Skip to content
Open Access Published by De Gruyter Open Access October 15, 2013

Medium to high-frequency static DGPS error reduction using multi-resolution de-noising vs. de-trending procedures

  • A. A. El-Ghazouly EMAIL logo , M. M. Elhabiby and N. M. El-Sheimy


Global positioning systems is known to create bias effects such as multipath, ionospheric and tropospheric delays that behave like lowfrequency noise. Random measurement errors can also occur and these are typically characterized as high-frequency noise. The lowfrequency nature of a multipath is what causes the largest error, which in carrier phase measurements can reach up to 5 cm. For a static base station it is required that both error components (low and high-frequency) are removed and not included in the static baseline processing. This paper will introduce two different multi-resolution techniques that can be used separately or combined to remove the low to highfrequency GPS errors. The first technique is applied using the wavelets as a de-noising tool to tackle the high-frequency errors in the double difference domain. A detailed analysis is also made to choose the best wavelet base function and threshold technique estimator by comparing different wavelet parameters along with different thresholding techniques. The second technique discussed in this paper uses the wavelets technique as a de-trending tool to tackle the low-frequency portion of the double differenced measurements. The results of this research paper indicate that the de-trending technique can reduce the double difference errors dramatically for short baselines when compared to the de-noising technique. Conversely, the de-trending technique can cause a biased solution for long baselines, as it will enhance the RMS value and indicate good statistics for the solution. However, the will be shifted from it depending on the low frequency part of the error (ionosphere, low multipath). Therefore, it is important to isolate ionospheric error by modeling (and not spectrum filtering) before dealing with multipath, as it is hard to separate between both errors in the spectral domain.


Dammalage T. L., Satirapod C., Kibe S. and Ogaja C., 2010, Wavelet transform application to C/A code multipath mitigation at GPS reference stations for improved differential GPS corrections, J. Sur. Rev., 42, 317, 240-255(16).10.1179/003962610X12572516251925Search in Google Scholar

Donoho D. L. and Johnstone I. M., 1994, Ideal spatial adaptation by wavelet shrinkage, Biom., 81 425-55.10.1093/biomet/81.3.425Search in Google Scholar

El-Ghazouly A., Elhabiby M. and El-Sheimy N., 2008, Wavelet Based Carrier Phase Multipath Reduction, the United States and Trade Mark Office(Submitted,September 28th,2008.12 pages).Search in Google Scholar

El-Ghazouly A., Elhabiby M. and El-Sheimy N., 2009, The use of Wavelets in GPS Error Analysis with Emphasis to Singularity Detection and Multipath Removal, Amer. Geoph. Union Joint Ass.Search in Google Scholar

Elhabiby, M., 2007, Wavelet Representation of Geodetic Operators, Ph.D. Uni. of Calgary.Search in Google Scholar

Han S. and Rizos C., 1997, Multipath effects on GPS in mine environments, 10th Int. Cong. of the Int. Soci. for Mine Sur., Fremantle, Australia, 447-457.Search in Google Scholar

Hofmann-Wellenhof B., Lichtenegger H. and Collins J., 2007, Global Positioning System theory and practice. Springer Wien New York.Search in Google Scholar

Hubbard B. B., 1998, The world according to wavelets: the story of a mathematical technique in the making. Wellesley, Mass.10.1201/9781439864555Search in Google Scholar

Hugentobler U., Schaer S., Fridez P., Beutler G., Bock H., Brockmann E., Dach R., Gurtner W., Ineichen D., Johnson J., Meindl M., Mervart L., Springer T. and R. Weber (2001), Bernese GPS Software, Version 4.2, University of Bern, 2001.Search in Google Scholar

Lee Y. W., Suh Y. C. and Shibasaki R., 2008, A simulation system for GNSS multipath mitigation using spatial statistical methods, Comp. & Geos., 34(11), 1597-609.10.1016/j.cageo.2008.01.004Search in Google Scholar

Linlin Ge., Han S. and Rizos C., 2000, Multipath mitigation of continuous GPS measurements using an adaptive filter, GPS Sol., 4(2), 19-30.10.1007/PL00012838Search in Google Scholar

Ogaja C. and Satirapod C., 2007, Analysis of high-frequency multipath in 1-Hz GPS kinematic solutions, GPS Sol., 11(4), 269-80.10.1007/s10291-007-0058-8Search in Google Scholar

Ogden R. T., 1997, Essential wavelets for statistical applications and data analysis, Birkhäuser.10.1007/978-1-4612-0709-2Search in Google Scholar

Raquet J. and Lachapelle G., 1996, Determination and reduction of GPS reference station multipath using multiple receivers, 9th Int. Tech. Meeting of the Sat. Div. of the Inst. of Nav., ION GPS-96. Part 1 (of 2), Kansas City, MO, USA, 673-81.Search in Google Scholar

Ray J. K., 2000, Mitigation of GPS Code and Carrier Phase Multipath Effects using a Multi-Antenna System, Ph.D. thesis Univ. of Calgary.Search in Google Scholar

Satirapod C. and Rizos C., 2005, Multipath mitigation by wavelet analysis for GPS base station applications, Sur. Rev., 38(295), 2-10.10.1179/sre.2005.38.295.2Search in Google Scholar

Souza E. M. and Monico J. F. G., 2004, Wavelet shrinkage: High-frequency multipath reduction from GPS relative positioning, GPS Sol., 8(3), 152-9.10.1007/s10291-004-0100-zSearch in Google Scholar

Tait M., Sheng L. and Cannon M. E., 2006, The Feasibility of Replacing Precise Levelling with GPS for Permafrost Deformation Monitoring, INGEO 2004 and FIG Reg. Cen. and Eastern Eur. Conf. on Eng. Surveying.Search in Google Scholar

Teunissen P. J. G., 1993, Least squares estimation of the integer GPS ambiguities, General Meeting of the IAG.Search in Google Scholar

Zhang Y. and Bartone C., 2004, Multipath mitigation in the frequency domain, PLANS, Piscataway, NJ, USA: IEEE, 486-95. Search in Google Scholar

Published Online: 2013-10-15
Published in Print: 2013-09-1

This content is open access.

Downloaded on 30.11.2023 from
Scroll to top button