Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Geomathematics: Its Role, Its Aim, and Its Potential Kapitel lesen Erstes Kapitel lesen

2010 | OriginalPaper | Buchkapitel

37. Mixed Integer Estimation and Validation for Next Generation GNSS

verfasst von : Peter J.G. Teunissen

Erschienen in: Handbook of Geomathematics

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The coming decade will bring a proliferation of Global Navigation Satellite Systems (GNSS) that are likely to revolutionize society in the same way as the mobile phone has done. The promise of a broader multi-frequency, multi-signal GNSS “system of systems” has the potential of enabling a much wider range of demanding applications compared to the current GPS-only situation. In order to achieve the highest accuracies one must exploit the unique properties of the received carrier signals. These properties include the multi-satellite system tracking, the mm-level measurement precision, the frequency diversity, and the integer ambiguities of the carrier phases. Successful exploitation of these properties results in an accuracy improvement of the estimated GNSS parameters of two orders of magnitude. The theory that underpins this ultraprecise GNSS parameter estimation and validation is the theory of integer inference. This theory is the topic of the present chapter.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Geodetic Deformation Analysis with Respect to an Extended UncertaintyBudget
Nächstes Kapitel Mixed Integer Linear Models
Literatur
Baarda W (1968) A testing procedure for use in geodetic networks. In: Publications in geodesy, 2(5). Netherlands Geodetic Commission, Delft
Betti B, Crespi M, Sanso F (1993) A geometric illustration of ambiguity resolution in GPS theory and a Bayesian approach. Manuscr Geod 18:317–330
Boon F, Ambrosius B (1997) Results of real-time applications of the LAMBDA method in GPS based aircraft landings. In: Proceedings of the KIS97, Banff, Canada, pp 339–345
Buist PJ, Teunissen PJG, Giorgi G, Verhagen S (2008) Instantaneous multi-baseline ambiguity resolution with constraints. In: Proceedings of the international symposium on GPS/GNSS, Tokyo, Japan, pp 862–871
Chang XW, Yang X, Zhou T (2005) MLAMBDA: a modified LAMBDA method for integer least-squares estimation. J Geod 79:552–565MATHCrossRef
Cox DB, Brading JDW (1999) Integration of LAMBDA ambiguity resolution with Kalman filter for relative navigation of spacecraft. In: Proceedings of the ION NTM 99, San Diego, pp 739–745
Dai L, Ling KV, Nagarajan N (2004) Real-time attitude determination for microsatellite by LAMBDA method combined with Kalman filtering. In: Proceedings of the AIAA-ICSS 2004, Montercy, vol 3118, pp 1–8
de Jonge PJ (1998) A processing strategy for the application of the GPS in networks. In: Publications on geodesy, vol 46. Netherlands Geodetic Commission, Delft
de Jonge PJ, Tiberius CCJM (1996a) The LAMBDA method for integer ambiguity estimation: implementation aspects. In: LGR-Series No. 12. Publications of the Delft Computing Centre, Delft
de Jonge PJ, Tiberius CCJM (1996b) Integer estimation with the LAMBDA method. In: Beutler G et al (eds) Proceedings of the IAG symposium, vol 115, GPS trends in terrestrial, airborne and spaceborne applications, Boulder. Springer, Berlin pp 280–284
de Jonge PJ, Tiberius CCJM, Teunissen PJG (1996) Computational aspects of the LAMBDA method for GPS ambiguity resolution. In: Proceedings of the ION GPS-96, Kansas City, pp 935–944
Eissfeller B, Tiberius CCJM, Pany T, Biberger R, Schueler T, Heinrichs G (2002) Instantaneous ambiguity resolution for GPS/Galileo RTK positioning. J Gyros Navigat 38(3):71–91
Farell JA, Barth M (1999) The global positioning system and inertial navigation. McGraw-Hill, New York
Giorgi G, Teunissen PJG, Buist P (2008) A search and shrink approach for the constrained LAMBDA method: experimental results. In: Proceedings of the international GPS/GNSS symposium, Tokyo, Japan, pp 797–806
Grafarend EW (1976) Geodetic applications of stochastic processes. Phys Earth Planet Interiors 12:151–179CrossRef
Grafarend EW (2000) Mixed integer-real valued adjustment problems: GPS initial cycle ambiguity resolution by means of the LLL algorithm. GPS Solut 4(2):31–44CrossRef
Gundlich B, Koch KR (2002) Confidence regions for GPS baselines by Bayesian statistics. J Geod 76:55–62MATHCrossRef
Gundlich B, Teunissen PJG (2004) Multiple models: fixed, switching and interacting. In: Sanso F (ed) Proceedings of the 5th Hotine-Marussi symposium. IAG symposia series, vol 127. Springer, Berlin, pp 129–136
Hobiger T, Sekido M, Koyama Y, Kondo T (2009) Integer phase ambiguity estimation in next generation very long baseline interferometry. Adv Space Res 43(1):187–192CrossRef
Hofmann-Wellenhof B, Lichtenegger H, Wasle E (2008) GNSS global navigation systems; GPS, GLONASS, Galileo and More. Springer, Wien
Ji S, Chen W, Zhao C, Ding X, Chen Y (2007) Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods. GPS Solut 11(4):259–268CrossRef
Kampes BM, Hanssen RF (2004) Ambiguity resolution for permanent scatterer interferometry. IEEE Trans Geosci Remote Sens 42(11):2446–2453CrossRef
Koch KR (1999) Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, BerlinMATH
Leick A (2004) GPS satellite surveying, 3rd edn. Wiley, New York
Liu LT, Hsu HT, Zhu YZ, Ou JK (1999) A new approach to GPS ambiguity decorrelation. J Geod 73:478–490MATHCrossRef
Misra P, Enge P (2006) Global positioning system: signals, measurements, and performance, 2nd edn. Ganga-Jamuna, Lincoln
Moenikes R, Wendel J, Trommer GF (2005) A modified LAMBDA method for ambiguity resolution in the presence of position domain constraints. In: Proceedings of the ION GNSS 2005, Long Beach, pp 81–87
Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. Publications on geodesy, vol 52. Netherlands Geodetic Commission, Delft
Park C, Teunissen PJG (2003) A new carrier phase ambiguity estimation for GNSS attitude determination systems. In: Proceedings of the international GPS/GNSS symposium, Tokyo, Japan, pp 1–8
Parkinson B, Spilker JJ (1996) GPS: theory and applications, vols 1 and 2. AIAA, Washington, DC
Robert CP, Casella G (1999) Monte Carlo statistical methods. Springer Texts in Statistics. Springer, New YorkMATH
Strang G, Borre K (1997) Linear algebra, geodesy, and GPS. Wellesley-Cambridge, WellesleyMATH
Svendsen JGG (2006) Some properties of decorrelation techniques in the ambiguity space. GPS Solut 10:40–44CrossRef
Teunissen PJG (1993) Least-squares estimation of the integer GPS ambiguities. In: Invited Lecture, Section IV theory and methodology, IAG general meeting, Beijing, China, August 1993. Also in: LGR Series, No. 6. Delft Geodetic Computing Centre, Delft
Teunissen PJG (1995a) The invertible GPS ambiguity transformations. Manus Geod 20:489–497
Teunissen PJG (1995b) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70:65–82CrossRef
Teunissen PJG (1998) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geod 72:606–612MATHCrossRef
Teunissen PJG (1999a) The probability distribution of the GPS baseline for a class of integer ambiguity estimators. J Geod 70:65–82CrossRef
Teunissen PJG (1999b) An optimality property of the integer least-squares estimator. J Geod 73: 587–593MATHCrossRef
Teunissen PJG (2000) ADOP based upper bounds for the bootstrapped and the least-squares ambiguity success-rates. Artifi Satel 35(4):171–179
Teunissen PJG (2002) The parameter distributions of the integer GPS model. J Geod 76:41–48MATHCrossRef
Teunissen PJG (2003a) Integer aperture GNSS ambiguity resolution. Artif Satel 38(3):79–88
Teunissen PJG (2003b) Theory of integer equivariant estimation with applications to GNSS. J Geod 77:402–410MATHCrossRef
Teunissen PJG (2005) GNSS ambiguity resolution with optimally controlled failure-rate. Artif Satel 40(4):219–227
Teunissen PJG (2006) Testing theory: an introduction, 2nd edn. VSSD, Delft
Teunissen PJG (2007a) Influence of ambiguity precision on the success rate of GNSS ambiguity bootstrapping. J Geod 81:351–358MATHCrossRef
Teunissen PJG (2007b) Least-squares prediction in linear models with integer unknowns. J Geod 81:565–579MATHCrossRef
Teunissen PJG, Kleusberg A (1998) GPS for geodesy, 2nd enlarged edn. Springer, Berlin
Teunissen PJG, Verhagen S (2008) GNSS carrier phase ambiguity resolution: challenges and open problems. In: IAG symposia series, vol 133. Springer, Berlin, pp 785–792
Teunissen PJG, Verhagen S (2009) The GNSS ambiguity ratio-test revisited: a better way of using it. Surv Rev 41:138–151CrossRef
Teunissen PJG, de Jonge PJ, Tiberius CCJM (1997) The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation time spans. J Geod 71:589–602MATHCrossRef
Thomsen H (2000) Evaluation of upper and lower bounds on the sucess probability. In: Proceedings of the ION GPS 2000, Salt Lake City, pp 183–188
Tiberius CCJM, de Jonge PJ (1995) Fast positioning using the LAMBDA method. In: Proceedings of the DSNS-95, Bergen, Norway, paper 30, 8 p
Tsai YF, Juang JC (2007) Ambiguity resolution validation based on LAMBDA and eigendecomposition. In: Proceedings of the 63rd AM-ION GPS, Portland, pp 299–304
Verhagen S (2003) On the approximation of the integer least-squares success-rate: which lower or upper bound to use? J Global Position Syst 2(2):117–124CrossRef
Verhagen S (2005a) The GNSS integer ambiguities: estimation and validation. In: Publications on geodesy, vol 58. Netherlands Geodetic Commission, Delft
Verhagen S (2005b) On the reliability of integer ambiguity resolution. Navigation 52(2):99–110
Verhagen S, Teunissen PJG (2004) PDF evaluation of the ambiguity residuals. In: Sanso F (ed) Proceedings of the 5th Hotine-Marussi symposium. IAG symposia series, vol 127. Springer, Berlin, pp 120–129
Verhagen S, Teunissen PJG (2005) Performance comparison of the BIE estimator with the float and fixed GNSS ambiguity estimator. In: Sanso F (ed) IAG symposia series, vol 128. Springer, Berlin, pp 428–433
Verhagen S, Teunissen PJG (2006) New global navigation satellite system ambiguity resolution method compared to existing approaches. J Guid Control Dynam 29(4):981–991CrossRef
Wu SC, Bar-Sever YE (2006) Real-time sub-cm differential orbit determination of two low-earth orbiters with GPS bias-fixing. In: Proceedings of the ION GNSS 2006, Fort Worth, pp 2515–2522
Wu F, Kubo N, Yasuda A (2004) Performance evaluation of GPS augmentation using quasi zenith satellite system. IEEE Trans Aerosp Electron Syst 40(4):1249–1260CrossRef
Xu P (2006) Voronoi cells, probabilistic bounds and hypothesis testing in mixed integer linear models. IEEE Trans Inform Theory 51(7):3122–3138
Metadaten
Titel
Mixed Integer Estimation and Validation for Next Generation GNSS
verfasst von
Peter J.G. Teunissen
Copyright-Jahr
2010
Verlag
Springer Berlin Heidelberg
Buch
Handbook of Geomathematics

Print ISBN: 978-3-642-01545-8

Electronic ISBN: 978-3-642-01546-5

Copyright-Jahr: 2010

DOI
https://doi.org/10.1007/978-3-642-01546-5_37