# Statistical Methods for Launch Vehicle Guidance, Navigation, and Control (GN&C) System Design and Analysis

5-2012

Dissertation

## Degree Name:

Doctor of Philosophy (PhD)

## Department:

Mechanical and Aerospace Engineering

David K. Geller

David K. Geller

R. Rees Fullmer

## Committee

Stephen A. Whitmore

## Committee

Charles M. Swenson

Byard D. Wood

## Abstract

A new tool for launch vehicle design and analysis is developed. The tool is capable of rapid analysis of requirements tradeoffs affecting system design and developed to reduce turnaround time for launch vehicle design and mission planning. It is streamlined to quickly determine trajectory and attitude control dispersions which represent how far the actual trajectory is expected to deviate from the nominal flight path, propellant dispersions which represent how much propellant is required to meet mission requirements, and navigation errors which represent how far the navigation filter’s estimate of the actual trajectory is expected to deviate from the actual trajectory. Moreover, the tool is able to measure sensitivities to instrument errors, engine performance uncertainties, and random disturbances.

The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear equations, algorithms, and models for a Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The nonlinear equations, algorithms, and models associated with the Monte Carlo simulation are linearized about the NRT. The linear covariance equations are formulated and the linear covariance simulation is developed.

The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance simulations and their results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for lunar ascent, the tools, techniques, and mathematical formulations that are discussed are applicable to launch vehicles on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles. This research was supported in part by National Aeronautics and Space Administration (NASA) Johnson Space Center and Draper Laboratory.

## Checksum

9ceab85c668927e0c982875c11f1c8e3

This work made publicly available electronically on July 30, 2012.

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#### DOI

https://doi.org/10.26076/ef8f-7cd9