Global attitude/position estimation using landmark and biased velocity measurements

Exponentially stable observer-based controller for VTOL-UAVs without velocity measurements

“…. Likewise, the measurement in ( 16) can be described with respect to It is worth mentioning that Assumption 1 is standard for pose filtering [8], [9]. Lemma 1.…”

“…Rigid-body's attitude can be reconstructed algebraically using inertial-frame observations and corresponding body-frame measurements [1], [2] followed by position reconstruction. However, better attitude and pose estimation solutions are offered by Kalman filters [3]- [5], nonlinear filters on the Special Orthogonal Group SO (3) that mimic the true attitude dynamics geometry [6], [7], and nonlinear filters on the Special Euclidean Group SE (3) that mimic the true pose (attitude + position) dynamics geometry [8], [9]. The true attitude dynamics representation relies on angular velocity typically measured by a gyroscope.…”

“…Hence, obtaining linear velocity in a GPS-denied region poses a challenge [10], [15]- [17]. Thereby, the filters in [3], [4], [6]- [9] are not suitable for pose estimation when a gyroscope fails and/or a reliable GPS signal is not available. Consequently, multiple GPS-independent navigation solutions that rely solely on angular velocity, landmark, and inertial measurements have been proposed for the estimation of attitude, position, and linear velocity of a vehicle, such as adaptive Kalman filter [18], extended Kalman filter [11], invariant extended Kalman filter on the Lie Group of Extended Special Euclidean Group SE 2 [19], and nonlinear stochastic filters on SE 2 [10], [17].…”

On the Design of Hybrid Pose and Velocity-bias Observers on Lie Group SE(3)

“…However, in GPS-denied environments such as indoor applications, recovering the position and linear velocity is a challenging task. Alternatively, inertial-vision systems combining IMU and on-board camera measurements have been considered for pose estimation [6][7][8]. In [7], local Riccati-based pose observers have been proposed relying on the system's linear and angular velocities and the bearing measurements of some known landmark points.…”

“…In [7], local Riccati-based pose observers have been proposed relying on the system's linear and angular velocities and the bearing measurements of some known landmark points. Another solution with global asymptotic stability (GAS) has been proposed in [8], which considers a non-geometric pose estimation problem using biased body-frame measurements of the system's linear and angular velocities as well as body-frame measurements of landmarks. The achieved global asymptotic stability results are due to the fact that the estimates are not confined to live in SE(3) for all times.…”