{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:51Z","timestamp":1760242251881,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,1,30]],"date-time":"2017-01-30T00:00:00Z","timestamp":1485734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) become fully-operational and has been provided with the operational name of NavIC (Navigation with Indian Constellation). It has been developed by the Indian Space Research Organization (ISRO) with the objective of offering positioning, navigation and timing (PNT) to the users in its service area. This contribution provides for the \ufb01rst time an assessment of the IRNSS L5-signal capability to achieve instantaneous attitude determination on the basis of data collected in Perth, Australia. Our evaluations are conducted for both a linear array of two antennas and a planar array of three antennas. A pre-requisite for precise and fast IRNSS attitude determination is the successful resolution of the double-differenced (DD) integer carrier-phase ambiguities. In this contribution, we will compare the performances of different such methods, amongst which the unconstrained and the multivariate-constrained LAMBDA method for both linear and planar arrays. It is demonstrated that the instantaneous ambiguity success rates increase from 15% to 90% for the linear array and from 5% to close to 100% for the planar array, thus showing that standalone IRNSS can realize 24-h almost instantaneous precise attitude determination with heading and elevation standard deviations of 0.05 and 0.10 degrees, respectively.<\/jats:p>","DOI":"10.3390\/s17020274","type":"journal-article","created":{"date-parts":[[2017,1,30]],"date-time":"2017-01-30T11:36:30Z","timestamp":1485776190000},"page":"274","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["IRNSS\/NavIC L5 Attitude Determination"],"prefix":"10.3390","volume":"17","author":[{"given":"Safoora","family":"Zaminpardaz","sequence":"first","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, GPO Box U1987, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Teunissen","sequence":"additional","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, GPO Box U1987, Perth, WA 6845, Australia"},{"name":"Department of Geoscience and Remote Sensing, Delft University of Technology, PO Box 5048, 2600 GA Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nandakumaran","family":"Nadarajah","sequence":"additional","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, GPO Box U1987, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,30]]},"reference":[{"key":"ref_1","unstructured":"Indian Space Research Organisation (ISRO) (2014). Indian Regional Navigation Satellite System: Signal in Space ICD for Standard Positioning Service."},{"key":"ref_2","unstructured":"Indian Space Research Organisation (ISRO) PSLV-C33\/IRNSS-1G, Available online: http:\/\/www.isro.gov.in\/sites\/default\/files\/pslv-c33-brochure.pdf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s10291-013-0351-7","article-title":"IRNSS-1A: Signal and clock characterization of the Indian regional navigation system","volume":"18","author":"Thoelert","year":"2014","journal-title":"GPS Solut."},{"key":"ref_4","first-page":"35","article-title":"Precise Modeling of Solar Radiation Pressure for IRNSS Satellite","volume":"5","author":"Kumari","year":"2015","journal-title":"J. Nat. Sci. Res."},{"key":"ref_5","first-page":"3","article-title":"IRNSS Satellite Parameter Estimation Using Combination Strategy","volume":"15","author":"Babu","year":"2015","journal-title":"Glob. J. Sci. Front. Res."},{"key":"ref_6","first-page":"1","article-title":"Modernized IRNSS Broadcast Ephemeris Parameters","volume":"5","author":"Chandrasekhar","year":"2015","journal-title":"Control Theory Inform."},{"key":"ref_7","unstructured":"Ganeshan, A.S., Ratnakara, S.C., Srinivasan, N., Rajaram, B., Tirmal, N., and Anbalagan, K. First position fix with IRNSS. Available online: http:\/\/www.insidegnss.com\/node\/4545."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/14498596.2016.1142398","article-title":"IRNSS stand-alone positioning: First results in Australia","volume":"61","author":"Zaminpardaz","year":"2016","journal-title":"J. Spat. Sci."},{"key":"ref_9","unstructured":"Montenbruck, O., and Steigenberger, S.R. (2015, January 26\u201328). IRNSS orbit determination and broadcast ephemeris assessment. Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, CA, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s10291-015-0450-8","article-title":"Assessing the IRNSS L5-signal in combination with GPS, Galileo, and QZSS L5\/E5a-signals for positioning and navigation","volume":"20","author":"Nadarajah","year":"2016","journal-title":"GPS Solut."},{"key":"ref_11","unstructured":"Cohen, C. (1992). Attitude Determination Using GPS. [Ph.D. Thesis, Stanford University]."},{"key":"ref_12","unstructured":"Lu, G. (1995). Development of a GPS Multi-Antenna System for Attitude Determination. [Ph.D. Thesis, University of Calgary]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"635","DOI":"10.2514\/1.1324","article-title":"Robust spacecraft attitude determination using global positioning system receivers","volume":"41","author":"Madsen","year":"2004","journal-title":"J. Spacecr. Rockets"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.2514\/1.18351","article-title":"Batch algorithm for global-positioning-system attitude determination and integer ambiguity resolution","volume":"29","author":"Psiaki","year":"2006","journal-title":"J. Guid. Control Dyn."},{"key":"ref_15","unstructured":"Hodgart, M.S., and Purivigraipong, S. (2000, January 13\u201316). New approach to resolving instantaneous integer ambiguity resolution for spacecraft attitude determination using GPS signals. Proceedings of the IEEE Position Location and Navigation Symposium, San Diego, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1515\/gps-2018-0017","article-title":"On-the-Fly GPS-Based Attitude Determination Using Single- and Double-Differenced Carrier Phase Measurements","volume":"8","author":"Li","year":"2004","journal-title":"GPS Solut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10291-008-0103-2","article-title":"A constrained LAMBDA method for GPS attitude determination","volume":"13","author":"Wang","year":"2009","journal-title":"GPS Solut."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.asr.2010.02.023","article-title":"Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms","volume":"46","author":"Giorgi","year":"2010","journal-title":"Adv. Space Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s10291-010-0164-x","article-title":"Testing of a new single-frequency GNSS carrier phase attitude determination method: Land, ship and aircraft experiments","volume":"15","author":"Teunissen","year":"2011","journal-title":"GPS Solut."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00863419","article-title":"The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation","volume":"70","author":"Teunissen","year":"1995","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/s001900050100","article-title":"A canonical theory for short GPS baselines. Part I: The baseline precision","volume":"71","author":"Teunissen","year":"1997","journal-title":"J. Geod."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s001900050269","article-title":"An optimality property of the integer least-squares estimator","volume":"73","author":"Teunissen","year":"1999","journal-title":"J. Geod."},{"key":"ref_23","unstructured":"Park, C., and Teunissen, P.J.G. (2003, January 15\u201318). A new carrier phase ambiguity estimation for GNSS attitude determination systems. Proceedings of the International GPS\/GNSS Symposium, Tokyo, Japan."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1007\/s12555-009-0408-0","article-title":"Integer least squares with quadratic equality constraints and its application to GNSS attitude determination systems","volume":"7","author":"Park","year":"2009","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"89","DOI":"10.2478\/v10018-007-0009-1","article-title":"The LAMBDA method for the GNSS compass","volume":"41","author":"Teunissen","year":"2006","journal-title":"Artif. Satell."},{"key":"ref_26","unstructured":"Buist, P.J. (2007, January 25\u201328). The baseline constrained LAMBDA method for single epoch, single-frequency attitude determination applications. Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, USA."},{"key":"ref_27","unstructured":"Yasuda, A. (2008, January 11\u201314). A search and shrink approach for the baseline constrained LAMBDA method: Experimental results. Proceedings of the International Symposium on GPS\/GNSS, Tokyo, Japan."},{"key":"ref_28","unstructured":"Giorgi, G., and Buist, P.J. (2008, January 10\u201312). Single-epoch, single-frequency, standalone full attitude determination: Experimental results. Proceedings of the Fourth ESA Workshop on Satellite Navigation User Equipment Technologies (NAVITEC), Noordwijk, The Netherlands."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Harville, D.A. (1997). Matrix Algebra From A Statistician\u2019s Perspective, Springer.","DOI":"10.1007\/b98818"},{"key":"ref_30","unstructured":"Magnus, J.R., and Neudecker, H. (1995). Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1007\/BF00806368","article-title":"On optimal filtering of GPS dual frequency observations without using orbit information","volume":"65","author":"Euler","year":"1991","journal-title":"Bull. Geod."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2478\/v10018-008-0002-3","article-title":"A general multivariate formulation of the multi-antenna GNSS attitude determination problem","volume":"42","author":"Teunissen","year":"2007","journal-title":"Artif. Satell."},{"key":"ref_33","unstructured":"Kuipers, J.B. (2002). Quaternions and Rotation Sequences, Princeton University Press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s00190-011-0538-z","article-title":"The affine constrained GNSS attitude model and its multivariate integer least-squares solution","volume":"86","author":"Teunissen","year":"2012","journal-title":"J. Geod."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s00190-010-0380-8","article-title":"Integer least-squares theory for the GNSS compass","volume":"84","author":"Teunissen","year":"2010","journal-title":"J. Geod."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00190-007-0157-x","article-title":"Least-squares variance component estimation","volume":"82","author":"Teunissen","year":"2008","journal-title":"J. Geod."},{"key":"ref_37","unstructured":"Teunissen, P.J.G. (1989, January 5\u20138). Estimation in Nonlinear Models. Proceedings of the II Hotine-Marussi Symposium on Mathematical Geodesy, Pisa, Italy."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1002\/navi.51","article-title":"Instantaneous GPS\/Galileo\/QZSS\/SBAS Attitude Determination: A Single- Frequency (L1\/E1) Robustness Analysis under Constrained Environments","volume":"61","author":"Nadarajah","year":"2014","journal-title":"Navigation"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1007\/s001900050199","article-title":"Success probability of integer GPS ambiguity rounding and bootstrapping","volume":"72","author":"Teunissen","year":"1998","journal-title":"J. Geod."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1002\/j.2161-4296.2005.tb01736.x","article-title":"On the reliability of integer ambiguity resolution","volume":"52","author":"Verhagen","year":"2005","journal-title":"Navigation"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/274\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:27:16Z","timestamp":1760207236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/274"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,30]]},"references-count":40,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["s17020274"],"URL":"https:\/\/doi.org\/10.3390\/s17020274","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,1,30]]}}}