Least-square based recursive optimization for distance-based source localization

TL;DR

This paper presents a recursive least-square optimization algorithm for real-time source localization that ensures stability and convergence, addressing practical issues like discrete-time implementation and input saturation.

Contribution

Introduces a stable, discrete-time recursive optimization method for source localization that accounts for input saturation and provides convergence guarantees.

Findings

Proven stability of the proposed recursive algorithm.

Numerical simulations demonstrate convergence to the source.

Addresses real-world implementation issues like input saturation.

Abstract

In this paper we study the problem of driving an agent to an unknown source whose location is estimated in real-time by a recursive optimization algorithm. The optimization criterion is subject to a least-square cost function constructed from the distance measurements to the target combined with the agent's self-odometry. In this work, two important issues concerning real world application are directly addressed, which is a discrete-time recursive algorithm for concurrent control and estimation, and consideration for input saturation. It is proven that with proper choices of the system's parameters, stability of all system states, including on-board estimator variables and the agent-target relative position can be achieved. The convergence of the agent's position to the target is also investigated via numerical simulation.