The paper “ Approach to GPS and Wavelet Decomposition” is a worthy version of the research paper on engineering and construction. High precision GPS positioning is vulnerable to multipath disturbance as it is one of the major sources of error impacting GPS positioning. The multipath disturbance is mainly dependent on the receiver’ s surroundings since satellite signals can arrive at the receiver via multiple paths, due to reflections from nearby objects such as trees, buildings, vehicles, etc. Multipath effects can be maintained by selecting alternative sites that limit multipath reflectors or by using optimization methods such as choke-ring antennas to mitigate the reflected signal.
Realistically it is difficult to eliminate all multipath effects from GPS observations. This is because multipath tends to exhibit similar patterns due to the identical geometrical locations between GPS satellites and the receiver-reflectors. This recurrence can then be useful for authenticating the existence of multipath through observations analysis made at a static receiver on different days. In this study, the authors apply a wavelet disintegration technique to extort multipath from GPS analysis. The extracted multipath is then applied directly to the GPS observations to correct for the multipath effects.
The results show that the proposed method can be used to considerably alleviate the multipath effects of a permanent GPS station. IntroductionGPS carrier-phase observations are widely used for all high precision static and kinematic positioning applications. The least-squares estimation method is usually employed for the processing of such GPS observations. The least-squares method is based on the formulation of a mathematical model consisting of the functional model and the stochastic model. If the function model is adequate, the residuals obtained from the least-squares solution should be randomly distributed.
However, the GPS observations are infected by several types of biases such as the orbital bias, the atmospheric biases, multipath disturbance, and receiver noise. A double-differencing technique is commonly used for constructing the functional model as it can eliminate or reduce many of the troublesome GPS biases(i. e. The atmospheric biases, the receiver and satellite clock biases and the orbital bias). A proportion of un-modeled biases still remain in the GPS observations, even after such data differencing. Multipath is a major residual error source in the double-differenced GPS observables, and it can have a significant impact on the positioning results. By minimizing the magnitude of multipath disturbance of the GPS observations, an accurate positioning from the GPS is obtained.
Recently, Fu, W.X. et al (1997) & Collin, F et al (1995) proposed innovative wavelet-based techniques that have been introduced in the field of GPS data processing. These methods have addressed some potential applications such as signal de-noising, outlier detection, bias separation and data compression. Ogaja, C et al (2001) & Satirapod, C (2001) proposed a new technique using wavelet decomposition for extracting or modeling multipath from GPS carrier-phase observations.
The technique is first applied in order to decompose GPS double-differenced residuals into low-frequency bias and high- frequency noise terms. The extracted bias component is then applied directly to the GPS observations to correct for the trend introduced by this error component. The remaining terms, largely characterized by the GPS range observations and high- frequency measurement noise, are expected to give the best linear unbiased solutions from a least-squares process.
Agnew, D.C. & Larson, K.M., 2007. Finding the repeat times of the GPS constellation. GPS Solutions. Springer
Collin, F. & Warnant, R., 1995. Applications of the wavelet transform for GPS cycle slip correction and comparison with Kalman filter. Manuscript a Geodaetica, page 161-172.
Dickson, B., 2005. The design and implementation of a GPS receiver channel. Open systems media.
Eddine, D., Mohamed, D., & Abddelmalik, T., 2012.Wavelet de-noising technique applied to the PLL of a GPS receiver embedded in an observation satellite. (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 3, No.2, 2012. Available online at,
Fu, W.X., & Rizos, C., 1997. The applications of wavelets to GPS signal processing. 10th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Kansas City, Missouri, and page 1385-1388.
Ogawa, C., Rizos, C., Wang, J. & Brownjohn, J., 2001. Towards the implementation of on-line structural monitoring using RTK-GPS and analysis of results using the wavelet transform. 10th FIGInt. Symp. on Deformation Observations, Orange, California, page 284-293.
Satirapod, C., Ogawa, C., Wang, J. & Rizos, C., 2001. An approach to GPS analysis incorporating wavelet decomposition. Artificial Satellites, page27-35.
Russell, R. M. & Hasik J. M., 2002. The precision Resolution: GPS and the Future of Aerial Warfare. Naval Institute Press.
Satirapod, C., Khoonphool, R. & Rizos, C., 2003. Multipath Mitigation of Permanent GPS Stations Using Wavelets. Available online at,