Geometric State Observers for Autonomous Navigation Systems

The development of reliable state estimation algorithms for autonomous navigation systems is of great interest in the control and robotics communities. This thesis studies the state estimation problem for autonomous navigation systems. The first part of this thesis is devoted to the pose estimation on the Special Euclidean group $\SE(3)$. A generic globally exponentially stable hybrid estimation scheme for pose (orientation and position) and velocity-bias estimation on $\SE(3)\times \mathbb{R}^6$ is proposed. Moreover, an explicit hybrid observer, using inertial and landmark position measurements, is provided. The second part of this thesis is devoted to the problem of simultaneous estimation of the attitude, position and linear velocity for inertial navigation systems (INSs). Three different types of nonlinear observers are developed to handle the following cases: continuous landmark position measurements, intermittent landmark position measurements and continuous stereo bearing measurements. First, a class of nonlinear geometric hybrid observers on the Lie group $\SE_2(3)$, with GES guarantees, using continuous IMU and landmark position measurements is developed. Then, a class of nonlinear state observers, with strong stability guarantees, using intermittent landmark measurements is proposed. Finally, a class of state observers, with strong stability guarantees, directly incorporating body-frame stereo-bearing measurements, is proposed