High-Precision Three-Dimensional Navigation: Continuous-Discrete Kalman Filtering on Lie Groups

• Grant number: 25/06865-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: January 01, 2026
• End date: December 31, 2027
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: João Bosco Ribeiro do Val
• Grantee: Jitesh Ashok Manilal Vassaram
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The project aims to develop and implement advanced techniques for high-precision inertial navigation, focusing on two key aspects: the application of Generalized Gaussian Filters and Continuous-Discrete Kalman Filtering, both adapted to Lie Groups. The main objective is to improve position and orientation estimation by combining GNSS and IMU sensor data, exploring more robust and precise approaches than the traditional Extended Kalman Filter (EKF) built in Euclidean Space.Generalized Gaussian Filters propose an alternative Gaussian approximation for the filter solution through the so-called "Moment Matching," aiming to overcome the limitations of the traditional EKF in dynamic systems with significant nonlinearities. To achieve this, both the mean and covariance are represented using an integral, and advanced numerical integration methods such as Cubature, Gauss-Hermite, and the Unscented Transformation are used for resolution.Continuous-Discrete Filtering, unlike Discrete-Discrete Filtering, represents a system's dynamics as a Stochastic Differential Equation (SDE), while the measurement model is described in discrete time. This allows the application of various numerical integration methods to solve the SDE, such as Euler's method, Fourth-Order Runge-Kutta, among others, enhancing the accuracy and precision of mean and covariance estimation in the prediction step.Finally, the application of Lie Group and Lie Algebra Theory enables the natural and efficient representation of uncertainties, particularly for rigid body navigation problems involving simultaneous translation and rotation. By considering noise as Gaussian, with zero mean and a determined variance in the Algebra, a Concentrated Gaussian Distribution is induced in the associated Group, providing a better representation of navigation uncertainties compared to Euclidean space.The work will be carried out in stages, including theoretical review, algorithm development, and experimental validation with both simulated and real data. The proposed methods are expected to improve the accuracy and precision of GNSS/IMU fusion estimations, contributing to advancements in inertial navigation algorithms that are crucial for various applications, such as 3D mapping, autonomous vehicle systems, and more. (AU)