Approach to GPS and Wavelet Decomposition - Research Paper Example

Approach to GPS and wavelet decomposition Name Lecturer Course Date Abstract 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 limits 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 shows that the proposed method can be used to considerably alleviate the multipath effects at a permanent GPS station. Introduction GPS 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 an innovative wavelet- based techniques which 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. This paper is organized as follows. An introduction to existing multipath mitigation techniques is present. The theory of wavelet decomposition and its application to GPS data processing is then described. A discussion of experimental results and analyses are presented in a subsequent section. Finally, some concluding remarks are made. Data acquisition Data acquisition involved collecting analog data from the site and this was done using photograph and mobile computing. The data was collected in static mode for two days at a rate of 20 seconds with the intention of investigating the noise characteristics for the receiver to collect from the street. There was a distance between points of data collection which was the baseline length is 12m. The 12m baseline length is the distance taken between the two receivers during the field study. This shows the exact position between the users of the electronic map. This will assist the users in recording the latitudes and longitude positions during the field study. Thereafter they will monitor their movements the and changes in signals by the GPS as well as the change in longitude and latitude. During the field study, the GPS receiver will be attached to less than three satellites for signal receiving. If there is a need to record longitude, altitude and latitude that is 3- D positions, four or more satellites are used to receive the signals. The data collected by these receivers are then sent to modern gadgets in the form of noise where errors are eliminated. The elimination of errors is to smoothen the information before processing. . Tropospheric, ionospheric errors and orbit biases were negligent leading to recording multipath and observation noise. The photograph below shows how data was collected from the site for two days Day one Photo 8 shows recording in latitudes and longitudes. It is to use latitudes and longitudes in obtaining 2-D objects and an addition of altitudes to latitudes and longitudes to obtain 3-D objects. It is also expected, apart from the determination of the position, to determine other parameters like bearings, destination distance, speed, sunrise, sunset, track and the distance of the trip among others (Agnew, & Larson, 2007). Day 2 When data was acquired through transducer and later it was digitized using mobile computing to form discrete data which was easier for the computer to process. The photographs were taken in day one and day two which were changed from analog to digital using the digital camera that was present. The procedure of data acquisition for the photograph was that the photograph was taken and changed to digital and was saved in memory card. This formed a method of data acquisition The use of GPS receivers in the current modern world has improved tremendously and made data acquisition easier because of hi- technology which assists in filtering signals and having a processing capacity which can be used to control the entry of signal that is allowing both low and high speed processing. However, in the modern technology the gadgets do not define the boundaries but the designers or users guess the boundaries for the signals. The guess about the boundaries can be justified if the results obtained are near expectation. However to avoid the problem of guessing, there is model based design which integrates information and its cost effective. It verifies designs, generates cords and portions the information. The capability to automatically generate codes is then finally used to implement, with no error, the model on the actual hardware. Data processing The aim was to collect data which was going to investigate the multipath effects on all GPS effects collecting data. After the data was collected, it was modified to suit our objective and the modification involved smoothing and noise elimination. The residual graph below shows multipath series on observations for the two days for data collection. This has been produced from excel spread sheet. The baseline data has been analyzed using Matlab and the residue graph shown below shows GPS observation noise overtime as collected. The wave length has been transformed by decomposing the residual. In order to necessary waves for de-noising multi-resolution analysis has been employed as a technique of data processing. This is because it helps studying of signals using after filtering using different frequencies them so that they have different features. This analysis is essential as it uses transformations of wavelets by filtering to either to produce low-frequency filters or what is called daughter wavelets. However this requires the matching of signal and wavelets that are wider so as they will act as the high pass filter. This leads to the decomposition of data in three levels that will lead to high frequency de-noising that has a similar trend. To begin with a low frequency noise was plotted as shown below; Day 1 Original data Residual Original data Residual in another form Choosing a filter which is Db3 Data analyzed on Wavelete1-D before de-noising The ability of Matlab to identify repetitive components in a given image is what makes it a favorable method for removing irregular noise from our data Data after de-noising Original data and de-noised data Corrected value + measured distance from each point where the GPS reading has been taken which is 12m Choosing the second filter to compare both which is Db8 Data after analyzed on Wavelete1-D before de-noising Data after de-noising Original data and de-noised data Corrected value + measured distance from each point where the GPS reading has been taken which is 12m Day 2 Original data Residual and in another form in the graph below Choosing the filter which is Db3 original data analyzed on Wavelete1-D analyzing Data after de-nosing Original data before de-noising and after Corrected value + measured distance from each point where the GPS reading has been taken which is 12m Choosing the second filter to compare both which is Db8 Original data analyzed on Wavelete1-D analyzing Data after de-nosing Original data before and after de-noising Corrected value + measured distance from each point where the GPS reading has been taken which is 12m If the de-noised signal frequency coincides with the center of one of the frequency bins, the correct peak level is displayed. If, however, the signal frequency is not at the center of a frequency bin, then a reduced level is displayed, causing an error which can be up to 8 dB. Part 2 Day 1 Data analyzed before de-noising Data analyzed after de-noising Data before and after de-noising Residual data and Gaussian histogram graphs Corrected value + measured distance from each point where the GPS reading has been taken which is 12m Part 2 Day 2 In order to reduce the noise level of the results before loop filtering, wavelet packet de-noising techniques is used. The wavelet packet de-noising plays an important role by reducing the noise in the bandwidth of the loop filter. It should be noted that a loop filter, filters out noise in not on only in the bandwidth but even beyond. When such noise passes through, it affects performance of the receiver. It should be noted that the wavelet packet de-noising technique can only reduce the noise level rather than eliminate the noise totally. Data analyzed before de-noising The waves below shows the analyzed data before wavelet packet de-noising was applied to to filter and de-noise. Data analyzed after de-noising This shows how the wavelets packet has been applied to de-noise the wavelets As it can be noted that de-noising reduces the Data before and after de-noising Residual data and Gaussian histogram graphs The wavelet packet de-noising technique may cut off some useful signals which are smaller than the threshold .This disadvantage will make the spend more time to lock due to the loss of some control signals and output from distorted. However the decrease of the noise will produce smaller phase error that will help to maintain locked and smooth the output Corrected value + measured distance from each point where the GPS reading has been taken which is 12m If the de-noised signal frequency coincides with the center of one of the frequency bins, the correct peak level is displayed. If, however, the signal frequency is not at the center of a frequency bin, then a reduced level is displayed, causing an error which can be up to 8 dB. Conclusion When using wavelet denouncing technique, the researcher intends to use noise from the data collected. The reduction of noise within a bandwidth ensures there fewer errors in the processing of data. Multipath mitigation techniques and wavelet transform have been briefly reviewed, and a new multipath mitigation technique based on the use of wavelet decomposition has been proposed. The optimal level for wavelet decomposition of multipath disturbance has been identified. The results from the proposed method indicate that carrier-phase multipath can be removed, leaving only the GPS observation noise. The proposed method can therefore be used to correct for multipath at permanent GPS stations which support many differential positioning applications. References 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, [ Accessed 22 April 2013]. 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. Ogaja, 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., Ogaja,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, [ Accessed 22 April 2013]. Read More