International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 77 Analysis of Pseudorange-Based DGPS after Multiath Mitigation ThilanthaDammalage Deartment of Remote Sensing and GIS, Sabaragamuwa University of Sri Lanka Abstract- In Differential GPS (DGPS) rocessing technique the ultimate accuracy of the user location deends on the combined effect of site-deendent errors (i.e. multiath, receiver clock error and etc.), which occur at the oints of observation and the reference. Out of which, multiath is recognized as the most dominant and intricate site-deendent error. Previous study by Dammalage et al. (2010) evaluated the ossible accuracy imrovement of seudorange-based DGPS ositioning by C/A code multiath mitigation at the GPS reference stations alying wavelets transform. In this aer, three factors, which degrade the obtainable accuracy of the roosed multiath mitigation method, are identified and results are resented. Index Terms- GPS Permanent Reference Station, Multiath, Pseudorange-based DGPS D I. INTRODUCTION ifferential GPS (DGPS) is one of the most oular and comaratively accurate techniques to enhance the GPS ositioning accuracies by minimizing most of the common mode errors (e.g. ionosheric, troosheric, satellite clock errors, and so forth) in a combined oeration (Bradford et al. 1996). The extent to which the common mode errors are diminished by DGPS deends on a number of factors, but mainly the searation of the reference and user GPS receivers (Hofmann-Wellenhof et al. 2001). Furthermore, DGPS observation accuracy is highly deendent on the receiver tye, which varies with the caability of the carriers ( and ) and/or code (C/A) measurements for osition estimation. Accordingly, DGPS technique has been classified into two categories, namely carrier hase and seudorange-based DGPS, where the accuracies vary from centimeter level to meter level resectively (Han et al.1997). Moreover, several DGPS rocessing techniques can also be found, for instance, single difference and double difference which are very common in ractice; yet deend on the caability of the receiver and the rocessing software (Baroni et al. 2005). Irresective of the rocessing technique utilized in DGPS, the ultimate accuracy of the user location deends on the residual common mode errors and the combined effect of site-deendent errors (e.g. multiath, receiver and measurement noises) at the reference and the oint of observation. Of the latter, the most dominant error has been identified to be the effect of multiath (Xu.G., 2003) and which is defined as the multile recetions, by a GPS antenna, of one satellite signal due to reflections by surrounding objects (Misra et al. 2004). It has also been found that the error caused by multiath is highly variable in the time domain, showing quasi-sinusoidal oscillations of short eriods of several minutes, hence creating comlexity in mathematical reresentations (e.g., Daubechies et al.1990; Ogaja et al. 2007). Based on the inevitability of multiath, most ermanent GPS reference stations are installed through careful site selection and/or augmentation with additional hardware (e.g., choke-ring) so that their differential correction data have minimal multiath effects (Chen et al. 2010; Maqsood et al. 2013). However, in most ractical situations, minimal multiath or multiath-free site selection is not an easy task. As a consequence, some residual multiath errors and receiver noises are always remain and degrade the quality of DGPS corrections generated at the reference stations (Fan et al. 2006). By utilizing the double difference DGPS rocessing method, the bias term of the receiver clock can be comletely eliminated (Baroni et al. 2005). Yet, the error terms caused by multiath and receiver noise remain unchanged as single difference DGPS. II. PSEUDORANGE (C/A CODE) MULTIPATH Having realized the fact, most of the modern GPS receivers are now emloying multiath mitigation algorithms for their osition estimations; there by ensure the negative influence of multiath from osition estimations. For instance, Multiath Elimination Technology (MET) and Multiath Elimination Delay Lock Loo (MEDLL) are two oular techniques used to mitigate multiath at the receiver signal rocessing level (Townsend et al. 1994; Chen et al. 2013; ). Unfortunately, these methods are not effective in eliminating combined multiath caused by reference and user stations, on DGPS observations. Moreover, the effect of C/A code multiath error, on seudorange-based DGPS observations, is more significant due to its magnitude. Which is almost ten times greater than that of the carrier hase measurements (Mertins, 1999) and it could be even about 150m due to the chi length of C/A code (Xu.G., 2003). Notwithstanding, a wide range of GPS receivers, from the low-cost to very exensive, offer seudorange-based DGPS and commonly racticed by most of the GPS users due to its extended oerational distance of several hundreds of kilometers from its reference station while the carrier hase DGPS oerations are limited to several tens of kilometers (Dammalage et al. 2006).
International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 78 In consideration of the merits and araising the constrain effect of multiath error on C/A code measurements; the study roosed by Dammalage et al. (2010) aims to investigate the mitigation of the multiath effect on seudorange-based DGPS corrections that are generated by a ermanent GPS reference station. Furthermore, the study utilized the carrier hase and seudorange measurements for M the derivation of C/A code (seudorange) multiath effect ( ), which has been formulated by Han et al. (1997), taking advantage of the fact that multiath and receiver noise on carrier hase are negligible comared to those of C/A code based seudorange measurments. The C/A code multiath based on and frequencies are reresented by equations (1) and (2), resectively. ε ε 9529 7200 ( M + ε ) = PR Φ + Φ + K1 (1) 2329 2329 11858 9529 ( M + ε ) = PR Φ + Φ + K 2 2329 2329 (2) Where; and reresent the noise of receiver and seudorange measurements of PR and PR resectively. Φ and Φ are the carrier hase measurements in meters. K1 and K2 are functions of the multiath on carrier hase which include the unknown integer ambiguities. The multiath effect is considered to be a combination of harmonic signals and can be averaged out to zero over a few hours. Therefore, K1 and K2 can be estimated by averaging over a eriod of few hours. The result of these code and hase linear combinations give the noise embedded C/A code (seudorange) multiath residuals and thus it is tyically referred to as noisier multiath residuals (Satiraod et al. 2005). An attemt has, therefore, been made to de-noise the results obtained by equations (1) and (2) utilizing Wavelet Transform (WT) for the recise estimation of C/A code based seudorange multiath error at ermanent GPS reference stations. The obvious challenge of WT alication in multi-resolution signal analysis is the selection of the best wavelet family and the level of decomosition (Fu et al. 1997, Gras A., 1995 and Mallat S. G., 1989). Consequently, based on several field exeriments and analyses, Dammalage et al. (2010) have identified the best wavelet family and the level of de-comosition for the said de-noising rocess. Moreover, they have evaluated the ossible accuracy imrovement of seudorange-based DGPS ositioning by alying the roosed C/A code multiath mitigation method at the GPS reference stations. However, to further evaluate that fundamental study, this aer aims to investigate the accuracy diminishing factors effecting on C/A code multiath mitigation from seudorange-based DGPS corrections with the alication of roosed mitigation ractice. In order to accomlish the said goal, the same data set collected through the field exeriment discussed by Dammalage et al. (2010) is utilized for the analyses in this aer as well. III. FIELD DATA ACQUISITION Dammalage et al. (2010) has established a field exeriment with three known ground controls, adoting two receivers as ermanent reference stations and the third as a user GPS. Three days of 24-hour observations with 1 second observation interval were recorded with an artificial signal reflector, made of concrete, wood and metal, at one of the references during day 1, 2 and 3 resectively as illustrated in figure 1(a). Day 4 observations were erformed as in figure 1(b) and that has chosen as reference observations, to evaluate the effects of artificial multiath environments. Moreover, they have recisely measured the base-line distances D1, D2 and D3 by an electronic distance measurement (EDM) technique. Based on this known configuration, of GPS receivers and the signal reflectors, the additional multiath introduced by the reflectors was recisely calculated for each segment of the observations. Day 1, Day 2 & Day 3 Day 4 Reference GPS 02 D 2 D 1 Rover GPS 03 Reference GPS 02 D 3 D 2 D 1 Rover GPS 03 Reference GPS 01 Observation setu with creating multiath for reference GPS 01 Reference GPS 01 (b) Reference observation setu with minimum multiath environment
International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 79 Figure 1: Field exeriment setu, Dammalage et al. (2010) Analyzing these field data, Dammalage et al. (2010) have concluded that the best wavelet family and the level of de-comosition for the recise extraction of C/A code multiath are bi-orthogonal wavelet family and the 8th level of de-comosition. Additionally, they have shown that about 60% of accuracy imrovement of seudorange-based DGPS is ossible by mitigating the effect of multiath on C/A code at GPS reference stations. IV. ANALYSIS OF RESULTS Accuracy and the recision of the C/A multiath residuals with resect to its accuracy and are very imortant to be considered while utilizing the revious multiath estimations (re-modeled) for later generation of multiath free DGPS corrections by reference stations. However, the revious study revealed that the ositional accuracy of DGPS observations, even after multiath mitigation, is still showing random deviations with time; most robably due to unmolded error terms including multiath. Therefore, this study is focused to investigate the constrains of roosed C/A code multiath estimation methodology resented by Dammalage, et al. (2010). Thereby to further enhance the accuracy and recision of C/A code multiath mitigation for accuracy imroved seudorange-based DGPS ositioning. Accordingly, three accuracy diminishing factors, which negatively affected on accurate and recise extraction of C/A code multiath, were identified and discussed herein. A. Effect of cycle sli Figure 2(a): Effect of cycle sli on multiath estimation
International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 80 Figure 2(b): Effect of cycle sli on multiath residuals. Figure 2(c): Multiath residuals after filtering for cycle sli effect. Figure 2: Effect of cycle sli on seudorange multiath error estimations; before and after filtering for cycle sli. In C/A code (seudorange) multiath ( M ) estimation based on and frequencies, K1 and K2 are taken as a function of the multiath on carrier hase with including the unknown integer ambiguities. In addition the multiath effect is considered to be a combination of harmonic signals and can be averaged out to zero over a few hours. Therefore, K1 and K2 can be estimated by averaging over a eriod of few hours (Han et al. 1997), which imlies that the occurrences of cycle sli on carrier hase measurements could diminish the accuracy of estimated K value. For instance, figure 2(a) illustrates the effect of cycle sli on multiath error calculated using equation (1). According to the figure an unexected drastic change of calculated multiath error, of about 70 meters (change from about -10 m to 60 m), has seen after about 5 hours (between 25,000 and 30,000 seconds) of static observations. It is aarent that a change of such magnitude, even after average out these multiath residuals to estimate the resective K values, obviously creates unrealistic consequence. As a result, figure 2(b) shows the said effect in the final seudorange multiath residuals. The figure verifies that at the oint where the cycle sli occurs, the smoothly changing multiath residuals were changed drastically of about 1.5 meters. Therefore, cycle sli has been identified as one of the main source of accuracy diminishing factors; and once it occurs, which often introduce significantly higher magnitude of seudorange multiath residuals. Therefore, this error source and the occurrences have to be identified carefully from the actual multiath variations and essentially filtered out to avoid its effect from accurate and recise seudorange multiath estimations. Realizing the imortance of eliminating the effect of cycle sli before estimating the seudorange multiath residuals; this research has been extended to minimize the said effect by erforming a filtering rocess to detect and eliminate it from the final multiath calculations. After alying the filtering rocess (without cycle sli effect) the resulted multiath residuals are shown in figure 2(c). For instance, seudorange multiath residuals before and after de-noising for cycle sli and receiver noise errors for satellite PRN 20 and 26 are illustrated in figure 3. The figure rovides a clear comarison for the magnitude differences of seudorange multiath residuals before and after de-noising. Hence, it again confirms that the cycle sli effect should essentially mitigate from the multiath calculated based on equations (1) and (2).
International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 81 Figure 3: Pseudo-range multiath residuals before and after de-noising for cycle sli and receiver noise errors. B. Effect of un-modeled linear error comonent Other than the effect of cycle sli the study has identified another significant factor, which effects negatively on calculated seudorange multiath residuals based on the equations (1) and (2). As discussed reviously, multiath is an error which forms quasisinusoidal oscillations with a eriod of several minutes and roagates along the zero magnitude of the time series distributions. However, the time series multiath residuals calculated based on equations (1) and (2), are incororated with un-modeled linear comonent as illustrated in figure 4. According to the figure, the time series multiath residual errors with the said linear comonent are reresented in red color. The direction of the liner trend is shown with a black double arrow. Therefore, to get the theoretical distribution trend and the actual magnitude of multiath error, the remaining un-model linear error terms have to be identified and eliminated. After eliminating the liner comonent the resulted multiath residuals are illustrated in blue color. Further, dissimilar magnitudes of these linear distributions for each and every satellite were observed. These different magnitudes imly that the liner trends are not caused by the receiver clock or other receiver deendent bias. Therefore, these remaining unmodeled linear error comonents, even after DGPS corrections, are redicted to be the effect of satellite clock or orbital arameters. The magnitude differences of these multiath residuals with and without linear comonents are observed to be significant. Therefore, the un-modeled linear comonent has also been identified as the other main source of accuracy diminishing factor for the accurate and recise multiath residuals estimated based on equations (1) and (2). Figure 4: Pseudo-range multiath residuals; before (red) and after (blue) eliminating the un-modeled
International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 82 linear error comonent. B. Effect of observation length Further analyses were carried out to investigate the effect of observation length on recise seudorange multiath extraction. Several hours long observations were utilized for the multiath comutation and the resulted accuracies were evaluated for the identification of the effect of observation length. For instance, the time series seudorange multiath residuals calculated for 1, 2, 3, and 4 hours of observation lengths, with 1 second eoch rate, for three different satellites (PRN 5, 30 and 22) are illustrated in figure 5. Each satellite selected for this illustration is observed with maximum of about 4 hours at GPS 1 station. Further, PRN 5 and 30 are two satellites with comaratively higher multiath effect and PRN 22 is relatively less effected and illustrated in figure 5(a), (b) and (c), resectively. Figure 5(a) and (b) effectively illustrate that when the multiath error is comaratively higher; then the observation length is an imortant factor to be conceded. The accuracy of the comuted multiath for 3 and 4 hours of observations for PRN 5 is almost similar; because after 3 hours of observations the multiath effect is comaratively low, the influence therefore become very less. However, the similar comarison for PRN 30 reflects significant deviations, due to the influence of comaratively high multiath effect between 3rd and 4th hour of observations. Most of the high multiath error hase is included within 1 and 2 hours for PRN 5 observations; therefore, the multiath residuals are not deviated significantly from 2 and 3 hours comutation. However, for PRN 30, the said difference is significant; because its higher multiath error hase is extended well over 2 hours of observation. Moreover, for both satellites the multiath comuted based on 1 hour observations are significantly different from all the other observation lengths and comaratively less accurate. However, the observation length is not a significant factor for satellites which has comaratively less magnitude of multiath effect. For instance, the comuted seudorange multiath residuals for PRN 22, illustrated in figure 5(c), have not shown any significant deviation between each observation lengths. The similar scenario has been observed for all the satellites which have comaratively less magnitude of multiath. Considering the given facts and erforming several more comarable analyses, it was found that the best ossible accuracy of multiath residuals were obtained when utilizing the satellite full observation eriod in seudorange multiath comutation based on equations (1) and (2). Moreover, this scenario is highly significant for satellites effect with comaratively higher magnitude of multiath errors Figure 5(a). PRN 5 Figure 5(b). PRN 30
International Journal of Scientific and Research Publications, Volume 7, Issue 11, November 2017 83 Figure 5(c). PRN 22 1 hour 2 hours 3 hours 4 hours Fig. 5. Time series multiath residuals with resect to the observation length. In order to evaluate the ositional accuracy of seudorange-based DGPS rior to and after multiath mitigation; analyses were carried out by assuming GPS 01 as reference station and GPS 02 as rover. Accordingly, results for the baseline, GPS 01 GPS 02, with four different (1, 2, 4, and 8 hour) observation lengths with 1 second eoch rate (DGPS rocessed) are illustrated in Table 1. Accordingly, the Root Mean Square Error (RMSE) is calculated for each observation lengths and illustrated in the table. A clear difference of RMSE is observed for each four different observation lengths. Further, the highest imrovement is observed for the 8 and 4 hours observations. However, the imrovement is comaratively lesser when the observation length is 1 and 2 hours, which reflects the resented effect of observation length on recise multiath estimation. Table 1. Root Mean Square Error (RMSE) for 1, 2, 4 and 8 hour observations with 1 second eoch rate Root Mean Square Error (RMSE) (in centimeters) 1 hour 2 hour 4 hour 8 hour Day1 36.7 34.4 22.1 21.8 Day2 43 41.5 34.7 30.5 Day3 35 34.1 23.8 20.9 Day4 37.9 36.7 24.2 21.1 V. CONCLUSION In this aer, cycle sli, remaining un-modeled linear error terms and observation length, were identified as accuracy diminishing sources of C/A code (seudorange) multiath residuals calculated based on carrier and code combination. The magnitude differences of seudorange multiath residuals before and after de-noising for cycle sli have identified as significant. Therefore, the effect of cycle sli should identified and eliminate before estimating the seudorange multiath residuals. The remaining un-modeled linear error comonents are redicted to be the effect of satellite clock or orbital arameters due to their dissimilar magnitudes. However, the magnitude differences of the multiath residuals with and without linear comonents are observed to be significant. Hence, it should identified and eliminate from each multiath residuals. Observation length is also a significant factor for satellites which has comaratively higher magnitude of multiath than less effected one's. By several comarable analyses, it was found that the best ossible accuracy of multiath residuals were obtained when utilizing the satellite full observation eriod in seudorange multiath comutation based on equations (1) and (2). In this study, these three negatively influencing factors have identification and minimized successfully from C/A code multiath mitigation rocess. Based on the accomlished accuracy and recision, this study also highlights the otential alication of multiath free real-time DGPS corrections at ermanent reference stations towards suorting a growing number of high recision GPS alications. ACKNOWLEDGMENT Author of this article is highly indebted to the co-authors of revious study Dammalage et al. (2010); secially Professor. ChalermchonSatiraod of Deartment of Survey Engineering, Faculty of Engineering, Chulalongkorn University, Thailand.
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