50
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Real‐time failure detection in the carrier phase measurements of GPS by robust and conventional kalman state estimates

&
Pages 41-65 | Received 28 Aug 1996, Accepted 02 Sep 1997, Published online: 10 Jan 2009

References

  • Anderson , T. W. 1984 . An introduction to multivariate statistical analysis , 2d ed. , New York : John Wiley .
  • Barnett , V. and Lewis , T. 1994 . Outliers in statistical data , 3d ed. , New York : John Wiley .
  • Brown , R. G. and Hwang , P. Y. C. 1992 . Introduction to random signals and applied Kalman filtering , 2d ed. , New York : John Wiley .
  • Chan , T. F. , Goloub , G. H. and Le Veque , R. J. 1983 . Algorithms for computing the sample variance: Analysis and recommendations . Amer. Statistician , 37 : 242 – 247 .
  • Chu , K. A. C. 1973 . Estimation and detection for linear systems with elliptical random processes . IEEE Trans. Automatic Control. Short Papers , October : 499 – 505 .
  • Fitzgerald , R. J. 1971 . Divergence of the Kalman filter . IEEE Trans. Automatic Control , AC‐16 : 736
  • Gelb , A. , ed. 1974 . Applied optimal estimation , Cambridge, MA : M.I.T. Press .
  • Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. A. 1986 . Robust statistics: The approach based on influence functions , New York : John Wiley .
  • Huber , P. J. 1981 . Robust statistics , New York : John Wiley .
  • Isermann , R. 1984 . Process fault detection based on modelling and estimation methods—A survey . Automatica. , 20 : 387 – 404 .
  • Johnson , R. A. and Wichern , D. W. 1988 . Applied multivariate statistical analysis , 2d ed. , Englewood Cliffs, NJ : Prentice‐Hall .
  • Kerr , T. H. 1977 . Real‐time failure detection: A nonlinear optimization problem that yields a two‐ellipsoid overlap test . J. Optimization Theory Appl. , 22 : 509 – 536 .
  • Masreliez , C. J. and Martin , R. D. 1977 . Robust Bayesian estimation for the linear model and robustifying the Kalman filter . IEEE Trans. Automatic Control , AC‐22 (3) : 361 – 371 .
  • Meinhold , R. J. and Singpurwalla , N. J. 1989 . Robustification of Kalman filter models . J. Amer. Statist. Assoc. , 84 (406) : 479 – 486 . Theory and Methods
  • Mertikas , S. P. 1994 . The description of accuracy using conventional and robust estimates of scale . Mar. Geod. , 17 : 251 – 269 .
  • Mertikas , S. P. and Rizos , C. 1997 . On‐line detection of abrupt changes in the carrier phase measurements of GPS . J. Geod. , 71 : 469 – 482 .
  • Minkler , G. and Minkler , J. 1993 . Theory and application of Kalman filtering , Palm Bay, FL : Magellan .
  • Stahel , W. and Weisberg , S. , eds. 1991 . Directions in robust statistics and diagnostics , New York : Springer‐Verlag .
  • Strang , G. 1980 . Linear algebra and its application , 2d ed. , New York : Academic Press .
  • Tanaka , M. and Katayama , T. 1987 . Robust Kalman filter for linear discrete time systems with Gaussian sum noises . Int. J. Systems Sci. , 18 (9) : 1721 – 1731 .
  • Tsai , C. and Kurz , L. 1983 . An adaptive robustizing approach to Kalman filtering . Automatica , 19 : 279 – 288 .
  • Tukey , J. W. 1960 . “ A survey of sampling from contaminated distributions ” . In Contributions to probability and statistics , Edited by: Olkin , I. Stanford, CA : Stanford University Press .
  • Wallace , D. L. 1959 . Bounds on normal approximations to Student's and the chi‐square distributions . Ann. Math. Statist. , 30 : 1121 – 1130 .
  • Wang , Y. J. and Kubik , K. K. 1993 . Robust Kalman filter and its geodetic applications . Manuscr. Geod. , 18 : 349 – 354 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.