EGL

Improving estimation accuracy in navigation and vision systems using information geometry

Modern engineering applications such as precision navigation, radar tracking, and computer vision often require estimating parameters like position, orientation, or motion that naturally lie on curved geometric spaces. These spaces, known as Lie groups, provide a powerful mathematical framework for modeling such problems. In this project, we focus on deriving estimation error bounds in scenarios where the observed data depends on both unknown Lie group parameters and a covariance matrix. To address this, we exploit the Lie group structure of the space of positive definite matrices, allowing us to treat the entire estimation problem within a unified geometric setting. This leads to a global parameter that lives on the product of two Lie groups, enabling the use of intrinsic tools from Lie group theory to analyze estimation performance. This approach not only deepens our theoretical understanding but also enhances the robustness and accuracy of estimation techniques in real-world systems that operate in complex geometric environments.