Nonlinear uncertainty propagation in space trajectories

Author: Malhotra, Sunil K.

Year: 1992

Degree: Engineer's thesis

Committee Member: Caughey, Thomas Kirk

Option: Mechanical Engineering

DOI: 10.7907/4012-RF25

Abstract

This thesis addresses the problem of nonlinear uncertainty propagation in space trajectories. This problem can be specifically stated as follows: Given the initial orbital state of a spacecraft trajectory as random variables, what is the orbital state at some later time?

This problem is currently encountered by mission designers at institutions such as the Jet Propulsion Laboratory. Before an expensive space probe is irretrievably launched, extensive trajectory analyses are conducted to determine the amount of fuel needed to correct for trajectory errors. This involves propagation of uncertainties in the trajectories.

The current method for uncertainty propagation involves linearizing about the nominal trajectory to obtain a state transition matrix used to map the covariance matrix to a later orbital state. This method neglects nonlinear effects.

Two new algorithms were developed to account for nonlinear effects in the propagation of uncertainties in space trajectories. The first utilized simplifying assumptions to obtain analytic expressions for the probabilistic quantities describing the final orbital state. This algorithm provided good trend information but lacked precision. The second algorithm utilized Gaussian quadrature techniques to numerically compute the desired quantities. While requiring significant computational effort, this algorithm provided high precision.

Example trajectories were analyzed to compare the results from the new algorithms to those from the current method. Nonlinear effects were shown to influence both the mean and the variance results.

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