Integer parameter estimation in linear models with applications to gps

IEEE Transactions on Signal Processing

Volumn 46, Issue 11, 1998, Pages 2918-2925

  Hassibi, Arash ^a   Boyd, Stephen ^a  

^a Stanford University   (United States)

Author keywords

GPS; Integer least squares; Integer parameter estimation; Linear model

Indexed keywords

EID: 33747647957     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.726806     Document Type: Article

References (32)

1. B. D. O. Andersen and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
2. L. Babai, "On Lovâsz' lattice reduction and the nearest lattice point problem," Combinatorica, vol. 6, pp. 1-13, 1986.
3. P. van Emde Boas, "Another NP-complete partition and the complexity of computing short vectors in a lattice," Tech. Rep. 81-04, Math. Inst., Univ. Amsterdam, Amsterdam, The Netherlands, 1981.
4. C. D. Burnside, Electromagnetic Distance Measurement. London, U.K.: Crosby Lockwood Staples, 1974.
5. T. Corazzini, A. Robertson, J. C. Adams, A. Hassibi, and J. P. How, "GPS sensing for spacecraft formation flying," in Proc. Inst. Navigation GPS-97 Conf.. Kansas City, MO, Sept. 1997.
6. M. Grötschel, L. Lovâsz, and A. Schrijver, Beometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics. New York: Springer-Verlag, 1988.
7. A. Hassibi and S. Boyd, "Interger parameter estimation in linear models with GPS applications," Tech. Rep., Inform. Syst. Lab., Stanford Univ., Stanford, CA, Feb. 1995.
8. "Integer parameter estimation in linear models with GPS applications," in Proc. IEEE Conf. Decision Contr., Kobe, Japan, 1996.
9. J. Hum, GPS: A Guide to the Next Utility. London, U.K.: Trimble Navigation, 1989.
10. Differential GPS Explained. London, U.K.: Trimble Navigation, 1993.
11. B. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, Global Positioning System, Theory and Practice, 4th ed. New York: SpringerVerlag, 1997.
12. P. J. de Jonge and C. C. J. M. Tiberius, The LAMBDA Method for Integer Ambiguity Estimation: Implementation Aspects, vol. 12 of LGR-Series, Delft Geodetic Computing Centre, 1996.
13. R. Kannan, "Improved algorithms for integer programming and related problems," in Proc. 23rd IEEE Symp. Foundations Comput. Sei., 1983.
14. K. R. Koch, Parameter Estimation and Hypothesis Testing in Linear Models. New York: Springer-Verlag, 1988.
15. A. Kleusberg and P. J. G. Teunissen, GPS for Geodesy, Lecture Notes in Earth Sciences. New York: Springer-Verlag, 1996.
16. A. Leik, GPS Satellite Surveying. New York: Wiley, 1995.
17. H. W. Lenstra, Jr., "Integer programming with a fixed number of variables," Tech. Rep. 81-03, Dept. Math., Univ. Amsterdam, Amsterdam, The Netherlands, 1981.
18. "Integer programming with a fixed number of variables," Math. Oper. Res., vol. 8, pp. 538-548, 1983.
19. A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovâsz, "Factoring polynomials with rational coefficients," Math. Ann., vol. 261, pp. 515-534, 1982.
20. A. Maleki-Tehrani, A. Hassibi, S. Boyd, and J. Cioffi, "An implementation of discrete multi-tone over slowly time-varying multipleinput/output channels," submitted for publication.
21. A. M. Odlyzko and H. te Riele, "Disproof of the Mertens conjecture," J. Reine Angew. Math., vol. 357, pp. 138-160, 1985.
22. B. W. Parkinson and J. J. Spilker, Jr., Global Positioning System: Theory and Applications, Amer. Inst. Aeronautics Astronautics, Washingon, DC, 1996.
23. G. Strang and K. Borre, Linear Algebra, Geodesy, andGPS. Wellesley, MA: Wellesley-Cambridge, Oct. 1997.
24. C. P. Schnorr, "A hierarchy of polynomial time basis reduction algorithms," in L. Lovâsz and E. Szemer, Eds., Theory of Algorithms. Amsterdam, The Netherlands: North-Holland, 1985, pp. 375-386.
25. P. J. G. Teunissen, Least-Squares Estimation of the Ineger GPS Ambiguities, LGR-Series, Delft Geodetic Computer Centre, 1993.
26. "A new method for fast carrier phase ambiguity estimation," in Proc. IEEE Position, Location and Navigation Symp., Las Vegas, NV, 1994.
27. "The invertible GPS ambiguity transformations," Manu. Geodaetica, vol. 20, no. 6, pp. 48997, Sept. 1995.
28. "The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation," J. Geodesy, vol. 70, nos. 1-2, pp. 65-82, Nov. 1995.
29. "A canonical theory for short GPS baselines, Part IV: Precision versus reliability," J. Geodesy, vol. 71, pp. 513-525, 1997.
30. "Closed form expressions for the volume of the GPS ambiguity search spaces," Artif. Satellites, vol. 32, no. 1, pp. 5-20, 1997.
31. P. J. G. Teunissen and P. J. de Jonge, "The volume of the GPS ambiguity search space and its relevance for integer ambiguity resolution," in Proc. Inst. Navigation GPS-97 Conf., 1996, pp. 889-898.
32. C. C. J. M. Tiberius and P. J. G. Teunissen, "Kinematic GPS: Performance and quality control," in Proc. KIS97, 1997.