PhD position « Constrained distributed moving horizon estimation for sensor networks with low-computation capabilities »

Date limite de candidature : 17/04/2022
Date de début : 01/10/2022
Date de fin : 30/09/2025

Pôle : Automatique et systèmes
Type de poste : Thèses
Contact : MANIU Cristina (

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PhD position

« Constrained distributed moving horizon estimation for sensor networks with low-computation capabilities« 

Supervising team:

General information: 3 years, starting from Oct.-Nov. 2022

Application deadline: 17 April 2022

Keywords: distributed state estimation, moving horizon estimation, sensor fault detection, multi-agent systems, sensor networks, drones, mobile robotics.


General context

This thesis is part of the collaboration between ONERA, CentraleSupélec/L2S (University Paris Saclay[1]) and University of Seville. This subject comes in the continuity of joint works in these institutions (see the previous PhD theses [Venturino20], [Merhy2018], [BenChabane2015], [Suwantong2014b], [Le2012]). In addition, it will offer the opportunity to obtain a European PhD label[2]. The starting point is based on the first developments of [Venturino2021] on distributed moving horizon estimation, rewarded with the Best Paper Award of the 24th International Conference on System Theory, Control and Computing, 2020.

Brief scientific description

In the more general context of distributed state estimation and multi-agent systems, the practical problem of interest explored in this PhD is the one of area surveillance using a network of sensors. Heterogeneous sensors are considered, in the sense that different technologies can be used (e.g. video camera, radar, LIDAR, etc.), hence providing measurements of different types. In addition, the sensors can also be fixed and/or mobile (e.g. embedded on robots or drones). The problem consists in estimating online the trajectory of an intruder infiltrating the monitored area. Assuming that computation and communication capabilities are associated to each sensor (or subset of sensors), distributed state observers will be considered, in order to increase the resilience with respect to the loss of one or more sensor(s). Different types of observers have been developed in the literature for distributed state estimation in sensor networks (see [Olfati2007], [He2020] and associated references).

Previous work proposed distributed moving horizon observers within this framework. These methods considered past measurements and constraints within the estimation process (e.g. constraints on the state of the system, noise or unknown inputs) [Farina 2010, Battistelli2018]. More specifically, the new algorithms developed by the supervising team [Venturino2020] allowed reducing the computation time, while increasing the accuracy, through the use of fused arrival cost and pre-estimation mechanism [Venturino2021]. This work was carried out in a linear framework (linear dynamical system and linear measurement equations).

In the first part of this thesis, we will focus on developing nonlinear extensions of these algorithms in order to broaden the spectrum of possible applications (e.g. distance or angular measurements, nonlinearities in the multi-agent system dynamics). We will provide stability guarantees (i.e. convergence of the estimation error) for the proposed estimation algorithms and we will validate the proposed approaches both in simulation and experimentally. We dispose of a fleet of several TurtleBots mobile robots and Crazyflie nano-drones to be used for experimentations in the indoor flight arena (equipped with an OptiTrack motion capture system) of CentraleSupélec.

In a second part, we will develop optimization-based moving horizon estimators and implement them in a distributed framework on low-cost sensor networks with limited computing capabilities.

Finally, a different research axis will focus on taking into account the data exchange capacities, the constraints of the communication network between the sensors, and its possible vulnerabilities with respect to cyber attacks. More precisely, we will extend the proposed methods to take into account a possible asynchronicity of the communications between the sensors, the presence of communication delay [Dubois2018], uncertainties [Le2013], [Zhang2013], a limited data exchange capacity (reducing the communications [Yin2021]), corrupted data, and/or variations of the communication network topology due, for instance, to a temporary or permanent loss of communication links between certain sensors. Extensions to large scale systems are also envisaged.


[Battistelli2018] G. Battistelli, “Distributed moving-horizon estimation with arrival-cost consensus”, in IEEE Transactions on Automatic Control, vol. 64, no. 8, pp. 3316–3323, 2018.

[BenChabane2015] S. Ben Chabane, “Techniques de détection de défauts à base d’estimation d’état ensembliste pour systèmes incertains”, PhD thesis Université Paris-Saclay, 13 Oct. 2015,

[Dubois2018] R. Dubois, S. Bertrand, A. Eudes, “Performance Evaluation of a Moving Horizon Estimator for Multi-Rate Sensor Fusion with Time-Delayed Measurements”, 22nd International Conference on System Theory Control and Computing, Sinaia, Romania, 2018.

[Farina2010] M. Farina, G. Ferrari-Trecate and R. Scattolini, “Distributed Moving Horizon Estimation for Linear  Constrained Systems”, in IEEE Transactions on Automatic Control, vol. 55, no. 11, pp. 2462-2475, 2010.

[He2020] Shaoming He, Hyo-Sang Shin, Shuoyuan Xu and Antonios Tsourdos, “Distributed estimation over a low-cost sensor network: A Review of state-of-the-art”, in Information Fusion, vol. 54, pp. 21-43, 2020.

[Le2012] V.T.H. Le, “Commande prédictive robuste par des techniques d’observateur à base d’ensembles zonotopiques”, PhD thesis Université Paris Sud, 22 Oct. 2012,

[Le2013] V.T.H. Le, C. Stoica, T. Alamo, E.F. Camacho, D. Dumur, “Zonotopic guaranteed state estimation for uncertain systems”, Automatica, no. 49(1), pp. 3418-3424, 2013.

[Merhy2018] D. Merhy, “Contribution à l’estimation d’état par méthodes ensemblistes ellipsoidales et zonotopiques”, PhD thesis Université Paris-Saclay, 24 Oct. 2019,

[Olfati2007] R. Olfati-Saber, “Distributed Kalman Filtering for Sensor Networks”, 46th IEEE Conference on Decision and Control, New Orleans, USA, 2007.

[Suwantong2014b] R. Suwantong, “Nouvelle structure d’estimateurs a horizon glissant.application a l’estimation de trajectoires de debris spatiauxpendant la rentree atmospherique”, PhD thesis Université Paris-Sud, 2 Dec. 2014,

[Venturino2020] A. Venturino, S. Bertrand, C. Stoica Maniu, T. Alamo, E. Camacho, “Distributed Moving Horizon Estimation with Pre-Estimating Observer”, 24th International Conference on System Theory, Control and Computing, Sinaia, Romania, 2020. Best Paper Award.

[Venturino2021] A. Venturino, S. Bertrand, C. Stoica Maniu, T. Alamo, E. Camacho, “A New l-step Neighbourhood Distributed Moving Horizon Estimator”, 60th IEEE Conference on Decision and Control, Austin, USA, 2021.

[Yin2021] Xunyuan Yin and Jinfeng Liu, “Event-Triggered State Estimation of Linear Systems Using Moving Horizon Estimation”, in IEEE Transactions on Contol Systems Technology, vol. 29, no. 2, pp. 901-909, 2021.

[Zhang2013] J. Zhang and J. Liu, “Distributed Moving Horizon State Estimation for Nonlinear Systems with Bounded Uncertainties”, in Journal of Process Control, vol. 23, pp. 1281-1295, 2013.

[1] Université Paris Saclay achieved the 13th position of the Shanghai ranking in 2021.

[2] To this aim, the selected PhD student will do a research visit of at least 3 months at University of Seville. For more information about the European PhD label please see the following link

Required profil and skills

This thesis requires automatic control skills (Master level or 3rd year ‘Grande Ecole’ in Automatic Control/Robotics/Mathematics/Signal Processing) with particular knowledge in state estimation and/or multi-agent systems (e.g. multi-robot). Good Matlab and/or Python and/or ROS skills and a good English level are required.

Acquired knowledge and skills during this PhD thesis

The proposed subject should allow acquiring solid knowledge in robust distributed estimation and multi-agent systems, more particularly related to surveillance missions for multi-sensor multi-robot systems. The knowledge acquired in this direction will provide an opening to several areas (both theoretical and applicative), which are currently at the forefront of research. This thesis has the advantage to allow deep explorations into the theoretical field with a significant part consisting to implement the academic results on a real multi-sensor robotic system, providing the possibility for future employment both in the academic and industrial sectors. During various professional training activities throughout the thesis, the PhD candidate will be able to acquire numerous transversal skills (e.g. pedagogical skills, scientific integrity and ethical skills, etc.). Teaching (TD, TP, projects, etc.) at CentraleSupélec is strongly encouraged, allowing the PhD candidate to acquire solid skills in pedagogy that will be useful for a possible academic career. Participation in international, national and local conferences will highlight the PhD student’s scientific results and will allow increasing the PhD candidate’s professional network. In addition, this thesis offers an international friendly working environment, permitting to develop multi-language communication skills and offering the opportunity to obtain a European PhD label.


Cristina STOICA   Å  +33 1 69 85 13 78

Sylvain BERTRAND   Å  +33 1 80 38 66 12


Application: CV, cover letter, recommendation letter (with date and signature) of the Master Program Director, and engineering and/or Master’s official transcripts sent by e-mail to: and with the subject « PhD thesis TIS-DTIS-2022-25 »

Application deadline: 17 April 2022


Locations (Paris region)

ONERA, DTIS, Palaiseau

8, Chemin de la Hunière, Palaiseau, France

L2S, CentraleSupélec, Université Paris-Saclay

3 rue Joliot Curie, 91190 Gif-sur-Yvette, France