# Nonlinear Pose Filters on the Special Euclidean Group SE(3) with Guaranteed Transient and Steady-state Performance

## TL;DR

This paper introduces two innovative nonlinear pose filters on SE(3) that guarantee prescribed transient and steady-state performance, improving robustness and convergence in pose estimation from low-cost sensors.

## Contribution

The paper presents two novel pose filters directly on SE(3) with guaranteed performance, one requiring pose reconstruction and the other operating directly on measurements, enhancing robustness and convergence.

## Key findings

- Filters achieve systematic convergence from large initial errors.
- Simulation confirms robustness under high uncertainties.
- Transient and steady-state errors are bounded as prescribed.

## Abstract

Two novel nonlinear pose (i.e, attitude and position) filters developed directly on the Special Euclidean Group SE(3)able to guarantee prescribed characteristics of transient and steady-state performance are proposed. The position error and normalized Euclidean distance of attitude error are trapped to arbitrarily start within a given large set and converge systematically and asymptotically to the origin from almost any initial condition. The transient error is guaranteed not to exceed a prescribed value while the steady-state error is bounded by a predefined small value. The first pose filter operates based on a set of vectorial measurements coupled with a group of velocity vectors and requires preliminary pose reconstruction. The second filter, on the contrary, is able to perform its function using a set of vectorial measurements and a group of velocity vectors directly. Both proposed filters provide reasonable pose estimates with superior convergence properties while being able to use measurements obtained from low-cost inertial measurement, landmark measurement, and velocity measurement units. Simulation results demonstrate effectiveness and robustness of the proposed filters considering large error in initialization and high level of uncertainties in velocity vectors as well as in the set of vector measurements. Attitude, position, pose estimation, nonlinear observer, estimate, special orthogonal group, special Euclidean group, SO(3), SE(3), prescribed performance function, transient, steady-state error, transformed error, Landmark, feature measurement, PPF, IMU, Lie algebra, Lie group, projection, Gyroscope, Inertial measurement units, rigid body, micro electromechanical systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving, Vehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle.