Observer design for position and velocity bias estimation from a single direction output

TL;DR

This paper presents a nonlinear observer for estimating an object's position and velocity bias from direction and velocity measurements, ensuring global exponential convergence under persistent excitation.

Contribution

It introduces a novel observer design that handles velocity bias and proves its exponential convergence with minimal assumptions.

Findings

Observer achieves accurate position estimation in simulations.

Convergence is guaranteed under persistent excitation.

Handles constant velocity bias effectively.

Abstract

This paper addresses the problem of estimating the position of an object moving in $R^n$ from direction and velocity measurements. After addressing observability issues associated with this problem, a nonlinear observer is designed so as to encompass the case where the measured velocity is corrupted by a constant bias. Global exponential convergence of the estimation error is proved under a condition of persistent excitation upon the direction measurements. Simulation results illustrate the performance of the observer.