The Effect of Multipath on Single Frequency C / A Code Based GPS Positioning

The differential GPS (DGPS) technique is one of the most popular and comparatively accurate techniques available to enhance the positioning accuracy by minimizing most of the common errors. However, the ultimate accuracy of the user location depends on the remaining non-common errors (multipath, receiver clock, and noise), which occur at the points of observation and reference. Out of these errors, multipath is the most dominant and challenging error to predict and minimize. Single frequency C/A code based GPS receivers are popular due to their comparatively low cost compared to dual frequency (L1/L2) GPS receivers. This paper focuses on evaluating the effect of multipath error on single frequency C/A code based GPS positioning. For the analysis, 72,000 continuous GPS observations with one-second interval under four different multipath environments were conducted by utilizing three geodetic GPS units. Accordingly, the observations with more than 5cm on the 2D positional error, created by the effected multipath, were always less than 25%. Here, an average of 16% of observations exceeded 20cm in 2D positional error. Further, it was noted that the presence of multipath introduces significantly higher and comparatively lower 3D positional errors on DGPS observations. This could be due to the compensation of negative and positive effects caused by the multipath and other remaining noncommon mode errors at the reference and user stations. In addition, C/A code based single frequency GPS observations were significantly influenced by multipath, not only by the close-by reflectors but also by the ground surface. The effect of multipath was about 50% of the total 3D positional error for the four tested multipath environments. Keywords-C/A code observations; DGPS; multipath


INTRODUCTION
Global positioning system (GPS) developed by the US Department of Defense, was first planned to have 24 satellites in operation.Each of the satellites continuously transmitted two high-frequency carrier waves L1 and L2, with frequencies of 1575.42MHz and 1227.60MHzrespectively [1].C/A-code (coarse-acquisition) is for civilian users and P-code (precision) for U.S. military or authorized users.The code signals are superimposed on the L1 carrier, while L2 carries only the Pcode [2].Both codes allow a GPS receiver to measure the signal propagation time from satellites to the receiver instantaneously using the distance from satellites to the receiver, (pseudo-range).Pseudo-ranges are then utilized for the estimation of GPS receiver position [3].Basically, there are two forms of observations depending on the capability of the receivers to process C/A code and L1/L2 carriers, referred to as code and carrier range observations respectively [4].Therefore, GPS based positioning accuracy directly depends on the accuracies of calculated ranges to at least four satellites [5].Most of the presently available GPS receivers utilize almost all the state-of-the-art technical improvements in GPS hardware and processing algorithms.However, still these GPS receivers suffer from significant positioning errors due to signal propagation delays through ionosphere and troposphere, satellite and receiver clock errors, bias on ephemeris data, multipath, and receiver and measurement noises [6][7][8].Hence, the standard positioning service (SPS) accuracy widely varies with time, place, and most importantly, GPS receiver performance [2].These measurement errors are generally classified as either common or non-common mode errors.The common errors (ionosphere delay, troposphere delay, satellite clock, and bias on ephemeris data) have similar effects on all receiver measurements operating in a limited geographic area [7].Non-common mode errors (multipath, receiver, and measurement noises) are distinctive and the amount of their influence depends on the surrounding obstructions at the observation site and the technical specification of receivers [9].
Numerous techniques are available to minimize the abovelisted sources of errors from GPS position estimation.A user equipped with a dual frequency (L1, L2) GPS receiver can estimate the ionospheric group delay and phase advance from the measurements themselves, and virtually eliminate the ionosphere as a source of error [10,11].Besides, many different models have been proposed to quantify the effect of ionospheric and tropospheric delay on GPS measurements.The Klobuchar model is one of the popular empirical models, which uses the satellite broadcast parameters to estimate the propagation zenith ionospheric delay [12].There is no dearth of tropospheric models, in particular, the Saastamoinen model, which was derived based on the gas laws and simplifying assumptions regarding changes in pressure, temperature, and humidity with altitude [13].However, none of these models as in (7), and g as the approp a derivation carrier phase a n [20], takin noise on ca ared to those ively represen  which the multipath effect is the most significant.According to the arrangement of the observation site, the possible source of multipath error at GPS01 was the reflector and/or the ground surface.
Reflector configuration at GPS 01 station At GPS02 and 03, the only possible source was the ground surface.A Trimble 5700 receiver was used at GPS03 with a Zephyr Geodetic L1/L2 antenna and Trimble Stealth ground plane technology, which could reduce most of the multipath created from the ground surface.Therefore, the negative influence that could be introduced by multipath on DGPS corrections generated at GPS03 reference station is assumed to be minimum.To evaluate the effect of multipath on C/A code based GPS positioning, 2D and 3D positioning accuracies at GPS1 and GPS2 were comparatively analyzed by utilizing the accurately measured baseline distances with GPS3 reference station.

A. Effect on 2D Positioning
The multipath effect is analyzed by evaluating the 2D positional accuracy of 72,000 observations recorded for 20hours with a 1-second interval.Table I presents the number of observations as a percentage of total records, within four different 2D positional error limits, less than or equal to 5cm, greater than 5cm, and greater than or equal to 20cm and 50cm (<5cm, >5cm, >20cm, and >50cm).The effect of multipath is calculated for both baselines, BL1 (GPS 03 -GPS 01) and BL2 (GPS 03 -GPS 02), as reported in Table I.Observations with the 2D positional error of less than or equal to 5cm could be considered as observations that are comparatively low affected by multipath.An average of about 78% and 85% were recorded with minimum multipath error for baselines BL1 and BL2 respectively.In addition, an average of about 22% and 15% observations were affected by higher multipath errors (more than 5cm of 2D positional errors for baselines BL1 and BL2 respectively).According to the condition of the observation site, the possible source of error for BL1 is the multipath at GPS01 created by the reflector and/or the ground surface.For BL2 it is the multipath at GPS02 created by the ground surface.Therefore, the percentage difference between BL1 and BL2 represents the additional multipath introduced by the artificial reflector separately from the ground.Accordingly, the artificial reflectors introduced both lower and higher than 5cm multipath errors on average of 7%.The highest difference percentage was observed for 2D positional error limit more than or equal to 20cm.When compared to the observations without reflector at GPS 01, the artificially-generated multipath diminished.However, for 2D positional error limit of more than or equal to 20cm, the number of observations were improved by 9.3%, 9.4%, and 10.6% over the observations without a reflector for concrete, wood, and metal, reflectors respectively.This confirms that the amount of multipath effect changes with the material of the reflector and is significant for higher 2D positional errors of greater than 20cm on C/A code based GPS observations.

B. Effect on 3D Positioning
Further analysis was conducted to investigate the effect of the multipath error on 3D positioning with single frequency analyzing the 2D and 3D positioning accuracies after DGPS processing.Based on the analysis, averages of 22% and 15% of the tested 72,000 observations were recorded with higher multipath errors of more than 5cm on 2D positioning for all the tested multipath conditions of baselines BL1 and BL2 respectively.It has observed that the magnitude of multipath error changed with the material of the reflector and was significant for higher 2D positional errors, greater than 20cm on C/A code based GPS observations.Further, it was noted that the presence of multipath introduces not only significantly higher positional errors, but also comparatively lower errors on C/A code single frequency GPS observations.Compensation of negative and positive errors caused by the multipath and other remaining non-common mode of errors at the reference and user stations could be the main reason for the observed irregular variation.Multipath has a significant influence on single frequency C/A code based GPS observations, and for the tested observations, the contribution was about 50% of total 3D positional errors of single frequency C/A code based GPS observations.

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