# Uncertainty propagation in approach GN&C using Differential Algebra

# Project overview

Future landing and close-approach missions (e.g. space debris removal, asteroid landing for mining, pinpoint planetary landing) will require increasingly more complex Guidance, Navigation & Control (GN&C) systems. It is important that the design and analysis of these non-linear and complex systems can be performed accurately and efficiently. Uncertainty propagation in models of GN&C systems has been traditionally either performed by linearizing them at the cost of accuracy or by performing accurate but computationally expensive Monte Carlo simulations.

A compromise between the two is offered by Differential Algebra (DA), a numerical technique to automatically compute high order Taylor expansions of a given function. In the DA framework, the Taylor expansion of a system model function is calculated once at relatively high computational expense. This expansion however can then be used to evaluate any input value around the nominal with negligible computational costs. DA thus offers the potential for a significant reduction of computational resources and time used for the design and analysis of complex approach GN&C systems.

In this project we investigate the use the application of the DA framework for non-linear uncertainty propagation in a GN&C model for approach operations. We do this in particular for the three critical high-level functions of advanced approach GN&C:

- guidance & control,
- navigation and mapping, and
- hazard detection and avoidance.

# References

- M. Rasotto et al. 2016. “Differential algebra space toolbox for nonlinear uncertainty propagation in space dynamics.” In 6th International Conference on Astrodynamics Tools and Techniques (ICATT), Darmstadt, Germany. https://eprints.soton.ac.uk/390313/
- F. Cavenago et al. 2019. "On-board spacecraft relative pose estimation with high-order extended Kalman filter." Acta Astronautica, vol. 158, pp. 55-67, http://www.sciencedirect.com/science/article/pii/S0094576518301516