Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2963667179', 'doi': 'https://doi.org/10.1109/cdc.2015.7402526', 'title': 'An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering', 'display_name': 'An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering', 'publication_year': 2015, 'publication_date': '2015-12-01', 'ids': {'openalex': 'https://openalex.org/W2963667179', 'doi': 'https://doi.org/10.1109/cdc.2015.7402526', 'mag': '2963667179'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1109/cdc.2015.7402526', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4363607724', 'display_name': '2021 60th IEEE Conference on Decision and Control (CDC)', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'conference'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'proceedings-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://arxiv.org/pdf/1503.04701', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5037120106', 'display_name': 'Silvère Bonnabel', 'orcid': 'https://orcid.org/0000-0002-6001-7766'}, 'institutions': [{'id': 'https://openalex.org/I4403386650', 'display_name': 'Centre de Robotique', 'ror': 'https://ror.org/0180r7w69', 'country_code': None, 'type': 'facility', 'lineage': ['https://openalex.org/I190752583', 'https://openalex.org/I2746051580', 'https://openalex.org/I4403386650', 'https://openalex.org/I70768539']}, {'id': 'https://openalex.org/I70768539', 'display_name': 'École Nationale Supérieure des Mines de Paris', 'ror': 'https://ror.org/04y8cs423', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I190752583', 'https://openalex.org/I2746051580', 'https://openalex.org/I70768539']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Silvere Bonnabel', 'raw_affiliation_strings': ['MINES ParisTech, Centre for robotics, Paris, France'], 'affiliations': [{'raw_affiliation_string': 'MINES ParisTech, Centre for robotics, Paris, France', 'institution_ids': ['https://openalex.org/I4403386650', 'https://openalex.org/I70768539']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5072919180', 'display_name': 'Axel Barrau', 'orcid': 'https://orcid.org/0000-0002-8957-8292'}, 'institutions': [{'id': 'https://openalex.org/I4403386650', 'display_name': 'Centre de Robotique', 'ror': 'https://ror.org/0180r7w69', 'country_code': None, 'type': 'facility', 'lineage': ['https://openalex.org/I190752583', 'https://openalex.org/I2746051580', 'https://openalex.org/I4403386650', 'https://openalex.org/I70768539']}, {'id': 'https://openalex.org/I70768539', 'display_name': 'École Nationale Supérieure des Mines de Paris', 'ror': 'https://ror.org/04y8cs423', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I190752583', 'https://openalex.org/I2746051580', 'https://openalex.org/I70768539']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Axel Barrau', 'raw_affiliation_strings': ['MINES ParisTech, Centre for robotics, Paris, France'], 'affiliations': [{'raw_affiliation_string': 'MINES ParisTech, Centre for robotics, Paris, France', 'institution_ids': ['https://openalex.org/I4403386650', 'https://openalex.org/I70768539']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 1.611, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 15, 'citation_normalized_percentile': {'value': 0.973337, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 88, 'max': 89}, 'biblio': {'volume': None, 'issue': None, 'first_page': '2158', 'last_page': '2163'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11325', 'display_name': 'Inertial Sensor and Navigation', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2202', 'display_name': 'Aerospace Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11325', 'display_name': 'Inertial Sensor and Navigation', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2202', 'display_name': 'Aerospace Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10711', 'display_name': 'Target Tracking and Data Fusion in Sensor Networks', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/1702', 'display_name': 'Artificial Intelligence'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10534', 'display_name': 'Structural Health Monitoring Techniques', 'score': 0.9941, 'subfield': {'id': 'https://openalex.org/subfields/2205', 'display_name': 'Civil and Structural Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/cramér–rao-bound', 'display_name': 'Cramér–Rao bound', 'score': 0.556118}, {'id': 'https://openalex.org/keywords/rotation-matrix', 'display_name': 'Rotation matrix', 'score': 0.5502097}, {'id': 'https://openalex.org/keywords/orthogonal-group', 'display_name': 'Orthogonal group', 'score': 0.42025778}, {'id': 'https://openalex.org/keywords/matrix', 'display_name': 'Matrix (chemical analysis)', 'score': 0.41761842}], 'concepts': [{'id': 'https://openalex.org/C77553402', 'wikidata': 'https://www.wikidata.org/wiki/Q13222579', 'display_name': 'Upper and lower bounds', 'level': 2, 'score': 0.7005552}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.64093196}, {'id': 'https://openalex.org/C185429906', 'wikidata': 'https://www.wikidata.org/wiki/Q1130160', 'display_name': 'Estimator', 'level': 2, 'score': 0.580201}, {'id': 'https://openalex.org/C4978587', 'wikidata': 'https://www.wikidata.org/wiki/Q1138810', 'display_name': 'Cramér–Rao bound', 'level': 3, 'score': 0.556118}, {'id': 'https://openalex.org/C178650346', 'wikidata': 'https://www.wikidata.org/wiki/Q201984', 'display_name': 'Covariance', 'level': 2, 'score': 0.5533554}, {'id': 'https://openalex.org/C83633838', 'wikidata': 'https://www.wikidata.org/wiki/Q1256564', 'display_name': 'Rotation matrix', 'level': 2, 'score': 0.5502097}, {'id': 'https://openalex.org/C200127275', 'wikidata': 'https://www.wikidata.org/wiki/Q173853', 'display_name': 'Quaternion', 'level': 2, 'score': 0.54981244}, {'id': 'https://openalex.org/C185142706', 'wikidata': 'https://www.wikidata.org/wiki/Q1134404', 'display_name': 'Covariance matrix', 'level': 2, 'score': 0.54445416}, {'id': 'https://openalex.org/C163716315', 'wikidata': 'https://www.wikidata.org/wiki/Q901177', 'display_name': 'Gaussian', 'level': 2, 'score': 0.50016}, {'id': 'https://openalex.org/C206833254', 'wikidata': 'https://www.wikidata.org/wiki/Q5421817', 'display_name': 'Extended Kalman filter', 'level': 3, 'score': 0.46759456}, {'id': 'https://openalex.org/C190470478', 'wikidata': 'https://www.wikidata.org/wiki/Q2370229', 'display_name': 'Invariant (physics)', 'level': 2, 'score': 0.42312813}, {'id': 'https://openalex.org/C146561895', 'wikidata': 'https://www.wikidata.org/wiki/Q1783179', 'display_name': 'Orthogonal group', 'level': 2, 'score': 0.42025778}, {'id': 'https://openalex.org/C106487976', 'wikidata': 'https://www.wikidata.org/wiki/Q685816', 'display_name': 'Matrix (chemical analysis)', 'level': 2, 'score': 0.41761842}, {'id': 'https://openalex.org/C180877172', 'wikidata': 'https://www.wikidata.org/wiki/Q5401390', 'display_name': 'Estimation of covariance matrices', 'level': 3, 'score': 0.41006494}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.40711427}, {'id': 'https://openalex.org/C157286648', 'wikidata': 'https://www.wikidata.org/wiki/Q846780', 'display_name': 'Kalman filter', 'level': 2, 'score': 0.39292496}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.3807005}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.35137367}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.23212212}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.20882577}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.08972666}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.084898114}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C192562407', 'wikidata': 'https://www.wikidata.org/wiki/Q228736', 'display_name': 'Materials science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C159985019', 'wikidata': 'https://www.wikidata.org/wiki/Q181790', 'display_name': 'Composite material', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1109/cdc.2015.7402526', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4363607724', 'display_name': '2021 60th IEEE Conference on Decision and Control (CDC)', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'conference'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1503.04701', 'pdf_url': 'http://arxiv.org/pdf/1503.04701', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1503.04701', 'pdf_url': 'http://arxiv.org/pdf/1503.04701', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 27, 'referenced_works': ['https://openalex.org/W1544646823', 'https://openalex.org/W1970789124', 'https://openalex.org/W1980215765', 'https://openalex.org/W1983104971', 'https://openalex.org/W1988520084', 'https://openalex.org/W1994088960', 'https://openalex.org/W2011586160', 'https://openalex.org/W2063005413', 'https://openalex.org/W2079249362', 'https://openalex.org/W2079329591', 'https://openalex.org/W2096491782', 'https://openalex.org/W2104130465', 'https://openalex.org/W2107929215', 'https://openalex.org/W2113174648', 'https://openalex.org/W2124422393', 'https://openalex.org/W2132240870', 'https://openalex.org/W2136517446', 'https://openalex.org/W2137448549', 'https://openalex.org/W2151870994', 'https://openalex.org/W2168573970', 'https://openalex.org/W2169772828', 'https://openalex.org/W2292586222', 'https://openalex.org/W2974222084', 'https://openalex.org/W3081157420', 'https://openalex.org/W3102317997', 'https://openalex.org/W3104122060', 'https://openalex.org/W74240361'], 'related_works': ['https://openalex.org/W4320038180', 'https://openalex.org/W4220867898', 'https://openalex.org/W2951160651', 'https://openalex.org/W2799307919', 'https://openalex.org/W2511668269', 'https://openalex.org/W2388930076', 'https://openalex.org/W2348328811', 'https://openalex.org/W2106549822', 'https://openalex.org/W2091132606', 'https://openalex.org/W2074615279'], 'abstract_inverted_index': {'In': [0], 'this': [1], 'note': [2], 'an': [3], 'intrinsic': [4, 23, 148], 'version': [5], 'of': [6, 36, 61, 75, 90, 116, 187], 'the': [7, 16, 25, 40, 72, 84, 94, 114, 140, 147, 153, 158, 173, 177, 184, 188], 'Cramér-Rao': [8, 149], 'bound': [9, 70, 138, 150, 178], 'on': [10, 15, 32, 38, 71, 101, 122], 'estimation': [11, 85, 96, 141], 'accuracy': [12], 'is': [13, 22, 42, 99, 105, 168, 190], 'established': [14], 'Special': [17], 'Orthogonal': [18], 'group': [19, 91], 'SO(3).': [20, 102], 'It': [21], 'in': [24, 88, 169], 'sense': [26], 'that': [27, 82], 'it': [28], 'does': [29], 'not': [30], 'rely': [31], 'a': [33, 68, 117, 136], 'specific': [34], 'choice': [35], 'coordinates': [37], 'SO(3):': [39], 'result': [41, 104], 'derived': [43], 'using': [44, 51], 'rotation': [45], 'matrices,': [46], 'but': [47], 'remains': [48], 'valid': [49], 'when': [50], 'other': [52], 'parameterizations,': [53], 'such': [54], 'as': [55], 'quaternions.': [56], 'For': [57], 'any': [58], 'estimator': [59], 'R̂': [60], 'R': [62], '∈': [63], 'SO(3)': [64, 123], 'we': [65, 112, 134], 'give': [66], 'indeed': [67], 'lower': [69, 137], 'covariance': [73, 143, 154], 'matrix': [74, 155], 'log': [76], '(RR̂': [77], '<sup': [78], 'xmlns:mml="http://www.w3.org/1998/Math/MathML"': [79], 'xmlns:xlink="http://www.w3.org/1999/xlink">T</sup>': [80], '),': [81], 'is,': [83], 'error': [86, 97, 142], 'expressed': [87], 'terms': [89], 'multiplication,': [92], 'whereas': [93], 'usual': [95], '(R̂-R)': [98], 'meaningless': [100], 'The': [103], 'first': [106], 'applied': [107], 'to': [108, 128, 139], "Whaba's": [109], 'problem.': [110], 'Then,': [111], 'consider': [113], 'problem': [115], 'continuous-time': [118], 'nonlinear': [119], 'deterministic': [120], 'system': [121, 189], 'with': [124, 152, 172], 'discrete': [125], 'measurements': [126], 'subject': [127], 'additive': [129], 'isotropic': [130], 'Gaussian': [131], 'noise,': [132], 'and': [133, 161], 'derive': [135], 'matrix.': [144], 'We': [145], 'prove': [146], 'coincides': [151], 'returned': [156], 'by': [157], 'Invariant': [159], 'EKF,': [160], 'thus': [162], 'can': [163, 179], 'be': [164, 181], 'computed': [165, 182], 'online.': [166], 'This': [167], 'sharp': [170], 'contrast': [171], 'general': [174], 'case,': [175], 'where': [176], 'only': [180], 'if': [183], 'true': [185], 'trajectory': [186], 'known.': [191]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2963667179', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 3}, {'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 2}, {'year': 2020, 'cited_by_count': 2}, {'year': 2019, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 2}, {'year': 2016, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}], 'updated_date': '2025-01-04T07:58:56.840646', 'created_date': '2019-07-30'}