Advanced statistical techniques for mission analysis

Lunar X prize teams are competing to be the first non-governmental spacecraft to soft land on the Moon. All the teams have small budgets that are severe restrictions for mission designers. Hence it is necessary to rely heavily on historical data analysis and simulation to characterize and quantify expected performance of mission components. Statistical methods such as Exploratory Data Analysis (EDA), Time Series Analysis and Design & Analysis of Computer Experiments (DACE) are ideally suited to the task of delivering maximum information on the operating windows of expected performance at minimum cost. A case study is presented from a Lunar X team (SpaceIL) using statistical methods to characterize the expected performance of the Universal Space Network (USN) tracking stations to be used in the mission, using residuals data from the NASA Lunar Reconnaissance Orbiter mission (LRO). A moving window Time Series method was used to model the occurrence and duration of jumps in residuals. A feature of our method is the ability to isolate transient signals (e.g. jumps) from the usual noise for improved characterization of tracking performance. The EDA process revealed features such as bimodal distribution of data at some stations, and periodic patterns in the autocorrelation between residual values by day and by pass. These actual tracking performance measures will be used as inputs to a simulation tool for performance analysis of SpaceIL’s orbit determination capabilities. To maximize the information from the minimum number of simulation runs we outline the use of statistical DACE – a method adapted from industrial experiments that is highly efficient at determining input/output functional relationships in complex multivariate systems. The case study indicates a way forward for increased use of statistical tools and approaches in Mission Design and Analysis, by adapting methods from other disciplines such as econometrics and industrial experimentation.