An Algorithm for Combined Code and Carrier Phase Based GPS Positioning

Chang, Xiao-Wen; Paige, Christopher C.

doi:10.1023/b:bitn.0000014566.23457.85

Cited by 9 publications

(8 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In each epoch, the iteration process stops when the difference between the position estimates at two consecutive iteration steps is less than 0.001 m. The tuning constant γ was set to be 1.5σ φ . For comparison, we also computed the LS estimates of the positions by a recursive LS method proposed in Chang and Paige (2003).…”

Section: Simulation Resultsmentioning

confidence: 99%

Huber’s M-estimation in relative GPS positioning: computational aspects

Chang

Guo

2005

J Geodesy

View full text Add to dashboard Cite

When GPS signal measurements have outliers, using least squares (LS) estimation is likely to give poor position estimates. One of the typical approaches to handling this problem is to use robust estimation techniques. We study the computational issues of Huber's M-estimation applied to relative GPS positioning. First for code-based relative positioning, we use simulation results to show that Newton's method usually converges faster than the iteratively reweighted least squares (IRLS) method, which is often used in geodesy for computing robust estimates of parameters. Then for code-and carrier-phase-based relative positioning, we present a recursive modified Newton method to compute Huber's M-estimates of the positions. The structures of the model are exploited to make the method efficient, and orthogonal transformations are used to ensure numerical reliability of the method. Economical use of computer memory is also taken into account in designing the method. Simulation results show that the method is effective.

show abstract

Section: Simulation Resultsmentioning

confidence: 99%

Huber’s M-estimation in relative GPS positioning: computational aspects

Chang

Guo

2005

J Geodesy

View full text Add to dashboard Cite

show abstract

“…see [28,29]. The geodetic least squares adjustment problem is to compute accurately the coordinates of points (or stations) on the surface of the Earth from a collection of measured distances and angles between these points.…”

Section: Adjustment Of Geodetic Networkmentioning

confidence: 99%

Orthogonal Factorization and Linear Least Squares Problems

Gallopoulos

Philippe

Sameh

2015

Parallelism in Matrix Computations

View full text Add to dashboard Cite

Orthogonal factorization (or QR factorization) of a dense matrix is an essential tool in several matrix computations. In this chapter we consider algorithms for QR as well as its application to the solution of linear least squares problems. The QR factorization is also a major step in some methods for computing eigenvalues; cf. Chap. 8. Algorithms for both the QR factorization and the solution of linear least squares problems are major components in data analysis and areas such as computational statistics, data mining and machine learning; cf. [1][2][3].

show abstract

“…The reader is referred to various published literature for detailed information on other geodetic techniques, e.g. GNSS 4 , VLBI 5 , DORIS [6][7][8] and LLR 9 .…”

Section: Introductionmentioning

confidence: 99%

Satellite laser ranging measurements in South Africa: Contributions to earth system sciences

Botai¹,

Combrinck²,

Botai³

2015

S. Afr. J. Sci.

View full text Add to dashboard Cite

This contribution reassesses progress in the development of satellite laser ranging (SLR) technology and its scientific and societal applications in South Africa. We first highlight the current global SLR tracking stations within the framework of the International Laser Ranging Service (ILRS) and the artificial satellites currently being tracked by these stations. In particular, the present work focuses on analysing SLR measurements at Hartebeesthoek Radio Astronomy Observatory (HartRAO), South Africa, based on the MOBLAS-6 SLR configuration. Generally, there is a weak geometry of ILRS stations in the southern hemisphere and the SLR tracking station at HartRAO is the only active ILRS station operating on the African continent. The SLR-derived products – such as station positions and velocities, satellite orbits, components of earth’s gravity field and their temporal variations, earth orientation parameters – are collected, merged, achieved and distributed by the ILRS under the Crustal Dynamic Data Information System. These products are used in various research fields such as detection and monitoring of tectonic plate motion, crustal deformation, earth rotation, polar motion, and the establishment and monitoring of International Terrestrial Reference Frames, as well as modelling of the spatio-temporal variations of the earth’s gravity field. The MOBLAS-6 tracking station is collocated with other geodetic techniques such as very long baseline interferometry and Global Navigation Satellite Systems, thus making this observatory a fiducial geodetic location. Some applications of the SLR data products are described within the context of earth system science.

show abstract

An Algorithm for Combined Code and Carrier Phase Based GPS Positioning

Cited by 9 publications

References 10 publications

Huber’s M-estimation in relative GPS positioning: computational aspects

Huber’s M-estimation in relative GPS positioning: computational aspects

Orthogonal Factorization and Linear Least Squares Problems

Satellite laser ranging measurements in South Africa: Contributions to earth system sciences

Contact Info

Product

Resources

About