[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85174-en":3,"doc-seo-85174-105":29,"detail-sidebar-cat-0-en-105":95},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85174,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Fully Multiplicative Attitude and Orbit Determination for Deep Space Navigation","Develops a geometry-consistent fully multiplicative unscented Kalman filter (FMUKF) for joint spacecraft attitude–orbit estimation with simultaneous dual star-tracker misalignment calibration. The method uses a 21-dimensional local error state on a mixed quaternion–Euclidean manifold, fusing gyroscope, star-tracker, and planet line-of-sight measurements while retaining celestial aberration to model velocity-dependent optical coupling. A multiplicative EKF baseline (MEKF) is implemented and compared via Monte Carlo tests, showing similar accuracy for fine propagation intervals, but FMUKF consistency where MEKF diverges at coarse intervals.","arXiv :2607 . 10072v1 [ ee ss . SY] 11 Jul 2026  \nAAS 26-948  \nFULLY MULTIPLICATIVE ATTITUDE AND ORBIT DETERMINATION  \nFOR DEEP SPACE NAVIGATION.  \nRidma Ganganath*, and Simone Servadio†  \nThis paper develops a geometry-consistent fully multiplicative unscented Kalman filter (FMUKF) for joint spacecraft attitude–orbit estimation with simultaneous dual star-tracker misalignment calibration. The estimator uses a 21-dimensional local error state combining attitude, angular velocity, gyroscope bias, inertial position and velocity, and two trackermisalignment vectors on a mixed quaternion–Euclidean manifold. Gyroscope, star-tracker, and planet line-of-sight measurements are fused, with celestial aberration retained to capture velocity-dependent optical coupling. A multiplicative extended Kalman filter (MEKF) is implemented as a first-order baseline using the same nominal state, attitude retraction, and unit-vector measurement geometry. Monte Carlo results show similar short-step performance, while at coarse propagation intervals the FM-UKF remains consistent and the MEKF  \nexhibits divergence.  \nINTRODUCTION  \nSequential Bayesian estimation is central to spacecraft guidance, navigation, and control because it enables recursive fusion of dynamics models and noisy measurements in real time. In spacecraft applications, this problem is naturally geometric: attitude evolves on the rotation group, optical line-of-sight measurements lie on the unit sphere, and orbital states, biases, and calibration parameters evolve in Euclidean space. Classical Kalman filtering and its nonlinear extensions provide the basic recursive framework, but their accuracy and consistency depend strongly on how well the estimator preserves this mixed geometry [1, 2, 5–7] .  \nFor attitude determination, vector observations from star trackers, sun sensors, magnetometers, and other optical instruments have long supported deterministic and recursive estimators, including QUEST-type and quaternion-based methods [3–5] . The multiplicative extended Kalman filter (MEKF) became a standard attitude-estimation approach because it preserves the unit-quaternion constraint while representing uncertainty in a minimal local error space [5–7] . However, the first-order linearization used by the MEKF can become fragile when propagation intervals are long, dynamics are nonlinear, or measurements couple multiple state components. This limitation motivated unscented and higher-order nonlinear attitude estimators, which propagate sigma points through the nonlinear model rather than relying only on local Jacobians [?, 8–11, 24] .  \nA related issue is the geometry of the measurements. Unit-vector observations should not be modeled asunconstrained Euclidean quantities because the measured directions remain on S2. Multiplicative measurement models and intrinsic residuals address this by representing direction error as a small rotation acting on the ideal line of sight, preserving unit norm and respecting the spherical measurement geometry [12, 25] . Quaternion averaging is similarly required in unscented attitude filtering so that the propagated attitude mean is formed on the manifold rather than by direct algebraic averaging in R4 [13] .  \nModern spacecraft navigation problems increasingly require estimation beyond attitude alone. Highaccuracy performance may depend on simultaneous estimation of gyroscope bias, sensor-alignment parameters, and translational states. Previous studies have addressed joint attitude and parameter estimation,  \n* Graduate Research Assistant, Department of Aerospace, Iowa State University, Ames, IA 50014 .†Assistant Professor, Department of Aerospace, Iowa State University, Ames, IA 50014 .  \nalignment calibration, moving-horizon estimation, and flight-calibration methods, showing that sensor misalignment can be an observable but slowly converging state that materially affects estimation accuracy and covariance credibility [14, 15, 19, 20] . In deep-space optic","cbCaihmSmlDfSajJ","https://ap.wps.com/l/cbCaihmSmlDfSajJ","pdf",16045262,1,21,"English","en",105,"# Introduction\n## Geometric foundations for Bayesian spacecraft estimation\n## Attitude determination with multiplicative filters\n## Measurement geometry and manifold-consistent residuals\n## Joint estimation: attitude, calibration, and orbital states\n## Proposed FM-UKF and MEKF comparison\n## Monte Carlo consistency and divergence results","[{\"question\":\"What estimation problem does the paper address for deep-space navigation?\",\"answer\":\"It addresses joint spacecraft attitude–orbit estimation while simultaneously calibrating dual three-axis star-tracker misalignment vectors using optical line-of-sight data and inertial sensing.\"},{\"question\":\"How is the proposed FMUKF constructed to respect geometry?\",\"answer\":\"It uses a fully multiplicative unscented Kalman filter with a 21-dimensional local error state defined on a mixed quaternion–Euclidean manifold, combining rotational components with Euclidean translational and bias states.\"},{\"question\":\"Why does the paper compare FMUKF with a multiplicative EKF (MEKF)?\",\"answer\":\"The MEKF serves as a first-order baseline using the same nominal state and measurement architecture, enabling evaluation of how linearized propagation and unit-vector update statistics affect consistency at different propagation intervals.\"},{\"question\":\"What do the Monte Carlo results indicate about the filters?\",\"answer\":\"For fine propagation intervals, FMUKF and MEKF perform similarly, but at coarse propagation intervals the MEKF becomes overconfident and diverges, while FMUKF remains consistent with the Monte Carlo error spread.\"}]",1784201546,53,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":90,"head_meta":92,"extra_data":94,"updated_unix":27},"fully-multiplicative-attitude-and-orbit-determination-for-deep-space-navigation","",{"@graph":35,"@context":89},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/fully-multiplicative-attitude-and-orbit-determination-for-deep-space-navigation/85174/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"What estimation problem does the paper address for deep-space navigation?","Question",{"text":75,"@type":76},"It addresses joint spacecraft attitude–orbit estimation while simultaneously calibrating dual three-axis star-tracker misalignment vectors using optical line-of-sight data and inertial sensing.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the proposed FMUKF constructed to respect geometry?",{"text":80,"@type":76},"It uses a fully multiplicative unscented Kalman filter with a 21-dimensional local error state defined on a mixed quaternion–Euclidean manifold, combining rotational components with Euclidean translational and bias states.",{"name":82,"@type":73,"acceptedAnswer":83},"Why does the paper compare FMUKF with a multiplicative EKF (MEKF)?",{"text":84,"@type":76},"The MEKF serves as a first-order baseline using the same nominal state and measurement architecture, enabling evaluation of how linearized propagation and unit-vector update statistics affect consistency at different propagation intervals.",{"name":86,"@type":73,"acceptedAnswer":87},"What do the Monte Carlo results indicate about the filters?",{"text":88,"@type":76},"For fine propagation intervals, FMUKF and MEKF perform similarly, but at coarse propagation intervals the MEKF becomes overconfident and diverges, while FMUKF remains consistent with the Monte Carlo error spread.","https://schema.org",{"og:url":51,"og:type":91,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":93,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":96},[97,101,105,109,114,119,124,127,132,135,139],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Story & 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