determining simultaneous effect of several input statistical variables on output variable

This paper presents a method for conducting a Monte Carlo simulation of a space mission when nonlinear effects must be considered and accounted for. The simulation uses precomputed relationships between variables to generate the Monte Carlo samples from which the appropriate statistical information is computed. The method reduces the computing time required for the Monte Carlo simulation to just about that required to perform a standard root-sum-square analysis. The results, however, are considerably greater in information content, allow definitive probabilistic statements to be made about the performance of the vehicle, and can be used in the analysis of a multiphase mission. Thus, a very realistic assessment of the over-all performance of a space vehicle can be made at a reasonable computing cost.

An alternative to Monte Carlo.

Analytic Monte Carlo error analysis.

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.

An alternative to Monte Carlo.

Citations

Analytic Monte Carlo error analysis.

Conditional performance error covariance analyses for commercial Titan launch vehicles

References

Random Number Generators

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