Code Multipath Error Research Articles

Extraction and analysis of short-term variation characteristics of code multipath error

Multipath errors (MP) can seriously affect positioning accuracy. Extracting and analyzing the variation characteristics of MP can provide a basis for mitigating it, but the current studies primarily focus on the characteristics of long-term variation of multipath errors while ignoring its short-term variation, which leads to incomplete understanding of the MP. Code and carrier phase dual-frequency observation combination and moving average method are combined to achieve accurate extraction of short-term code multipath error variation (MPvar), and different moving average strategies are adopted to satisfy the needs of real-time and after-the-fact extraction. The variation characteristics of MPvar between sea and land, among different GNSS systems, among different orbits of the BDS system are compared and analyzed. Study indicates that the carrier-to-noise ratio (C/N0) at sea is low and fluctuates greatly compared with the C/N0 at land, but the MPvar at sea is much smoother. There are differences in the magnitude of MPvar for each GNSS system, but they are all correlated with the elevation angle. For BDS GEO satellites, although the elevation angle variations are minimal, the MPvar has significant variations. Therefore, this study suggests that the MP variations of the BDS GEO satellites cannot be regarded as a smooth process when MP sources exist in the vicinity of the static observation stations. The extraction method and analysis results in this study helps to provide ideas for mitigating MP from a perspective of short-term variation.

Contribution of BDS-3 observations to the precise orbit determination of LEO satellites: a case study of TJU-01

The precise orbit determination (POD) of scientific low Earth orbit (LEO) satellites is a prerequisite for the successful implementation of scientific missions. In recent years, global navigation satellite systems have become the main means of determining the orbits of LEO satellites. The global navigation satellite system receiver onboard the Tianjin University No. 1 (TJU-01) satellite receives both GPS and BDS-2/3 signals, with the addition of BDS-2/3 observations playing an important role in improving the POD of LEO satellites. This study comprehensively analyzes the spaceborne GPS/BDS data quality, including BDS-2/3 and GPS code multipath errors. Appreciable code multipath errors are found for the B1I signal of BDS-2 medium Earth orbit (MEO) satellites at elevations higher than 40°, whereas slight near-field relevant multipath errors of both frequencies are found for GPS and BDS-3 MEO satellites. The GPS and BDS-2/3 code multipath errors are estimated through elevation/azimuth-relevant piece-wise modeling and applied in the POD calculations. Several schemes, namely GPS-based, BDS-based, BDS-based without geo-synchronous (GEO) satellites, and GPS/BDS combined schemes, are designed to evaluate the POD performance. Fourteen days of data are calculated and the average three-dimensional (3D) orbital root mean square (RMS) of orbit overlapping differences obtained from GPS-based and BDS-based POD (without GEO satellites) solutions are 37.4 and 27.1 mm, respectively. The BDS-based solutions are obviously better than the GPS-based solutions, mainly owing to better data availability. The GPS/BDS combined solutions have the best accuracy, with a 3D RMS value of 20.6 mm. In addition, when BDS GEO satellites are included, the 3D RMS of the overlapping orbit differences reduces to 32.9 and 27.4 mm for BDS-based and GPS/BDS combined solutions, respectively. Double-difference (DD) and single-difference (SD) integer ambiguity resolution (IAR) are adopted to further improve the POD performance. The fixed orbit of the TJU-01 satellite is solved through DD IAR and SD IAR, and the contribution of the TJU-01 satellite to ambiguity fixing is analyzed. Relative to the float solution, the improvements made using the two ambiguity fixing approaches are equivalent, both being approximately 13%. The importance of this research is not only the precise determination of the orbit of TJU-01 for occultation service but also the demonstration of the contribution of BDS observations to the performance of the POD of LEO satellites.

Real‐time precise orbit determination for FY‐3C and FY‐3D based on BDS and GPS onboard observation

AbstractThe code multipath error associated with elevation in BDS‐2 is one of the main factors whose impact on the precision of real‐time reduced‐dynamic precise orbit determination (POD) using spaceborne multi‐global navigation satellite systems (GNSS) observation data for FengYun‐3C (FY‐3C) and FengYun‐3D (FY‐3D) satellites. The aim is to construct a code multipath piece‐wise linear error model and analyse the contribution of BDS‐2 to the performance of low earth orbit POD. Conclusions are drawn out from the experimental results: (1) the real‐time POD average precision of FY‐3C and FY‐3D is improved by about 11% and 12% after the correction of BDS‐2 code multipath error; (2) Due to the small number of available BDS‐2 satellites and the limited accuracy of geostationary earth orbit (GEO) satellite real‐time orbit products, the precision of the real‐time overlapping comparison for FY‐3C/FY‐3D by using the BDS‐2 onboard observation data can only reach the decimetre level. However, with the BDS‐2 signal capture capability of the FY‐3D onboard GNSS Occultation Sounder upgraded, the average precision of the BDS‐2‐based POD for FY‐3D is better than that of FY‐3C in each direction and with 10% improvement in the average 3 dimensional‐root mean square (3D‐RMS); (3) Cases of onboard global positioning system (GPS), GPS + BDS‐2 (with GEO), and GPS + BDS‐2 (without GEO) for real‐time POD can meet 5–8 cm precision requirement. The average 3D‐RMS of the real‐time POD for FY‐3C/FY‐3D, which utilises onboard GPS + BDS‐2 data is inferior only to GPS data, owing to the influence of the orbit accuracy of GEO satellites. However, after excluding the influence of GEO satellites, the average result (3D‐RMS) of the real‐time POD for FY‐3C (6.11 cm) and FY‐3D (5.95 cm) is better than those of other cases.

Multipath Mitigation Methods of BOC-Family Signals Based on Dual BPSK Tracking Techniques

It is well known that for binary offset carrier (BOC) signals the notorious ambiguity problem due to the multipeaked autocorrelation function must be tackled first in order to obtain the potential of improving ranging performance promised by its broader Gabor bandwidth. The existence of multipath makes it more difficult to solve. Dual binary phase-shift keying (BPSK) tracking (DBT) is a kind of low complexity, unambiguous tracking method for BOC-family signals, which makes full use of the coherence between the upper and lower sidebands and employs subcarrier phase locked loop (SLL) and delay locked loop (DLL) to track subcarrier and code components, respectively. Considering that the thermal noise performance of DBT has been fully studied, this article focuses on the analysis of multipath performance and the design of antimultipath methods under DBT framework. The influence of multipath on SLL and DLL of DBT is analyzed first and the corresponding subcarrier and code multipath error envelopes are obtained. Then according to different requirements of subcarrier and code multipath errors, a multipath mitigation scheme specially designed for DBT is proposed, in which SLL and DLL adopt offset correlator and narrow correlation, respectively. Theoretical analysis and simulation are given to verify the effectiveness of the proposed methods.

Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

Analysis of the Impact of Multipath on Galileo System Measurements

Multipath is one of the major source of errors in precise Global Navigation Satellite System positioning. With the emergence of new navigation systems, such as Galileo, upgraded signals are progressively being used and are expected to provide greater resistance to the effects of multipath compared to legacy Global Positioning System (GPS) signals. The high quality of Galileo observations along with recent development of the Galileo space segment can therefore offer significant advantages to Galileo users in terms of the accuracy and reliability of positioning. The aim of this paper is to verify this hypothesis. The multipath impact was determined both for code and phase measurements as well as for positioning results. The code multipath error was determined using the Code-Minus-Carrier combination. The influence of multipath on phase observations and positioning error was determined using measurements on a very short baseline. In addition, the multipath was classified into two different types: specular and diffuse, using wavelet transform. The results confirm that the Galileo code observations are more resistant to the multipath effect than GPS observations. Among all of the observations examined, the lowest values of code multipath errors were recorded for the Galileo E5 signal. However, no advantage of Galileo over GPS was observed for phase observations and for the analysis of positioning results.

Code multipath error extraction based on the wavelet and empirical mode decomposition for Android smart devices

Code multipath error extraction based on the wavelet and empirical mode decomposition for Android smart devices

Single-Differenced Ambiguity Resolution for Orbit Determination of the Haiyang-2B

In ambiguity resolution, the Hatch-Melbourne-Wübbena code and carrier phase combination is usually used to fix the wide-lane (WL) ambiguity, and thus, the quality of the code observations directly affects the fixing success rate, especially when there are some kind of serious bias errors. Unfortunately, we found that the P1 code multipath (MP) errors of the Haiyang-2B calculated using the MP combination formula rapidly increases from sub-meter to several meters at elevation less than 40°. These rapid variations lead to biases in the fixed WL ambiguities. In this article, we create a static correction map on a grid with 5° x 5° resolution. Using this correction map, we reduced the root mean square of the P1 code bias errors from 1.04 to 0.47 m, which corresponds to an improvement of 54.8%. By comparing the different precise orbit determination solutions, we found that the ambiguity resolution significantly reduced the satellite laser ranging (SLR) residuals from 1.63 to 1.31 cm with an average improvement of 19.6%. However, because of the code errors, the ambiguity fixing rate of the P1 ambiguity-fixed solutions was much lower than that of the C1 solutions. By modeling this static correction, the impact of these errors was effectively reduced. The ambiguity fixing rate for the P1 solutions was improved by 15.6% and a 1-3 mm reduction in the SLR residuals was small but noticeable.

High-precision orbit determination for a LEO nanosatellite using BDS-3

The Tianping-1B is a 20-kg low earth orbit nanosatellite with a commercial multi-GNSS receiver based on a microelectromechanical system. This receiver collects concurrent code and phase dual-frequency measurements from the global positioning system (GPS) and the second and third generations of the BeiDou Global Navigation Satellite System (i.e., BDS-2 and BDS-3). However, BDS-3 signals with pseudorandom noise code numbers greater than 32 cannot be received. In this study, onboard GPS and BDS measurements from Tianping-1B are collected for days 133–147 of 2019. The performance of the onboard BDS-3 measurements is analyzed, and the potential of the BDS-3-based precise orbit determination (POD) for Tianping-1B is assessed. The carrier-to-noise-density ratio of the BDS-3 is higher than that of the BDS-2 and approaches that of the GPS. The BDS-3 has a smaller code multipath error than the BDS-2 and the GPS and therefore a higher quality of code measurements. The results of the overlap comparison show a GPS-based orbit consistency below 3.5 cm in three dimensions (3D) and below 1.2 cm in the radial direction. The mean of satellite laser ranging validation residual RMS is 1.7 cm. The orbit obtained using onboard BDS measurements is assessed using the GPS-based orbit as a reference: The mean 3D root mean square (RMS) difference between the BDS-3-only-based POD and the reference orbit is 4.57 cm. Thus, a sub-dm-level orbit can be achieved using only onboard BDS-3 measurements. A POD with slightly higher precision than the BDS-3-only-based POD is obtained using both BDS-3 and BDS-2 measurements, using higher weights for the BDS-3 data than the BDS-2 data. Then, the combined BDS-3/GPS POD is performed: The RMS difference between this joint orbit and the GPS-based orbit is 1 cm in 3D. This study can be used as a reference for the development of BDS-3 based POD, which will approve in accuracy and precision upon completion of BDS-3.

Analysis of Tiangong-2 orbit determination and prediction using onboard dual-frequency GNSS data

Tiangong-2 is the first Chinese real space laboratory, launched into earth orbit with an altitude of approximately 393 km on September 15, 2016. Precise orbit determination (POD) is one of the essential conditions for conducting onboard scientific research. The precise orbit of Tiangong-2 is mainly determined by the reduced-dynamic method using space-borne global navigation satellite system (GNSS) data, which are collected by an onboard dual-frequency GNSS receiver. The in-flight performance of the receiver is first assessed in terms of tracking ability, code multipath errors and noise levels of code and carrier phase observations. Then, the effects of refined non-gravitational force models and GNSS antenna phase center variations (PCVs) on the POD are analyzed. The estimated empirical accelerations are substantially reduced by 45% in the along-track direction using a macro-model compared to that using a cannonball model for drag computation. The application of antenna PCVs correction leads to better consistency between reduced-dynamic and kinematic orbit solutions. Satellite laser ranging validation shows that the accuracy of Tiangong-2 precise orbits is 1.7 cm after using the improved reduced-dynamic method. Based on the orbit determination results, the quality of Tiangong-2 orbit predictions is assessed for periods without and with the refined non-gravitational force models. The use of the macro-model and high-quality density models for drag computation is shown to help improve orbit prediction quality.

Corrections of BDS Code Multipath Error in Geostationary Orbit Satellite and Their Application in Precise Data Processing.

Multipath error is a main error source in Global Navigation Satellite System (GNSS) data processing, which cannot be removed by a differential technique because of the strong relationship with the environment around the station. The multipath effect of the code observables is more complex than that of the carrier-phase observables, especially for BeiDou Navigation Satellite System (BDS) geostationary orbit (GEO) satellites. In this contribution, we deeply analyzed the characteristic and effect on the precise data processing of GEO satellite multipath errors based on a large number of permanent GNSS stations. A linear combination of code and carrier-phase observables was used to analyze the characteristics of repeatability for BDS GEO’s multipath. Then, a correction method was proposed to eliminate the multipath error of the GEO code observables, based on wavelet transform. The experiment data were collected at 83 globally distributed stations, from multi-GNSS experiments and national BDS augmentation systems, from days 32 to 66 in 2017. The results show that the systematic multipath variation component of the GEO code observables can be obtained with wavelet transform, which can significantly contribute to correcting the multipath error of GEO satellites. The average root mean square error (RMSE) of the multipath series is decreased by approximately 19.5%, 20.2%, and 7.5% for B1, B2, and B3, respectively. In addition, some experiments, including ionospheric delay extraction and satellite clock estimation, were conducted in simulated real-time mode in order to validate the effect of the correction methods. For the ionospheric delay estimation, the average RMSE of the slant ionospheric delay is reduced by approximately 15.5%. Moreover, the multipath correction can contribute greatly to shortening the convergence time of the satellite clock estimation of the BDS GEO satellites.

Centimeter-Level Orbit Determination for TG02 Spacelab Using Onboard GNSS Data.

Tiangong-2, the second Chinese manned spacecraft, was launched into low Earth orbit on 15 September 2016. The dual-frequency geodetic GNSS receiver equipped on it is supporting a number of scientific experiments in orbit. This paper uses the onboard GNSS data from 3–31 December 2016 (in the attitude mode of three-axis Earth-pointing stabilization) to analyze the data quantity, as well as the code multipath error. Then, the dynamic and reduced-dynamic methods are adopted to perform the post Precise Orbit Determination (POD) based on the carrier phase measurements, respectively. After that, the orbit accuracy is evaluated using a number of tests, which include the analysis of observation residuals, Overlapping Orbit Differences (OODs), orbit comparison between dynamic and reduced-dynamic and Satellite Laser Ranging (SLR) validation. The results show that: (1) the average Root Mean Square (RMS) of the on-board GNSS phase fitting residuals is 8.8 mm; (2) regarding the OODs determined by the reduced-dynamic method, the average RMS in radial (R), along-track (T) and cross-track (N) directions is 0.43 cm, 1.34 cm and 0.39 cm, respectively, and there are no obvious system errors; (3) the orbit accuracy of TG02 determined by the reduced-dynamic method is comparable to that of the dynamic method, and the average RMS of their differences in R, T, N and 3D directions is 3.05 cm, 3.60 cm, 2.52 cm and 5.40 cm, respectively; (4) SLR data are used to validate the reduced-dynamic orbits, and the average RMS along the station-satellite direction is 1.94 cm. It can be seen that both of these two methods can meet the demands of 3D centimeter-level orbit determination for TG02.

A distribution model of the GNSS code noise and multipath error considering both elevation angle and orbit type

Commonly, the code noise and multipath error is considered to fully obey the Gaussian distribution. While in the cases with different elevation angles and orbit types, the assumption may be inappropriate. Based on an empirical study, by considering both the elevation angle and the orbit type, a new code noise and multipath distribution model is proposed to describe a more accurate code noise and multipath distribution in this paper. Actual code noise and multipath data from 10 observation stations during two months are researched, and the parameters and elevation angle range of code noise and multipath distribution model are determined. The code noise and multipath distribution model is verified to be more accurate than the model presented in the Global Navigation Satellite System Evolutionary Architecture Study report, according to the analysis on the code noise and multipath overbounding, position error overbounding, and the availability of receiver autonomous integrity monitoring. This model provides more accurate prior information for receiver autonomous integrity monitoring, especially its availability.

GPS and BeiDou Differential Code Bias Estimation Using Fengyun-3C Satellite Onboard GNSS Observations

Differential code biases (DCBs) are important parameters in GNSS (Global Navigation Satellite System) applications such as positioning as well as ionosphere remote sensing. In comparison to the conventional approach, which utilizes ground-based observations and parameterizes global ionosphere maps together with DCBs, a method is presented for GPS and BeiDou system (BDS) satellite DCB estimation using onboard observations from the Chinese Fengyun-3C (FY3C) satellite. One month worth of GPS and BDS data during March 2015 was exploited and the GPS C1C-C2W and BDS C2I-C7I DCBs were explored. To improve DCB estimation precision, the dual frequency carrier phase measurements leveled by code measurements were used to form basic observation equation. Code multipath errors of the FY3C onboard GPS/BDS observations were assessed and modeled as grid maps, and their impact on DCB estimation was analyzed. By correcting code multipath errors, the stability of DCB estimates was improved by 5.0%, 3.1%, 16.2% and 13.6% for GPS, and BDS geosynchronous orbit satellites (GEOs), inclined geosynchronous satellite orbit satellites (IGSOs) and medium Earth orbit satellites (MEOs), respectively. The monthly stability of FY3C-based DCBs was at the order of 0.1 ns for GPS satellites, 0.2 ns for BDS GEOs and 0.1 ns for BDS IGSOs and MEOs. By comparison to the ground-based DCB products issued by other institutions, FY3C-based DCBs showed stability degradation for BDS C02 and C05 satellites, while, for other satellites, the stability reached a similar or even superior level. The estimated FY3C receiver DCB stability was at the order of 0.2 ns for both GPS and BDS. In addition to the DCB estimates, the obtained vertical total electron content above the FY3C satellite orbit was also investigated and its realism was examined in physical and numerical aspects.

BDS satellite-induced code multipath: Mitigation and assessment in new-generation IOV satellites

This article is dedicated to the developments of the new-generation of BDS satellites and the mitigation of the satellite-induced code multipath error. Basic signal parameters of three new-generation BDS IOV satellites were introduced. A monitoring receiver connected to a wideband choke ring antenna GNSS-750 from NovAtel on the rooftop of a tall building. The used antenna has high quality and is multipath insensitive at the user's end. Code multipath errors of their triple-frequency civil signals were assessed based on data of several days in Xi’an. The means and standard deviations of MP series for IOV BDS civil signals across different elevation-intervals were calculated to assess the multipath error variations across different elevation-intervals. Thorough hypothesis-testing experiments were carried out to determine whether the code multipath errors significantly change with elevation using one-way analysis of variance. The code multipath errors of three BDS IOV satellites and three operational BDS satellites are compared under the same condition demonstrating the effective mitigation of satellite-induced code multipath errors for the new-generation BDS IOV satellites. Experimental results show that the satellite-induced code multipath bias is not obvious for the new-generation BDS IOV satellites under analysis.

Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations

The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in 2{^{circ }}times 2{^{circ }} grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.

Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system

BeiDou regional navigation satellite system (BDS) also called BeiDou-2 has been in full operation since December 27, 2012. It consists of 14 satellites, including 5 satellites in Geostationary Orbit (GEO), 5 satellites in Inclined Geosynchronous Orbit (IGSO), and 4 satellites in Medium Earth Orbit (MEO). In this paper, its basic navigation and positioning performance are evaluated preliminarily by the real data collected in Beijing, including satellite visibility, Position Dilution of Precision (PDOP) value, the precision of code and carrier phase measurements, the accuracy of single point positioning and differential positioning and ambiguity resolution (AR) performance, which are also compared with those of GPS. It is shown that the precision of BDS code and carrier phase measurements are about 33 cm and 2 mm, respectively, which are comparable to those of GPS, and the accuracy of BDS single point positioning has satisfied the design requirement. The real-time kinematic positioning is also feasible by BDS alone in the opening condition, since its fixed rate and reliability of single-epoch dual-frequency AR is comparable to those of GPS. The accuracy of BDS carrier phase differential positioning is better than 1 cm for a very short baseline of 4.2 m and 3 cm for a short baseline of 8.2 km, which is on the same level with that of GPS. For the combined BDS and GPS, the fixed rate and reliability of single-epoch AR and the positioning accuracy are improved significantly. The accuracy of BDS/GPS carrier phase differential positioning is about 35 and 20 % better than that of GPS for two short baseline tests in this study. The accuracy of BDS code differential positioning is better than 2.5 m. However it is worse than that of GPS, which may result from large code multipath errors of BDS GEO satellite measurements.

A new method to mitigate multipath error in single-frequency GPS receiver with wavelet transform

One of the major errors in high-precision GPS positioning is multipath. Multipath effect modeling and reduction have been a challenging issue in high-accuracy GPS positioning applications due to its special properties. Different methods have been employed to mitigate this error including hardware and software approaches. We reduce C/A code multipath error by adopting an efficient software method which uses wavelet transform as a basic data processing trend. The key idea of the proposed method is using stationary wavelet transform (SWT) in GPS signal data processing. Since we have used SWT, there is complete access to high-frequency and low-frequency terms in both time and frequency domains, and we can apply appropriated procedures to mitigate this error. The multipath error mostly is a low-frequency term. In our proposed method, the double difference (DD) residuals are applied to the SWT to identify the multipath disturbance. The extracted multipath is then used to correct DD observations. Our experiments include three data sets to investigate the proposed method and compare it with existing algorithms. We used simulations for two of these data sets. The results indicate the efficiency of the proposed method over existing algorithms.

A Unified Framework for GPS Code and Carrier-Phase Multipath Mitigation Using Support Vector Regression

Multipath mitigation is a long-standing problem in global positioning system (GPS) research and is essential for improving the accuracy and precision of positioning solutions. In this work, we consider multipath error estimation as a regression problem and propose a unified framework for both code and carrier-phase multipath mitigation for ground fixed GPS stations. We use the kernel support vector machine to predict multipath errors, since it is known to potentially offer better-performance traditional models, such as neural networks. The predicted multipath error is then used to correct GPS measurements. We empirically show that the proposed method can reduce the code multipath error standard deviation up to 79% on average, which significantly outperforms other approaches in the literature. A comparative analysis of reduction of double-differential carrier-phase multipath error reveals that a 57% reduction is also achieved. Furthermore, by simulation, we also show that this method is robust to coexisting signals of phenomena (e.g., seismic signals) we wish to preserve.

GPS multipath mitigation: a nonlinear regression approach

Under the assumption that the surrounding environment remains unchanged, multipath contamination of GPS measurements can be formulated as a function of the sidereal repeatable geometry of the satellite with respect to the fixed receiver. Hence, multipath error estimation amounts to a regression problem. We present a method for estimating code multipath error of GPS ground fixed stations. By formulating the multipath estimation as a regression problem, we construct a nonlinear continuous model for estimating multipath error based on well-known sparse kernel regression, for example, support vector regression. We will empirically show that the proposed method achieves state-of-the-art performance on code multipath mitigation with 79 % reduction on average in terms of standard deviation of multipath error. Furthermore, by simulation, we will also show that the method is robust to other coexisting signals of phenomena, such as seismic signals.