Snow water equivalent (SWE) is a key variable for various hydrological applications. It is defined as the depth of water that would result upon complete melting of a mass of snow. However, until now, ...continuous measurements of the SWE are either scarce, expensive, labor-intense, or lack temporal or spatial resolution especially in mountainous and remote regions. We derive the SWE for dry-snow conditions using carrier phase measurements from the Global Navigation Satellite System (GNSS) receivers. Two static GNSS receivers are used, whereby one antenna is placed below the snow and the other antenna is placed above the snow. The carrier phase measurements of both receivers are combined in double differences (DDs) to eliminate clock offsets and phase biases and to mitigate atmospheric errors. Each DD carrier phase measurement depends on the relative position between both antennas, an integer ambiguity due to the periodic nature of the carrier phase signal, and the SWE projected into the direction of incidence. The relative positions of the antennas are determined under snow-free conditions with millimeter accuracy using real-time kinematic positioning. Subsequently, the SWE and carrier phase integer ambiguities are jointly estimated with an integer least-squares estimator. We tested our method at an Alpine test site in Switzerland during the dry-snow season 2015-2016. The SWE derived solely by the GNSS shows very high correlation with conventionally measured snow pillow (root mean square error: 11 mm) and manual snow pit data. This method can be applied to dense low-cost GNSS receiver networks to improve the spatial and temporal information on snow.
Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these ...parameters with a global network of reference stations is presented. The method processes
uncombined
and
undifferenced
measurements of an
arbitrary
number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense
global
networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.
Real-Time Kinematic (RTK) positioning with lowcost mass-market Global Navigation Satellite System (GNSS) receivers and antennas is attractive for precise landing of Unmanned Air Vehicles (UAV). Code ...multipath mitigation and a reliable resolution of the carrier phase integer ambiguities are two challenges. In this paper, we describe an RTK method which estimates a code multipath parameter for each double difference to fully exploit the temporal correlation of multipath and to prevent a mapping of the multipath into the baseline and ambiguities. The ambiguity fixing is performed in two phases: In the first phase, sets of integer candidate vectors are derived from the float solution at multiple epochs. We merge the sets of candidate vectors to increase the likelihood of including the correct candidate vector in the set of candidates. In the second phase, we track each candidate vector by determining a single epoch baseline estimate for each candidate vector. The respective measurement residuals are accumulated over time to increase the likelihood of selecting the correct candidate. The proposed method was applied to real measurements from two low-cost ANavS GPS modules and enabled a millimeterlevel positioning accuracy despite code multipath of up to 50 m.
Snow water equivalent (SWE) can be measured using low-cost Global
Navigation Satellite System (GNSS) sensors with one antenna placed below the
snowpack and another one serving as a reference above ...the snow. The
underlying GNSS signal-based algorithm for SWE determination for dry- and
wet-snow conditions processes the carrier phases and signal strengths and
additionally derives liquid water content (LWC) and snow depth (HS). So far,
the algorithm was tested intensively for high-alpine conditions with
distinct seasonal accumulation and ablation phases. In general, snow
occurrence, snow amount, snow density and LWC can vary considerably with
climatic conditions and elevation. Regarding alpine regions, lower
elevations mean generally earlier and faster melting, more rain-on-snow
events, and shallower snowpack. Therefore, we assessed the applicability of
the GNSS-based SWE measurement at four stations along a steep elevation
gradient (820, 1185, 1510 and 2540 m a.s.l.) in the eastern Swiss Alps
during two winter seasons (2018–2020). Reference data of SWE, LWC and HS
were collected manually and with additional automated sensors at all
locations. The GNSS-derived SWE estimates agreed very well with manual
reference measurements along the elevation gradient, and the accuracy
(RMSE = 34 mm, RMSRE = 11 %) was similar under wet- and dry-snow
conditions, although significant differences in snow density and
meteorological conditions existed between the locations. The GNSS-derived
SWE was more accurate than measured with other automated SWE sensors.
However, with the current version of the GNSS algorithm, the determination
of daily changes of SWE was found to be less suitable compared to manual
measurements or pluviometer recordings and needs further refinement. The
values of the GNSS-derived LWC were robust and within the precision of the
manual and radar measurements. The additionally derived HS correlated well
with the validation data. We conclude that SWE can reliably be determined
using low-cost GNSS sensors under a broad range of climatic conditions, and
LWC and HS are valuable add-ons.
Linear code combinations have been considered for suppressing the ionospheric error. In the L-band, this leads to an increased noise floor. In a combined L- and C-band (5010–5030 MHz) approach, the ...ionosphere can be eliminated and the noise floor reduced at the same time. Furthermore, combinations that involve both code- and carrier-phase measurements are considered. A new L-band code-carrier combination with a wavelength of 3.215 meters and a noise level of 3.92 centimeters is found. The double difference integer ambiguities of this combination can be resolved by extending the system of equations with an ionosphere-free L-/C-band code combination. The probability of wrong fixing is reduced by several orders of magnitude when C-band measurements are included. Carrier smoothing can be used to further reduce the residual variance of the solution. The standard deviation is reduced by a factor 7.7 if C-band measurements are taken into account. These initial findings suggest that the combined use of L- and C-band measurements, as well as the combined code and phase processing are an attractive option for precise positioning.
Carrier phase measurements of pseudoranges often allow for millimeter precision. The periodic nature of the carrier phase, however, leads to integer ambiguities. These ambiguities need to be resolved ...for accurate positioning. Blewitt and Teunissen provide two methods for the associated estimation process. The present paper complements their work with an improved real-valued diagonalization of the ambiguity covariance matrix, and a functional determination of an integer decorrelation transformation. The proposed method achieves a similar performance as Teunissen's LAMBDA method-in terms of the probability of wrong fixing, but with a reduced complexity. Furthermore, it shows a slightly different path towards ambiguity resolution.
Precise point positioning with multipath estimation Henkel, Patrick; Iafrancesco, Michele; Sperl, Andreas
2016 IEEE/ION Position, Location and Navigation Symposium (PLANS),
04/2016
Conference Proceeding, Journal Article
Odprti dostop
Precise Point Positioning with low-cost GNSS receivers is attractive for numerous applications, as it can provide centimeter-level positioning without the exchange of raw measurements from a ...reference station. However, pseudorange multipath has to be accurately considered for a reliable ambiguity fixing. In this paper, we derive a precise model for the pseudorange multipath from the received signal, the correlator and discriminator function. We consider multiple reflections with individual amplitudes, phasings, Doppler shifts and code delays. We estimate a pseudorange multipath parameter for each satellite in our precise position solution to exploit the temporal correlation of multipath and to prevent a mapping of multipath to other state parameters. The method was tested with real measurements from a low-cost receiver and SSR corrections and showed that a millimeter-level positioning accuracy is achievable.
Global navigation satellites of the European Galileo system transmit code signals on four carriers in the L1, E5a, E5b and E6 band.
New geometry-free linear combinations are presented that eliminate ...the geometry terms (user to satellite ranges and orbital errors), the clock errors of the user and satellites and the tropospheric delay. The remaining parameters of these carrier phase combinations include integer ambiguities, ionospheric delays, carrier phase multipath and phase noise. The weighting coefficients are designed such that the integer nature of ambiguities is maintained. The use of four frequency combinations is highly recommended due to a noise reduction of up to 14.4
dB and an ionospheric reduction of up to 25.6
dB compared to two frequency geometry-free combinations.
Moreover, a modified Least-squares Ambiguity Decorrelation Adjustment (LAMBDA) algorithm is suggested, which differs in two points from the traditional approach: the baseline is replaced by the ionospheric delay and the correlation is caused by linear combinations instead of double differences. For correct ambiguity resolution, the ionospheric delay can be determined with millimeter accuracy. This is quite beneficial as the ionosphere represents the largest source of error for absolute positioning.
Different techniques have been developed for determining carrier phase ambiguities, ranging from float approximations to the efficient solution of the integer least square problem by the LAMBDA ...method. The focus so far was on double-differenced measurements. Practical implementations of the LAMBDA method lead to a residual probability of wrong fixing of the order one percent. For safety critical applications, this probability had to be reduced by eight orders of magnitude, which could be achieved by linear multi-frequency code–carrier combinations. Scenarios with single or no differences include biases due to orbit errors, satellite clock offsets, as well as residual code and phase biases. For this case, a linear combination of Galileo E1 and E5 code and carrier phase measurements with a wavelength of 3.285 m and a noise level of a few centimeters is derived. This ionosphere-free combination preserves the orbit and clock errors, and suppresses the E1 code multipath by 12.6 dB. Since integer decorrelation transformations, as used in the LAMBDA method, inflate biases, the number of such transformations must be limited, and applied in a judicious order. With a Galileo type constellation, this leads to a vertical standard deviation of ca. 20 cm, while keeping the probability of wrong fixing extremely low for code biases of 10 cm, and phase biases of 0.1 cycle, combined in a worst case.
PDF
