{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T21:25:18Z","timestamp":1782336318907,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T00:00:00Z","timestamp":1652227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A reliable quantification of the worst-case influence of model uncertainty and external disturbances is crucial for the localization of vessels in marine applications. This is especially true if uncertain GPS-based position measurements are used to update predicted vessel locations that are obtained from the evaluation of a ship\u2019s state equation. To reflect real-life working conditions, these state equations need to account for uncertainty in the system model, such as imperfect actuation and external disturbances due to effects such as wind and currents. As an application scenario, the GPS-based localization of autonomous DDboat robots is considered in this paper. Using experimental data, the efficiency of an ellipsoidal approach, which exploits a bounded-error representation of disturbances and uncertainties, is demonstrated.<\/jats:p>","DOI":"10.3390\/a15050162","type":"journal-article","created":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T10:19:46Z","timestamp":1652264386000},"page":"162","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Experimental Validation of Ellipsoidal Techniques for State Estimation in Marine Applications"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1548-6547","authenticated-orcid":false,"given":"Andreas","family":"Rauh","sequence":"first","affiliation":[{"name":"Group: Distributed Control in Interconnected Systems, Department of Computing Science, Carl von Ossietzky Universit\u00e4t Oldenburg, D-26111 Oldenburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2842-254X","authenticated-orcid":false,"given":"Yohann","family":"Gourret","sequence":"additional","affiliation":[{"name":"Lab-STICC, ENSTA Bretagne, 29806 Brest, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2846-9834","authenticated-orcid":false,"given":"Katell","family":"Lagattu","sequence":"additional","affiliation":[{"name":"Lab-STICC, ENSTA Bretagne, 29806 Brest, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2325-1497","authenticated-orcid":false,"given":"Bernardo","family":"Hummes","sequence":"additional","affiliation":[{"name":"Lab-STICC, ENSTA Bretagne, 29806 Brest, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0938-0615","authenticated-orcid":false,"given":"Luc","family":"Jaulin","sequence":"additional","affiliation":[{"name":"Lab-STICC, ENSTA Bretagne, 29806 Brest, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2069-5682","authenticated-orcid":false,"given":"Johannes","family":"Reuter","sequence":"additional","affiliation":[{"name":"Institute of System Dynamics, University of Applied Sciences Konstanz, D-78462 Konstanz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7430-3835","authenticated-orcid":false,"given":"Stefan","family":"Wirtensohn","sequence":"additional","affiliation":[{"name":"Institute of System Dynamics, University of Applied Sciences Konstanz, D-78462 Konstanz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6815-8010","authenticated-orcid":false,"given":"Patrick","family":"Hoher","sequence":"additional","affiliation":[{"name":"Institute of System Dynamics, University of Applied Sciences Konstanz, D-78462 Konstanz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fossen, T. (2021). Handbook of Marine Craft Hydrodynamics and Motion Control, Wiley. [2nd ed.].","DOI":"10.1002\/9781119575016"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xue, Y., Liu, Y., Xue, G., and Chen, G. (2021). Identification and Prediction of Ship Maneuvering Motion Based on a Gaussian Process with Uncertainty Propagation. J. Mar. Sci. Eng., 9.","DOI":"10.3390\/jmse9080804"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mayer, G. (2017). Interval Analysis and Automatic Result Verification, De Gruyter. De Gruyter Studies in Mathematics.","DOI":"10.1515\/9783110499469"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rauh, A., Bourgois, A., and Jaulin, L. (2021). Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design. Algorithms, 14.","DOI":"10.3390\/a14030088"},{"key":"ref_5","first-page":"399","article-title":"A Computationally Inexpensive Algorithm for Determining Outer and Inner Enclosures of Nonlinear Mappings of Ellipsoidal Domains","volume":"31","author":"Rauh","year":"2021","journal-title":"Int. J. Appl. Math. Comput. Sci. AMCS"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1137\/140976807","article-title":"Stable Set-Valued Integration of Nonlinear Dynamic Systems using Affine Set-Parameterizations","volume":"53","author":"Houska","year":"2015","journal-title":"Siam J. Numer. Anal."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kurzhanskii, A.B., and V\u00e1lyi, I. (1997). Ellipsoidal Calculus for Estimation and Control, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-0277-6"},{"key":"ref_8","unstructured":"Becis-Aubry, Y. (2022, March 13). Ellipsoidal Constrained State Estimation in Presence of Bounded Disturbances. Available online: arxiv.org\/pdf\/2012.03267v1.pdf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109638","DOI":"10.1016\/j.automatica.2021.109638","article-title":"Set-Valued State Estimation of Nonlinear Discrete-Time Systems with Nonlinear Invariants Based on Constrained Zonotopes","volume":"129","author":"Rego","year":"2021","journal-title":"Automatica"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1023\/A:1024467732637","article-title":"Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models","volume":"4","author":"Berz","year":"1998","journal-title":"Reliab. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112511","DOI":"10.1016\/j.cam.2019.112511","article-title":"A Taylor Model Toolbox for Solving ODEs Implemented in MATLAB\/INTLAB","volume":"368","year":"2020","journal-title":"J. Comput. Appl. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"785795","DOI":"10.3389\/fcteg.2022.785795","article-title":"An Ellipsoidal Predictor\u2013Corrector State Estimation Scheme for Linear Continuous-Time Systems with Bounded Parameters and Bounded Measurement Errors","volume":"3","author":"Rauh","year":"2022","journal-title":"Front. Control Eng."},{"key":"ref_13","unstructured":"K\u00fchn, W. (2022, March 06). Rigorous Error Bounds for the Initial Value Problem Based on Defect Estimation. Technical Report. Available online: http:\/\/www.decatur.de\/personal\/papers\/defect.zip."},{"key":"ref_14","unstructured":"Stengel, R. (1994). Optimal Control and Estimation, Dover Publications, Inc."},{"key":"ref_15","unstructured":"Anderson, B.D.O., and Moore, J.B. (2005). Optimal Filtering, Dover Publications, Inc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106569","DOI":"10.1016\/j.ast.2021.106569","article-title":"A Geometric Nonlinear Stochastic Filter for Simultaneous Localization and Mapping","volume":"111","author":"Hashim","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Borisov, A., Bosov, A., Miller, B., and Miller, G. (2020). Passive Underwater Target Tracking: Conditionally Minimax Nonlinear Filtering with Bearing-Doppler Observations. Sensors, 20.","DOI":"10.3390\/s20082257"},{"key":"ref_18","unstructured":"Narendra, K.S. (1986). The Potential Field Approach And Operational Space Formulation In Robot Control. Adaptive and Learning Systems: Theory and Applications, Springer."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/BF02481251","article-title":"Dynamic Control of Redundant Manipulators Using the Artificial Potential Field Approach with Time Scaling","volume":"3","author":"Tanaka","year":"1999","journal-title":"Artif. Life Robot."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1729881418799562","article-title":"An Improved Artificial Potential Field Method of Trajectory Planning and Obstacle Avoidance for Redundant Manipulators","volume":"15","author":"Wang","year":"2018","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1080\/00207179508921959","article-title":"Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples","volume":"61","author":"Fliess","year":"1995","journal-title":"Int. J. Control"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Rauh, A., Bourgois, A., Jaulin, L., and Kersten, J. (2021, January 3\u20135). Ellipsoidal Enclosure Techniques for a Verified Simulation of Initial Value Problems for Ordinary Differential Equations. Proceedings of the 5th International Conference on Control, Automation and Diagnosis (ICCAD\u201921), Grenoble, France.","DOI":"10.1109\/ICCAD52417.2021.9638755"},{"key":"ref_23","unstructured":"John, F. (1948). Extremum Problems with Inequalities as Subsidiary Conditions. Studies and Essays Presented to R. Courant on his 60th Birthday, Interscience Publishers, Inc."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Tarbouriech, S., Garcia, G., Gomes da Silva, J., and Queinnec, I. (2011). Stability and Stabilization of Linear Systems With Saturating Actuators, Springer.","DOI":"10.1007\/978-0-85729-941-3"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Halder, A. (2018, January 17\u201319). On the Parameterized Computation of Minimum Volume Outer Ellipsoid of Minkowski Sum of Ellipsoids. Proceedings of the IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA.","DOI":"10.1109\/CDC.2018.8619508"},{"key":"ref_26","unstructured":"Noack, B., Klumpp, V., and Hanebeck, U. (2009, January 6\u20139). State Estimation with Sets of Densities Considering Stochastic and Systematic Errors. Proceedings of the 2009 12th International Conference on Information Fusion, FUSION, Seattle, WA, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1026454804250","article-title":"LMI Approximations for the Radius of the Intersection of Ellipsoids: Survey","volume":"108","author":"Henrion","year":"2001","journal-title":"J. Optim. Theory Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"Trans. Asme\u2014J. Basic Eng."},{"key":"ref_29","unstructured":"Becis-Aubry, Y. (2022, March 13). Bounded-Error Constrained State Estimation in Presence of Sporadic Measurements 2022. Available online: arxiv.org\/abs\/2202.13900."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"343","DOI":"10.14232\/actacyb.24.3.2020.5","article-title":"Towards Analyzing the Influence of Measurement Errors in Magnetic Resonance Imaging of Fluid Flows\u2014Development of an Interval-Based Iteration Approach","volume":"24","author":"John","year":"2020","journal-title":"Acta Cybern."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"786152","DOI":"10.3389\/fcteg.2021.786152","article-title":"Robust Feedback Control for Discrete-Time Systems Based on Iterative LMIs with Polytopic Uncertainty Representations Subject to Stochastic Noise","volume":"2","author":"Dehnert","year":"2022","journal-title":"Front. Control Eng."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/5\/162\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:09:09Z","timestamp":1760137749000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/5\/162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,11]]},"references-count":31,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["a15050162"],"URL":"https:\/\/doi.org\/10.3390\/a15050162","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,11]]}}}