# Single-frequency L5 attitude determination from IRNSS/NavIC and GPS: a single- and dual-system analysis

- 300 Downloads

## Abstract

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) reached its full operational capability. In this contribution, we provide the very first L5 attitude determination analyses of the fully operational IRNSS as a standalone system and also in combination with the fully operational GPS Block IIF along with the corresponding ambiguity resolution results. Our analyses are carried out for both a linear array of two antennas and a planar array of three antennas at Curtin University, Perth, Australia. We study the noise characteristics (carrier-to-noise density, measurement precision, time correlation), the integer ambiguity resolution performance (LAMBDA, MC-LAMBDA) and the attitude determination performance (ambiguity float and ambiguity fixed). A prerequisite for precise and fast IRNSS attitude determination is the successful resolution of the double-differenced integer carrier-phase ambiguities. In this contribution, we will compare the performance of the unconstrained and the multivariate-constrained LAMBDA method. It is therefore also shown what improvements are achieved when the known body geometry of the antenna array is rigorously incorporated into the ambiguity objective function. As our ambiguity-fixed outcomes show consistency between empirical and formal results, we also formally assess the precise attitude determination performance for several locations within the IRNSS service area.

## Keywords

IRNSS NavIC GPS Block IIF Integer carrier-phase ambiguity resolution Attitude determination Multivariate-constrained integer least squares MC-LAMBDA## Notes

### Acknowledgements

The second author is the recipient of an Australian Research Council (ARC) Federation Fellowship (Project Number FF0883188). This support is gratefully acknowledged.

## References

- Amiri-Simkooei AR, Tiberius CCJM (2007) Assessing receiver noise using GPS short baseline time series. GPS Solut 11(1):21–35CrossRefGoogle Scholar
- Babu R, Mula P, Ratnakara SC, Ganeshan AS (2015) IRNSS satellite parameter estimation using combination strategy. Glob J Sci Front Res 15(3):87–95Google Scholar
- de Bakker PF, Tiberius CCJM, van der Marel H, van Bree RJP (2012) Short and zero baseline analysis of GPS L1 C/A, L5Q, GIOVE E1B, and E5aQ signals. GPS Solut 16(1):53–64CrossRefGoogle Scholar
- Buist PJ (2007) The baseline constrained LAMBDA method for single epoch, single-frequency attitude determination applications. In: Proceedings of the 20th international technical meeting of the satellite division of The Institute of Navigation (ION GNSS 2007), ION, pp 2962–2973Google Scholar
- Chandrasekhar MV, Rajarajan D, Satyanarayana G, Tirmal N, Rathnakara SC, Ganeshan AS (2015) Modernized IRNSS broadcast ephemeris parameters. Control Theory Inform 5(2):1–9Google Scholar
- Cohen C (1992) Attitude determination using GPS. Ph D Thesis Stanford UniversityGoogle Scholar
- Euler HJ, Goad CC (1991) On optimal filtering of GPS dual frequency observations without using orbit information. Bull Geod 65(2):130–143CrossRefGoogle Scholar
- Ganeshan AS, Ratnakara SC, Srinivasan N, Rajaram B, Tirmal NKA (2015) First position fix with IRNSS. Inside GNSS 10(4):48–52Google Scholar
- Giorgi G, Buist PJ (2008) Single-epoch, single-frequency, standalone full attitude determination: experimental results. In: Proceedings of the fourth ESA workshop on satellite navigation user equipment technologies, NAVITEC. ESA-ESTEC, The NetherlandsGoogle Scholar
- Giorgi G, Teunissen PJG, Buist PJ (2008) A search and shrink approach for the baseline constrained LAMBDA method: experimental results. In: Yasuda A (ed) Proceedings of international symposium on GPS/GNSS, Tokyo University of Marine Science and Technology, pp 797–806Google Scholar
- Giorgi G, Teunissen PJG, Verhagen S, Buist PJ (2010) Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms. Adv Space Res 46(2):118–129CrossRefGoogle Scholar
- GPS Directorate (2011) Navstar GPS space segment/user segment L5 interfaces (IS-GPS-705B). Technical reportGoogle Scholar
- Harville DA (1997) Matrix algebra from A statistician’s perspective. Springer, New YorkCrossRefGoogle Scholar
- Hauschild A, Grillmayer G, Montenbruck O, Markgraf M, Vörsmann P (2008) GPS based attitude determination for the flying laptop satellite. In: Small satellites for earth observation, Springer, pp 211–220Google Scholar
- Hide C, Pinchin J, Park D (2007) Development of a low cost multiple GPS antenna attitude system. In: Proceedings of ION GNSS, pp 88–95Google Scholar
- Hodgart MS, Purivigraipong S (2000) New approach to resolving instantaneous integer ambiguity resolution for spacecraft attitude determination using GPS signals. In: Proceedings of IEEE position location and navigation symposium, IEEE, pp 132–139Google Scholar
- ISRO (2014) INDIAN REGIONAL NAVIGATION SATELLITE SYSTEM: signal in space ICD for standard positioning service, Version 1.0. ISRO Satellite Centre, June 2014Google Scholar
- ISRO (2016) PSLV-C33/IRNSS-1G. http://www.isro.gov.in/sites/default/files/pslv-c33-brochure.pdf, published April 2016. Accessed 1 June 2016
- Kuipers JB (2002) Quaternions and rotation sequences. Princeton University Press, PrincetonGoogle Scholar
- Kumari A, Samal K, Rajarajan D, Swami U, Babu R, Kartik A, Rathnakara SC, Ganeshan AS (2015) Precise modeling of solar radiation pressure for IRNSS satellite. J Nat Sci Res 5(3):35–43Google Scholar
- Li Y, Zhang K, Roberts C, Murata M (2004) On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements. GPS Solut 8(2):93–102CrossRefGoogle Scholar
- Lu G (1995) Development of a GPS multi-antenna system for attitude determination. Ph.D. Thesis University of CalgaryGoogle Scholar
- Madsen J, Lightsey EG (2004) Robust spacecraft attitude determination using global positioning system receivers. J Spacecr Rockets 41(4):635–644CrossRefGoogle Scholar
- Magnus JR, Neudecker H et al (1995) Matrix differential calculus with applications in statistics and econometrics. Wiley, New YorkGoogle Scholar
- Montenbruck O, Steigenberger SR (2015) IRNSS orbit determination and broadcast ephemeris assessment. In: Proceedings of the 2015 international technical meeting of the institute of navigation, Dana Point, California, January 2015, pp 185–193Google Scholar
- Nadarajah N, Khodabandeh A, Teunissen PJG (2015) Assessing the IRNSS L5-signal in combination with GPS, Galileo, and QZSS L5/E5a-signals for positioning and navigation. GPS Solut 20(2):289–297CrossRefGoogle Scholar
- Odijk D, Teunissen PJG (2008) ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models. J Geod 82(8):473–492CrossRefGoogle Scholar
- Odijk D, Teunissen PJ (2013) Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution. GPS Solut 17(4):521–533CrossRefGoogle Scholar
- Odijk D, Teunissen PJG, Huisman L (2012) First results of mixed GPS + GIOVE single-frequency RTK in Australia. J Spat Sci 57(1):3–18CrossRefGoogle Scholar
- Odijk D, Nadarajah N, Zaminpardaz S, Teunissen PJG (2016) GPS, Galileo, BDS, QZSS and IRNSS differential ISBs: estimation and application. GPS Solut. doi: 10.1007/s10291-016-0536-y
- Park C, Teunissen PJG (2003) A new carrier phase ambiguity estimation for GNSS attitude determination systems. In: Proceedings of international GPS/GNSS symposium, Tokyo, vol 8, pp 283–290Google Scholar
- Park C, Teunissen PJG (2009) Integer least squares with quadratic equality constraints and its application to GNSS attitude determination systems. Int J Control Autom 7(4):566–576CrossRefGoogle Scholar
- Psiaki ML (2006) Batch algorithm for global-positioning-system attitude determination and integer ambiguity resolution. J Guid Control Dyn 29(5):1070–1079CrossRefGoogle Scholar
- Tegedor J, Øvstedal O (2014) Triple carrier precise point positioning (ppp) using gps l5. Surv Rev 46(337):288–297CrossRefGoogle Scholar
- Teunissen P (2006) The LAMBDA method for the GNSS compass. Artif Satell 41(3):89–103CrossRefGoogle Scholar
- Teunissen P (2007) A general multivariate formulation of the multi-antenna GNSS attitude determination problem. Artif Satell 42(2):97–111CrossRefGoogle Scholar
- Teunissen PJ (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82CrossRefGoogle Scholar
- Teunissen PJ (2010) Integer least-squares theory for the GNSS compass. J Geod 84(7):433–447CrossRefGoogle Scholar
- Teunissen PJ, Giorgi G, Buist PJ (2011) Testing of a new single-frequency GNSS carrier phase attitude determination method: land, ship and aircraft experiments. GPS Solut 15(1):15–28CrossRefGoogle Scholar
- Teunissen PJG (1989) Estimation in nonlinear models, II. Hotine-Marussi symposium on mathematical geodesy, Pisa, Italy, June 5–8Google Scholar
- Teunissen PJG (1997) A canonical theory for short GPS baselines. Part I: the baseline precision. J Geod 71(6):320–336CrossRefGoogle Scholar
- Teunissen PJG (1998) Success probability of integer gps ambiguity rounding and bootstrapping. J Geod 72(10):606–612CrossRefGoogle Scholar
- Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593CrossRefGoogle Scholar
- Teunissen PJG (2012) The affine constrained GNSS attitude model and its multivariate integer least-squares solution. J Geod 86(7):547–563CrossRefGoogle Scholar
- Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geod 82(2):65–82CrossRefGoogle Scholar
- Thoelert S, Montenbruck O, Meurer M (2014) IRNSS-1A: signal and clock characterization of the Indian regional navigation system. GPS Solut 18(1):147–152CrossRefGoogle Scholar
- Wang B, Miao L, Wang S, Shen J (2009) A constrained LAMBDA method for GPS attitude determination. GPS Solut 13(2):97–107CrossRefGoogle Scholar
- Zaminpardaz S, Teunissen PJG, Nadarajah N (2016a) GLONASS CDMA L3 ambiguity resolution and positioning. GPS Solut. doi: 10.1007/s10291-016-0544-y
- Zaminpardaz S, Teunissen PJG, Nadarajah N (2016b) IRNSS stand-alone positioning: first results in Australia. J Spat Sci 61(1):5–27CrossRefGoogle Scholar