Robust Double-k-Type Ridge Estimation and Its Applications in GPS Rapid Positioning

It is well-known that there are both multicollinearities and outliers in DD (Double Difference) model which is commonly employed in GPS rapid positioning. For the complicated complexion, we present the robust double-k-type ridge estimator (RDKRE) by combining the double-k-type ridge estimator (DKRE) and correlative equivalent weight, and we improve the LAMBDA method through replacing the cofactor matrix computed by the LSE with the cofactor matrix computed by the RDKRE. A new algorithm of GPS rapid positioning based on the RDKRE is proposed. It is concluded after investigations that the RDKRE is highly efficient and reliable to GPS rapid positioning even when both ill-conditioning and outliers exist.

[1]  Tim Springer,et al.  New IGS Station and Satellite Clock Combination , 2001, GPS Solutions.

[2]  L. Sjöberg,et al.  Rapid GPS ambiguity resolution for short and long baselines , 2002 .

[3]  P. Teunissen.  The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation , 1995 .

[4]  Peter Teunissen,et al.  GPS for geodesy , 1996 .

[5]  P. Teunissen.  Least-squares estimation of the integer GPS ambiguities , 1993 .

[6]  J. Zhang,et al.  Robust biased estimation and its applications in geodetic adjustments , 1998 .

[7]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[8]  Jikun Ou,et al.  An improved regularization method to resolve integer ambiguity in rapid positioning using single frequency GPS receivers , 2004 .

[9]  D. J. Allerton,et al.  Book Review: GPS theory and practice. Second Edition, HOFFMANNWELLENHOFF B., LICHTENEGGER H. and COLLINS J., 1993, 326 pp., Springer, £31.00 pb, ISBN 3-211-82477-4 , 1995 .

[10]  E. Grafarend.  Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm , 2000, GPS Solutions.

[11]  Peter Teunissen,et al.  The invertible GPS ambiguity transformations , 1995 .

[12]  Gerhard Beutler,et al.  Rapid static positioning based on the fast ambiguity resolution approach , 1990 .

[13]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[14]  Stephen P. Boyd,et al.  Integer parameter estimation in linear models with applications to GPS , 1998, IEEE Trans. Signal Process..

[15]  Peiliang Xu.  Random simulation and GPS decorrelation , 2001 .

[16]  P. Teunissen.  An optimality property of the integer least-squares estimator , 1999 .

[17]  A. E. Hoerl,et al.  Ridge Regression: Applications to Nonorthogonal Problems , 1970 .

[18]  Richard B. Langley,et al.  An Optimized Least-Squares Technique for Improving Ambiguity Resolution and Computational Efficiency , 1999 .

[19]  Guo Jian-feng.  A New Ambiguity Resolution Based on Partial Ridge Estimator , 2004 .