Decentralised navigation systems for bearing-based position and velocity estimation in tiered formations

Abstract

This paper presents a novel decentralised navigation system based on bearing measurements for tiered vehicle formations. In the proposed framework, some vehicles have access to measurements of their own position, whereas others have access to bearing measurements to one or more neighbouring vehicles. Depth measurement may also be available. Local observers for the position and fluid velocity are designed based on the derivation of an equivalent observable linear time-varying system, thus yielding globally exponentially stable error dynamics. The local observers rely on local measurements, as well as limited communications between the vehicles. The stability of the system as a whole is analysed by studying the robustness of the local observers to exponentially decaying perturbations. Thorough Monte Carlo simulations are presented and discussed to compare the performance of the proposed solution with the extended Kalman filter, the unscented Kalman filter, and the Bayesian Cramér-Rao bound.

Keywords:

• Bearings
• navigation
• decentralised estimation
• Kalman filters
• sensor fusion

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Fundação para a Ciência e a Tecnologia (FCT) through LARSyS - FCT Project UIDB/50009/2020 and through the FCT project DECENTER [LISBOA-01-0145-FEDER-029605], funded by the Lisboa 2020 and PIDDAC programs; and by the Macau Science and Technology Development Fund under grants FDCT/0146/2019/A3 and FDCT/0031/2020/AFJ. This work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 101017808 (RAMONES project). The work of Paulo Oliveira is financed by national funds through the FCT, through IDMEC, under LAETA, project UIDB/50022/2020.

Notes on contributors

David Santos

David Santos received the Mestrado Integrado degree in Aerospace Engineering, in 2020 from the Instituto Superior Técnico (IST), Lisbon, Portugal. Since 2019, he has been working in the Industry as a Data Scientist for Feedzai. His main research interests fall in the area of distributed control, computer vision and artificial intelligence.

Pedro Batista

Pedro Batista received the Licenciatura degree in Electrical and Computer Engineering, in 2005, and the PhD degree, in 2010, both from the Instituto Superior Técnico (IST), Lisbon, Portugal. From 2004 to 2006, he was a Monitor with the Department of Mathematics, IST. Since 2012, he has been with the Department of Electrical and Computer Engineering of IST, where he is currently Assistant Professor. His research interests include sensor-based navigation and control of single and multiple autonomous vehicles. Dr. Batista received the Diploma de Mérito twice during his graduation and his PhD thesis was distinguished with the Best Robotics PhD Thesis Award by the Portuguese Society of Robotics.

Paulo Oliveira

Paulo Oliveira (SM IEEE) received the PhD degree in Electrical and Computer Engineering, in 2002, and the Habillitation in Mechanical Engineering in 2016, all from Instituto Superior Técnico (IST), Lisbon, Portugal. Since 2020, he holds a joint position as Full Professor in the Mechanical Engineering and Eletrotechnical and Computer Engineering Departments of IST, is the Vice-president for the Research Affairs at the Associated Laboratory for Energy, Transports, and Aeronautics, and the Coordinator on Aerospace Engineering, at IST. His research interests are on Autonomous Robotic Vehicles with a focus on Mechatronic Systems Integration, Sensor Fusion, GPS and Positioning Systems, and Guidance, Navigation and Control Systems (GNC). He is author or co-author of more than 90 journal papers (90% in first quartile,) and 180 conference communications and participated in more than 40 European and Portuguese research projects, over the last 30 years.

Carlos Silvestre

Carlos Silvestre received the Licenciatura degree in Electrical Engineering from the Instituto Superior Técnico (IST) of Lisbon, Portugal, in 1987 and the Master degree in Electrical Engineering and the PhD degree in Control Science from the same school in 1991 and 2000, respectively. In 2011 he received the Habilitation in Electrical Engineering and Computers also from IST. Since 2000, he is with the Department of Electrical Engineering of the Instituto Superior Técnico, where he is currently on leave. Since 2012 he is also with Faculty of Science and Technology of the University of Macau where he currently holds a Professor position with the Department of Electrical and Computers Engineering. His current research interests include linear and nonlinear control theory; hybrid systems; multi-agent control systems; networked control systems; inertial navigation systems and real time architectures for complex autonomous systems with application to unmanned air and underwater vehicles.