Carrier-Phase Multipath Calibration of GPS Reference Stations

Multipath, where GPS signals arrive by more than one path and thereby create a range error, has remained the long-lasting major error source in GPS solutions although having been a target of the GPS research community since the day the system started operating. Seeking to understand the GPS multipath errors, this report aims to ef?ciently mitigate multipath effects at observable levels to improve the accuracy and precision of GPS solutions.Based on an analysis of the geometry of a multipath signal's reflections, and the principle of GPS receiver's tracking loop, geometrical models of multipath errors are developed at observable levels (both code and carrier-phase multipath). More specifically, multipath errors corresponding to a satellite are mathematically proven to be functions of the satellite's geometry with respect to a receiver which is parameterized by azimuth and elevation angles. Hence, the problem of multipath error estimation amounts to a regression problem where the multipath functions are approximated using training data. Whereas the theory behind regression problem is robust, the regression problem solution would be feasible as long as a priori data (e.g. training data) is available. As code multipath errors can be easily isolated using a combination of GPS measurements and satellites' geometrical information can be computed using orbital information broadcast from the satellites, training data for the problem code multipath error estimation can be extracted. An experiment was conducted to demonstrate the performance of the proposed method. A real data set was recorded at 0.1 Hz during 5 days to use for the experiment. After training the multipath estimators with data from 31 visible satellites over four days using the epsilon-SVR algorithm, multipath estimation and correction have been performed on the data from the successive day. Results show approximately 80% reduction in term of code multipath error standard deviation, the proposed method shows great promise for understanding and removing multipath errors. Advantageously, while being scalable with data rate, the proposed method is shown to be not harmful to other signals (simulation). An analogous experiment was also conducted to address carrier-phase multipath error. Unfortunately, for a standalone receiver, carrier-phase multipath error cannot be isolated by a combination of measurements as has been done with code multipath error, a carrier-phase double difference between two short-basedlined receivers needs to be made. It results in combinatorial carrier-phase multipath error of 4 satellite-receiver pairs involved in double-difference. Mitigation of this error is beneficial for relative positioning applications. With the same rationale, the multipath error is modeled as a function of the geometries of 4 satellite-receiver pairs. Training the multipath estimation using 1-Hz data from two short-baselined stations of IGS network, preliminary experimental result showed 57% reduction in multipath error for a pair of satellites. My next target is to unify an evaluation framework for multipath mitigation problems with well-defined tests, and evaluation criteria, as this is missing in the literature. Whereas further experiments on carrier-phase multipath mitigation as well as on data recorded from the field need to be done, there is also still room for improvement in multipath estimation algorithms with the focus on computational complexity reduction and incremental learning ability. Integration of the new signals in GPS modernization plans is also worth exploring.

The multipath error is the primary pseudorange measuring error factor in Compass system, in dual-frequency positioning mode, it is difficult to be eliminated by modeling methods, and on the contrary, it is always amplified because of the combination of measuring error. As a result, certain kind of user terminal has lower vertical positioning precision under dual-frequency mode than under single-frequency mode. This paper makes simulation of the impact of multipath error on pseudorange UERE under single-band mode and dual-band mode, obtains the interrelation of ionosphere modeling error, multipath error and the vertical positioning precision of single-band and dual-band respectively. This paper extracts multipath error in pseudorange of GEO and IGSO satellite by pseudorange carrier phase combination method, and uses the ionosphere delay calculated by dual-band carrier phase measurements as a benchmark, makes assessment of the ionosphere delay calculated by dual-band pseudorange combination method and ionospheric delay model correction method, analyses the amount of error correction brought into the Compass system by pseudorange of distinct orbit satellite. Data processing results show that, under current multipath mitigation measures, the pseudorange multipath error will cause that the error of GEO satellite ionosphere delay correction measured by dual-band is larger than by single-band, make a reasonable interpretation of the phenomena that dual-band vertical positioning accuracy is lower than single-band vertical positioning accuracy, and the ionospheric delay correction errors brought by pseudorange multipath error of GEO satellites are greater than the IGSO satellites, verify the phenomenon of “standing multipath error” brought by GEO satellite orbital characteristics.

In view of the problem of the long-term variation of code multipath error (called code multipath bias) in the IGSO and MEO satellite observable, code multipath bias of BDS is analyzed using iGMAS data of multiple earth stations. In addition, the GPS and BDS multipath error variation is analyzed comparatively. The results show that the variation of BDS multipath error is related to the elevation angle, satellite orbit type and carrier frequency, but independent with the location of the receivers. And for the carrier frequency B1, B2, and B3, the code multipath bias for MEO satellite is 1.66, 1.05 and 0.53 m, respectively. For IGSO satellite the code multipath bias is 0.65, 0.44, and 0.31 m accordingly, which are smaller than that reported by earlier papers. Especially, for IGSO at frequency B2 and B3, the code multipath bias is smaller than half of that reported earlier. At the same time, in order to reduce the multipath bias, a two-order polynomial fitting algorithm is proposed in this paper. The results show that: compared with the results of piecewise linear model with 10 correction parameters, the two-order polynomial correction algorithm with three correction parameters can correct the multipath error and reduce the RMS of the multipath error more effectively. The two-order polynomial model in this paper is more convenient considering broadcasting the correction information to the users.

A multipath error is one of the main sources of GNSS positioning errors. It cannot be eliminated by forming double-difference and other methods, and it has become an issue in GNSS positioning error processing, because it is mainly related to the surrounding environment of the station. To address multipath errors, three main mitigation strategies are employed: site selection, hardware enhancements, and data processing. Among these, data processing methods have been a focal point of research due to their cost-effectiveness, impressive performance, and widespread applicability. This paper focuses on the review of data processing mitigation methods for GNSS carrier-phase multipath errors. The paper begins by elucidating the origins and mitigation strategies of multipath errors. Subsequently, it reviews the current research status pertaining to data processing methods using stochastic and functional models to counter multipath errors. The paper also provides an overview of filtering techniques for extracting multipath error models from coordinate sequences or observations. Additionally, it introduces the evolution and algorithmic workflow of sidereal filtering (SF) and multipath hemispherical mapping (MHM), from both coordinate and observation domain perspectives. Furthermore, the paper emphasizes the practical significance and research relevance of multipath error processing. It concludes by delineating future research directions in the realm of multipath error mitigation.

With the rapid development of global navigation satellite system (GNSS) technology, IGS signals play a crucial role in many fields such as positioning, navigation, and time synchronization. Nevertheless, the multipath error problem seriously affects the performance of IGS signals in practical applications. In this paper, the multipath error problem of IGS signals is studied in depth, and an improvement method based on a digital filtering technique is proposed. The article first provides a comprehensive analysis of the impact of multipath error and identifies the shortcomings of existing studies, thus clarifying the motivation of this study. Subsequently, this paper uses digital filtering techniques to estimate the multipath error accurately and designs a corresponding improvement strategy. Through experimental verification, this paper demonstrates the significant effect of the improved method in improving signal quality and positioning accuracy. Finally, the article summarises the research results. It discusses their potential promotion value in IGS signal reception and related applications, which provides important theoretical support and practical guidance for future technology development and applications.

One of the most important functions for the safety of autonomous driving is the self-localisation of a moving platform. The GNSS (Global Navigation Satellite System) sensor is - compared to other sensors as, e.g., video, radar or camera - the only sensor that provides absolute positioning. Under clear sky conditions, GNSS positioning methods yield high level of accuracy and integrity. Poor signal propagation conditions make precise GNSS positioning challenging under urban conditions where multipath degrades the attainable accuracy and integrity. In the last decades, various correction or mitigation approaches for multipath errors have been developed and tested, but for carrier phase observations it is still the most critical error with magnitudes of up to a quarter of the wavelength. Since the carrier phase multipath error is location dependent, this property can be used to construct a correction map. In this paper, we report on the necessary steps to construct such a multipath correction map. The carrier phase error is a function of the multipath characteristics and the extra path delay. Hence, it is dependent on the distance to the reflection surface. Using a 3D building model, the geometry between the building and potentially multipath affected satellite signals is established to obtain one periodic cycle of the carrier phase error. A pseudo-kinematic experiment in an urban environment is planned and designed based on simulation studies of a ray-tracing algorithm to ensure ideal receiving properties for multipath signals in a realistic scenario. Two different approaches of carrier phase residuals will be compared to derive the multipath error from the observations. Firstly, double difference residuals are computed. Secondly, carrier phase residuals extracted from a positioning engine will be analysed. Finally, the developed functions are evaluated in the context of generating GNSS multipath correction maps for moving platforms.

It is well known that code and carrier-phase multipath, which has been under study for over two decades, is the limiting error sources in high-precision differential GPS applications. In virtually every study, however, the effects of autocorrelation function are considered little. This article focuses on the bounds of code and carrier-phase multipath error in terms of GNSS (Global Navigation Satellite Systems) signals autocorrelation functions, which result from a fundamental theoretical description and mathematical modeling of GNSS receiver. Firstly, an overview of the characteristics of the BOC (Binary Offset Carrier) signal ACF (autocorrelation function) is given in the paper. The impact on the DLL (delay-lock loop) and PLL (phase lock loop) discriminator functions are derived in the followed section and consequently a general description of multipath errors are obtained for the BOC signals. This quantifies the influence of limited bandwidth on receiver tracking error due to multipath. Finally, the simulation results show a distinct change in the error envelope for BOC signals from which has been got using current GPS C/A code signal.

The Global Climate Observing System has identified the need for systematic global daily snow cover data sets over land. Current in situ snow cover data sets have limited spatial coverage while satellite‐based snow cover records have either limited historical extent or limited temporal and spatial resolution because of cloud cover or specific sensor availability. NOAA Advanced Very High Resolution Radiometer (AVHRR) data offers nearly complete daily global coverage of the Northern Hemisphere, extending back to the early 1980s with successors slated to continue into the next decade. In this paper, we apply a new algorithm, Snowcover, to estimate daily snow cover, including periods of cloudy conditions, from AVHRR Polar Pathfinder (APP) data over Northern Hemisphere land surfaces. This new snow cover product is compared to snow cover estimates derived from long‐term in situ snow depth measurements over Canada and the northern Eurasia. The APP snow cover maps showed an 80% agreement rate or better at 95% of the in situ sites. This performance was comparable to the agreement of MODIS 0.05 degree snow cover products over the same sites; although the MODIS product was only retrieved ∼20% of the time corresponding to clear sky conditions in contrast to over 95% of the time with the APP snow product. The almost continuously temporal and spatial coverage for the past 23 years from 1982 to 2004 over Northern Hemisphere makes the new daily snow cover product especially suitable for analysis of large‐scale patterns of spring snowmelt in association with variability of circumpolar climate and ecological parameters.

The orbit manoeuvre, known as CRYO2ICE, that periodically aligned CryoSat-2 with ICESat-2, allows for unprecedented near-coincident radar and lidar observations targeted the polar regions. This is of particular interest to sea ice thickness studies, since snow on sea ice remains the largest contributor to altimetry-derived sea ice thickness uncertainties. To date, snow depth estimates from space have been acquired from passive microwave radiometers, and by using dual-frequency observations (Ku- and Ka-band, or laser and Ku-band). However, until now, dual-frequency observations have only been based on monthly averaged estimates at basin-scales, and while passive microwave-derived snow estimates are provided daily, they are only reliable over first-year ice. CRYO2ICE presents the possibility of investigating along-track snow depth on sea ice using observations at two different frequencies, along with an opportunity for further investigation of penetration capabilities and footprint-related issues of high interest to the altimetry community.Some of the most noticeable differences between CryoSat-2 and ICESat-2 are found in their measurement configuration and sampling rates. This difference in measurement configuration between retrieving surface elevation using conventional ways, such as re-tracking of the synthetic aperture radar (SAR) waveform of CryoSat-2 in comparison to re-tracking the surface from high-density photon clouds of ICESat-2, as well as the difference in sampling rates, presents additional challenges. Here, we investigate the challenge of binning these different type of observation strategies into comparable observations and what we can expect from the CRYO2ICE observations over sea ice. We examine near-coincident radar and laser freeboards from CryoSat-2 and ICESat-2 (CRYO2ICE observations) and the resulting snow depth observations in the Arctic. We utilise three CryoSat-2 products (Baseline-D, CCI and LARM) representing a variety of re-trackers used in sea ice altimetry studies, and the ATL10 product from ICESat-2. Our focus is on how the CryoSat-2 and ICESat-2 derived freeboards respond along-track to various ice and snow conditions, and how this affects the possibility to retrieve snow depth.This study investigates the freeboards and the derived snow depth in relation to changes in surface roughness, sea ice concentration and sea ice lead identifications. Here, we find inconsistencies in the radar freeboard estimates across the changing ice conditions. By comparison with sea ice concentration, identified leads and roughness estimates, the inconsistencies relate to retrieval methodology of CryoSat-2 (re-tracking to a backscattering interface using a threshold-based re-tracker or a physical re-tracker) and binning methodology (posing the question of when CRYO2ICE observations are truly comparable). Other inconsistencies relate to how the condition of the surface impacts the radar signal. We also present comparisons of radar and laser freeboards with daily estimates of snow depth based on passive-microwave observations (AMSR-2) and snow evolution models (SnowModel-LG). Here, large discrepancies are observed: AMSR-2 observations show little variation over first-year ice, compared to both estimates from SnowModel-LG and CRYO2ICE observations. CRYO2ICE snow depths are comparable across the used CryoSat-2 products but shows significantly larger variation compared to SnowModel-LG estimates. Future work includes delving more into the changing ice conditions and their impact on the radar signal.

Snow plays an important role in global hydrological cycle and climate system. In addition, snow as a key variable factor is important indicator to climate change. In recent years, applying passive microwave remote sensing to retrieval snow depth has made greatly progress. Snow depth retrieval algorithms and snow products can provide spatial and temporal information on snow cover distribution, which is an important data source to snow monitor. Based on the survey project of snow cover characteristics and snow distribution in Northeast China, Advanced Microwave Scanning Radiometer 2 (AMSR2) brightness temperature data and MODIS product data are used in this paper. Original resolution brightness temperature observations are used in AMSR2 algorithm, except for the 89GHz channel which is resampled according to 36GHz footprint, and brightness temperature corrections made on the original measurements rather than using the aggregated brightness temperature observations. The original algorithm takes advantage of the expanded range of channels available on the AMSR2 instrument compared with the SSM/I and SMMR, and it undertakes a forest correction. However, the original AMSR2 snow depth retrieval algorithm greatly overestimate measured snow depth, especially in forest areas where is a challenge to retrieval snow depth, the error between 20 to 30cm. In order to improve the retrieval accuracy of snow depth in Northeast China, an improved snow depth retrieval algorithm in forest areas is proposed in this paper, the improved snow depth retrieval algorithm in forest areas is SD f = 1/ln(pol 36 ) × (Tb 18V − Tb 36V )/(1 − fd × 0.6). The results proved that the error is less than 5cm after using the improved algorithm, the root mean square error and deviation are 4.82cm, 3.55cm, respectively.

Studies have shown that geodetic Global Navigation Satellite System (GNSS) stations can be used to measure snow depths using GNSS interferometric reflectometry (GNSS-IR). Here, we study the results from a customized GNSS setup installed in March through August 2020 at the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) automatic weather station NUK-K located on a small glacier outside Nuuk, Greenland. The setup is not optimized for reflectometry purposes. The site is obstructed between 85 and 215 degrees, and as the power supply is limited due to the remote location, the logging time is limited to 3 h per day. We estimate reflector heights using GNSS-IR and compare the results to a sonic ranger also placed on the weather station. We find that the snow melt measured by GNSS-IR is comparable to the melt measured by the sonic ranger. We expect that a period of up to 45 cm difference between the two is likely related to the much larger footprint GNSS-IR and the topography of the area. The uncertainty on the GNSS-IR reflector heights increase from approximately 2 cm for a snow surface to approximately 5 cm for an ice surface. If reflector height during snow free periods are part of the objective of a similar setup, we suggest increasing the logging time to reduce the uncertainty on the daily estimates.

Winter snowfall is increasing in many Arctic regions and climate models predict this trend will persist in the coming century. We examined the effects of two levels of increased winter snow accumulation on soil microclimate, plant and soil nutrient status, plant phenology and ecosystem CO2 exchange after five years of treatment in a widespread High Arctic ecosystem. Increased snow cover resulted in greater winter CO2 efflux, altered growing season soil nutrient availability and greater leaf nitrogen concentrations during the snow-free season. Modest increases in snow cover (+0.25 m above ambient) increased gross ecosystem photosynthesis (GEP) without increasing ecosystem respiration (ER), while the deepest snow cover (+0.75 m above ambient) increased both GEP and ER. The area of intermediate snow addition was a smaller source of CO2 to the atmosphere during the growing season when compared to the ambient and deep snow areas. The intermediate and deep snow areas apparently had similar effects on the functioning of the vegetation community (increased GEP), but divergent effects on the soil microbial respiration, as evidenced by the changes in ER. This nonlinear response to increasing snow depth demonstrates the potential for complex High Arctic ecosystem responses to changes in winter precipitation.

Napropamide and Oryzalin Effect on Simazine Tolerance of Four Ornamental Species

Analysis of the hourly Canadian Prairie data for the past 60 years has transformed our quantitative understanding of land–atmosphere–cloud coupling. The key reason is that trained observers made hourly estimates of the opaque cloud fraction that obscures the sun, moon, or stars, following the same protocol for 60 years at all stations. These 24 daily estimates of opaque cloud data are of sufficient quality such that they can be calibrated against Baseline Surface Radiation Network data to yield the climatology of the daily short-wave, long-wave, and total cloud forcing (SWCF, LWCF and CF, respectively). This key radiative forcing has not been available previously for climate datasets. Net cloud radiative forcing changes sign from negative in the warm season, to positive in the cold season, when reflective snow reduces the negative SWCF below the positive LWCF. This in turn leads to a large climate discontinuity with snow cover, with a systematic cooling of 10 °C or more with snow cover. In addition, snow cover transforms the coupling between cloud cover and the diurnal range of temperature. In the warm season, maximum temperature increases with decreasing cloud, while minimum temperature barely changes; while in the cold season with snow cover, maximum temperature decreases with decreasing cloud, and minimum temperature decreases even more. In the warm season, the diurnal ranges of temperature, relative humidity, equivalent potential temperature, and the pressure height of the lifting condensation level are all tightly coupled to the opaque cloud cover. Given over 600 station-years of hourly data, we are able to extract, perhaps for the first time, the coupling between the cloud forcing and the warm season imbalance of the diurnal cycle, which changes monotonically from a warming and drying under clear skies to a cooling and moistening under cloudy skies with precipitation. Because we have the daily cloud radiative forcing, which is large, we are able to show that the memory of water storage anomalies, from precipitation and the snowpack, goes back many months. The spring climatology shows the memory of snowfall back through the entire winter, and the memory in summer, goes back to the months of snowmelt. Lagged precipitation anomalies modify the thermodynamic coupling of the diurnal cycle to the cloud forcing, and shift the diurnal cycle of the mixing ratio, which has a double peak. The seasonal extraction of the surface total water storage is a large damping of the interannual variability of precipitation anomalies in the growing season. The large land-use change from summer fallow to intensive cropping, which peaked in the early 1990s, has led to a coupled climate response that has cooled and moistened the growing season, lowering cloud-base, increasing equivalent potential temperature, and increasing precipitation. We show a simplified energy balance of the Prairies during the growing season, and its dependence on reflective cloud.

Analysis of the unique hourly Canadian Prairie data for the past 60 years has transformed our quantitative understanding of land–atmosphere–cloud coupling at northern latitudes. The Canadian Prairie data is exceptional, because observers, typically at most major airports, were trained to estimate hourly the opaque cloud fraction in tenths, by cloud level and in total. These trained observersmade hourly estimates of the opaque cloud fraction that obscures the sun, moon, or stars, following the same protocol for 60 years at all stations. These 24 daily estimates of opaque cloud data are of sufficient quality that they can be calibrated against Baseline Surface Radiation Network data to yield the climatology of the daily short-wave, long-wave, and total cloud forcing (SWCF, LWCF and CF, respectively). This key cloud radiative forcing has not been available previously for surface climate datasets. Net cloud radiative forcing changes sign from negative in the warm season, to positive in the cold season, when reflective snow reduces the negative SWCF below the positive LWCF. This in turn leads to a large climate discontinuity with snow cover, with a systematic cooling of 10°C or more with snow cover. In addition, snow cover transforms the coupling between cloud cover and the diurnal range of temperature. In the warm season, maximum temperature increases with decreasing cloud, while minimum temperature barely changes; while in the cold season with snow cover, maximum temperature decreases with decreasing cloud, and minimum temperature decreases even more. In the warm season, the diurnal ranges of temperature, relative humidity, equivalent potential temperature, and the pressure height of the lifting condensation level are all tightly coupled to the opaque cloud cover. Given over 600 station-years of hourly data, we are able to extract, perhaps for the first time, the coupling between the cloud forcing and the warm season imbalance of the diurnal cycle, which changes monotonically from a warming and drying under clear skies to a cooling and moistening under cloudy skies with precipitation. Because we have the daily cloud radiative forcing, which is large, we are able to show that the memory of water storage anomalies, from precipitation and the snowpack, goes back many months. The spring climatology shows the memory of snowfall back through the entire winter, and the memory in summer, goes back to the months of snowmelt. Lagged precipitation anomalies modify the thermodynamic coupling of the diurnal cycle to the cloud forcing, and shift the diurnal cycle of the mixing ratio, which has a double peak. The seasonal extraction of the surface total water storage is a large damping of the interannual variability of precipitation anomalies in the growing season. The large land-use change from summer fallow to intensive cropping, which peaked in the early 1990s, has led to a coupled climate response that has cooled and moistened the growing season, lowering cloud-base, increasing equivalent potential temperature, and increasing precipitation. We show a simplified energy balance of the Prairies during the growing season, and its dependence on reflective cloud.