{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T21:38:59Z","timestamp":1775165939894,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T00:00:00Z","timestamp":1692144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development (CNPq)","doi-asserted-by":"publisher","award":["307255\/2018-2"],"award-info":[{"award-number":["307255\/2018-2"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development (CNPq)","doi-asserted-by":"publisher","award":["403801\/2021-4"],"award-info":[{"award-number":["403801\/2021-4"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>An extension of the linear H\u221e filter, presented here as the extended H\u221e particle filter (EH\u221ePF), is used in this work for attitude estimation, which presents a process and measurement model with nonlinear functions. The simulations implemented use orbit and attitude data from CBERS-4 (China\u2013Brazil Earth Resources Satellite-4), making use of the robustness characteristics of the H\u221e filter. The CBERS-4 is the fifth satellite of an advantageous international scientific interaction between Brazil and China for the development of remote sensing satellites used for strategic application in monitoring water resources and controlling deforestation in the Legal Amazon. In the extended H\u221e particle filter (EH\u221ePF) the nature of the system, composed of dynamics and noises, seeks to degrade the state estimate. The EH\u221ePF deals with this by aiming for robustness, using a performance parameter in its cost function, in addition to presenting an advantageous feature of using a reduced number of particles for state estimation. The justification for the application of this method is because the non-Gaussian uncertainties that appear in the attitude sensors impair the estimation process and the EH\u221ePF minimizes in signal estimation the worst effects of disturbance signals without a priori knowledge of them, as shown in the results, in addition to presenting good precision within the prescribed requirements, with 100 particles representing a processing time 2.09 times less than the PF with 500 particles.<\/jats:p>","DOI":"10.3390\/rs15164052","type":"journal-article","created":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T10:08:09Z","timestamp":1692180489000},"page":"4052","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Extended H\u221e Particle Filter for Attitude Estimation Applied to Remote Sensing Satellite CBERS-4"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4843-0267","authenticated-orcid":false,"given":"William Reis","family":"Silva","sequence":"first","affiliation":[{"name":"Gama Campus (FGA), University of Brasilia (UnB), \u00c1rea Especial de Ind\u00fastria, Proje\u00e7\u00e3o A, Setor Leste (Gama), Bras\u00edlia 72444-240, DF, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0633-6272","authenticated-orcid":false,"given":"Roberta Veloso","family":"Garcia","sequence":"additional","affiliation":[{"name":"Lorena School of Engineering (EEL), University of S\u00e3o Paulo (USP), Estrada Municipal do Campinho, S\/N. Ponte Nova, Lorena 12602-810, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1046-6587","authenticated-orcid":false,"given":"Paula C. P. M.","family":"Pardal","sequence":"additional","affiliation":[{"name":"Collaborative Laboratory (CoLAB), Center of Engineering and Product Development (CEiiA), PACT, Rua Lu\u00eds Adelino Fonseca, 1, 7005-841 \u00c9vora, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0259-0724","authenticated-orcid":false,"given":"H\u00e9lio Koiti","family":"Kuga","sequence":"additional","affiliation":[{"name":"Space Mechanics and Control Division (DMC), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, Jardim da Granja, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9940-2146","authenticated-orcid":false,"given":"Maria Cec\u00edlia F. P. S.","family":"Zanardi","sequence":"additional","affiliation":[{"name":"Campus Guaratinguet\u00e1 (FEG), S\u00e3o Paulo State University (UNESP), Av. Dr. Ariberto Pereira da Cunha, 333, Pedregulho, Guaratinguet\u00e1 12516-410, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1078-7201","authenticated-orcid":false,"given":"Leandro","family":"Baroni","sequence":"additional","affiliation":[{"name":"Engineering, Modeling and Applied Social Sciences Center (CECS), Federal University of ABC (UFABC), Av. dos Estados, 5001, Bang\u00fa, Santo Andr\u00e9 09210-580, SP, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,16]]},"reference":[{"key":"ref_1","first-page":"1195","article-title":"Spacecraft Attitude Estimation using Unscented Kalman Filters, Regularized Particle Filter and Extended H\u221e Filter","volume":"162","author":"Silva","year":"2017","journal-title":"Adv. Astronaut. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/MM.2021.3114903","article-title":"Advances in Microprocessor Cache Architectures Over the Last 25 Years","volume":"41","author":"Iyer","year":"2021","journal-title":"IEEE Micro"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). Optimal State Estimation, Kalman, H\u221e, and Nonlinear Approaches, Wiley.","DOI":"10.1002\/0470045345"},{"key":"ref_4","first-page":"149","article-title":"Singular value decomposition based robust cubature Kalman filtering for an integrated GPS\/SINS navigation system","volume":"68","author":"Zhang","year":"2014","journal-title":"J. Navig."},{"key":"ref_5","unstructured":"Banavar, R. (1992). A Game Theoretic Approach to Linear Dynamics Estimation. [Ph.D. Thesis, University of Texas at Austin]."},{"key":"ref_6","unstructured":"Shen, X. (1995, January 9\u201312). Discrete H\u221e filter design with application to speech enhancement. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Detroit, MI, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1109\/78.564201","article-title":"Game theory approach to H\u221e discrete filter design","volume":"45","author":"Shen","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.1109\/TSP.2011.2138700","article-title":"Second-Order Extended H\u221e Filter for Nonlinear Discrete-Time Systems Using Quadratic Error Matrix Approximation","volume":"59","author":"Hu","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2596","DOI":"10.1109\/78.782219","article-title":"Robust Extended Kalman Filtering","volume":"47","author":"Einicke","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","first-page":"102","article-title":"CKF-based robust filtering algorithm for GNSS\/INS integrated train positioning","volume":"10","author":"Liu","year":"2010","journal-title":"J. Traffic Transp. Eng."},{"key":"ref_11","unstructured":"Carrara, V. (2016, February 16). An Open Source Satellite Attitude and Orbit Simulator Toolbox for Matlab, International Symposium on Dynamic Problems of Mechanics, Natal, RN. Available online: http:\/\/mtc-m21b.sid.inpe.br\/rep\/sid.inpe.br\/mtc-m21b\/2015\/04.07.13.24?."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"417","DOI":"10.2514\/3.56190","article-title":"Kalman filtering for spacecraft attitude estimation","volume":"5","author":"Lefferts","year":"1982","journal-title":"J. Guid."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12","DOI":"10.2514\/1.22452","article-title":"Survey of nonlinear attitude estimation methods","volume":"30","author":"Crassidis","year":"2007","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Shojaie, K., Ahmadi, K., and Shahri, A.M. (2007, January 4\u20137). Effects of iteration in Kalman Filters family for improvement of estimation accuracy in simultaneous localization and mapping. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Zurich, Switzerland.","DOI":"10.1109\/AIM.2007.4412453"},{"key":"ref_15","first-page":"445","article-title":"Using extended Kalman filter and least squares method for spacecraft attitude estimation","volume":"2","author":"Garcia","year":"2011","journal-title":"Math. Eng. Sci. Aerosp."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"985429","DOI":"10.1155\/2012\/985429","article-title":"Unscented Kalman filter applied to the spacecraft attitude estimation with euler angles","volume":"2012","author":"Garcia","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_17","unstructured":"Garcia, R.V., Kuga, H.K., and Zanardi, M.C. (March, January 28). Unscented Kalman filter for spacecraft attitude estimation using quaternions and euler angles. Proceedings of the International Symposium on Space Flight Dynamics, S\u00e3o Jos\u00e9 dos Campos, Brazil."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"395","DOI":"10.5028\/jatm.v5i4.252","article-title":"Analyzing the Unscented Kalman Filter Robustness for Orbit Determination through Global Positioning System Signals","volume":"5","author":"Pardal","year":"2013","journal-title":"J. Aerosp. Technol. Manag."},{"key":"ref_19","unstructured":"Pardal, P.C.P.M., de Moraes, R.V., and Kuga, H.K. (2014, January 4\u20137). Orbit Determination Using Nonlinear Particle Filter and GPS Measurements. Proceedings of the AAS\/AIAA Astrodynamics Specialist Conference, San Diego, CA, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.actaastro.2021.07.049","article-title":"Rao-Blackwellized Particle Filter for the CBERS-4 attitude and gyros bias estimation","volume":"193","author":"Silva","year":"2022","journal-title":"Acta Astronaut."},{"key":"ref_21","first-page":"439","article-title":"A Survey of Attitude Representations","volume":"41","author":"Shuster","year":"1993","journal-title":"J. Astronaut. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wertz, J.R. (1978). Spacecraft Attitude Determination and Control, D. Reidel.","DOI":"10.1007\/978-94-009-9907-7"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Crassidis, J.L., and Junkins, J.L. (2011). Optimal Estimation of Dynamic Systems, Chapman and Hall\/CRC Applied Mathematics and Nonlinear Science.","DOI":"10.1201\/b11154"},{"key":"ref_24","unstructured":"Fuming, H., and Kuga, H.K. (1999). CBERS Simulator Mathematical Models, CBTT Project, CBTT\/ 2000\/ MM\/ 001, Instituto Nacional de Pesquisas Espaciais (INPE)."},{"key":"ref_25","first-page":"930","article-title":"An improved robust H\u221e multiple fading fault-tolerant filtering algorithm for INS\/GPS integrated navigation","volume":"30","author":"Chen","year":"2009","journal-title":"J. Astronaut."},{"key":"ref_26","unstructured":"Rawicz, P.L. (2000). H\u221e \/ H2 \/ Kalman Filtering of Linear Dynamics Systems via Variational Techniques with Applications to Target Tracking. [Ph.D. Thesis, Drexel University]."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Doucet, A., de Freitas, N., and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice, Springer.","DOI":"10.1007\/978-1-4757-3437-9"},{"key":"ref_28","unstructured":"(2022, November 10). CBERS\/INPE, Sat\u00e9lite Sino-Brasileiro de Recursos Terrestres-CBERS-INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS. Available online: http:\/\/www.cbers.inpe.br\/sobre\/historia.php."},{"key":"ref_29","unstructured":"(2023, June 20). CBERS4\/INPE, Sat\u00e9lite Sino-Brasileiro de Recursos Terrestres-CBERS-4-INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS. Available online: http:\/\/www.cbers.inpe.br\/sobre\/orbita\/cbers3-4.php."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ristic, B., Arulampalam, S., and Gordon, N. (2004). Beyound the Kalman Filter, Particle Filters for Tracking Applications, Artech House.","DOI":"10.1155\/S1110865704405095"},{"key":"ref_31","first-page":"1343","article-title":"Application of the Regularized Particle Filter for Attitude Determination Using Real Measurements of CBERS-2 Satellite","volume":"15","author":"Silva","year":"2015","journal-title":"Adv. Astronaut. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Borges, R.A., dos Santos, A.C., Silva, W.R., Aguayo, L., Borges, G.A., Karam, M.M., de Sousa, R.B., Garc\u00eda, B.F.-A., Botelho, V.M.d.S., and Fern\u00e1ndez-Carrillo, J.M. (2022). The AlfaCrux CubeSat Mission Description and Early Results. Appl. Sci., 12.","DOI":"10.3390\/app12199764"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Dimino, I., Vendittozzi, C., Reis Silva, W., Ameduri, S., and Concilio, A. (2023). A Morphing Deployable Mechanism for Re-Entry Capsule Aeroshell. Appl. Sci., 13.","DOI":"10.3390\/app13052783"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/16\/4052\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:35:10Z","timestamp":1760128510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/16\/4052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,16]]},"references-count":33,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["rs15164052"],"URL":"https:\/\/doi.org\/10.3390\/rs15164052","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,16]]}}}