Master thesis : Kalman filtering solutions in the context of a laser-guided missile application

Abstract

Introduced in 1960 by Rudolf Emil Kálmán, the Kalman filter is one of the most widely used filters in various fields. It recursively estimates the state of a system using its transition model and measurements from one or more sensors, and is the optimal estimator in terms of mean-square error under certain assumptions. This thesis explores the implementation, limitations, and comparison of two Kalman filtering solutions in the context of the FZ275 LGR, a laser-guided missile designed and produced by Thales Belgium SA, a Belgian subsidiary of the French multinational Thales Group. The first solution aims to replace the current estimator of the missile, an alpha-beta filter, with a linear Kalman filter. The two models considered perform better with respect to certain defined metrics, and they provide less noisy estimates. However, due to reasons detailed in this work, the current estimator provides better results in terms of impact results. The second solution studies the design and implementation of an inertial navigation system based on an invariant extended Kalman filter. A Global Navigation Satellite System based filter and a semi-active laser seeker based filter are compared to the current implementation and to two extended Kalman filters, which are considered to be the industry standard. The use of an inertial navigation system dramatically improves both the estimates and the impact results compared to the current implementation. There is no significant difference between the two GNSS-based filters. On the other hand, the seeker-based invariant extended Kalman filter provides better results than the seeker-based extended Kalman filter. The performance gain is mainly due to different assumptions that introduce additional constraints. These limitations make a real-world implementation more challenging and would require further research to assess feasibility.