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Abstract: Abstract Seafloor transponder coordinates are determined by measurements between a ship-borne GNSS-acoustic transducer and the transponder. Differencing techniques can be applied to eliminate the impact of measurement biases for precise positioning effectively. The problem is that the correlations between differenced measurements must be adequately considered in the covariance matrix, which might cause a great number of calculations. This paper presents a set of conversion formulae to derive the differenced solution from the undifferenced model without nuisance parameters, and then we propose a dimension-reduction algorithm to fast solve the Gauss–Markov model augmented with nuisance parameters. The equivalence of the differenced and undifferenced solution is discussed within a wider range. It shows that: (1) the undifferenced solution can be converted into the differenced solution with only a few additional calculations; (2) there are a class of differencing schemes which are completely equivalent to each other having unique differencing equivalence weight (DEW) matrix; (3) the proposed algorithm is more efficient and has a good numerical stability relative to the blocking–stacking algorithm and the one-by-one elimination. The simulation and the real trial performed in a 3000-m depth sea area verified the proposed results. PubDate: 2022-05-20

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Abstract: Abstract I suggest a method for converting geodetic height and latitude from one oblate ellipsoid of revolution to another having the same center and symmetry axis. Unlike other approaches, the method here does not obtain height and latitude from Earth-centered, Earth-fixed (ECEF) Cartesian coordinates; this feature allows height conversion with high accuracy even in cases where the data format limits the precision of the latitude data. Height and latitude conversions can be expressed as a Fourier series in even multiples of latitude, with height changes having only cosines and latitude changes having only sines. The absolute difference of the flattenings of the two ellipsoids furnishes a simple upper bound on the maximum absolute latitude change. Conversions between the TOPEX and WGS84 ellipsoids, a practical necessity for the inter-mission comparison of satellite laser and radar altimeter data, illustrate the findings. Because the differences in the flattenings and semi-major axes of these ellipsoids are small, truncating the Fourier series after the term in twice the latitude gives an approximate conversion with an error less than 9 \(\times \) 10–12 radians of latitude and about 6 \(\times \) 10–6 m of height. PubDate: 2022-05-04

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Abstract: Abstract We employ the barotropic, data-unconstrained ocean tide model TiME to derive an atlas for degree-3 tidal constituents including monthly to terdiurnal tidal species. The model is optimized with respect to the tide gauge data set TICON-td that is extended to include the respective tidal constituents of diurnal and higher frequencies. The tide gauge validation shows a root-mean-square (RMS) deviation of 0.9–1.3 mm for the individual species. We further model the load tide-induced gravimetric signals by two means (1) a global load Love number approach and (2) evaluating Greens-integrals at 16 selected locations of superconducting gravimeters. The RMS deviation between the amplitudes derived using both methods is below \(0.5 \ \) nGal ( \(1 \ \) nGal \(= 0.01 \frac{\text {nm}}{\text {s}^2}\) ) when excluding near-coastal gravimeters. Utilizing ETERNA-x, a recently upgraded and reworked tidal analysis software, we additionally derive degree-3 gravimetric tidal constituents for these stations, based on a hypothesis-free wave grouping approach. We demonstrate that this analysis is feasible, yielding amplitude predictions of only a few 10 nGal, and that it agrees with the modeled constituents on a level of 63–80% of the mean signal amplitude. Larger deviations are only found for lowest amplitude signals, near-coastal stations, or shorter and noisier data sets. PubDate: 2022-04-30

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Abstract: Abstract The ionospheric mapping function (MF) converts the line-of-sight slant total electron content (STEC) into the vertical total electron content (VTEC) and vice versa, and it is an important function in the creation and use of ionospheric models. Most of the existing MFs are only related to satellite elevation angle, the accuracy is low, and it is necessary to establish a MF with higher accuracy. Therefore, this paper considers the differences of MF for different local time (LT) and DOY (day of year), and uses the Global Navigation Satellite Systems (GNSS) STEC observation data from International GNSS Service (IGS) tracking stations in the northern hemisphere mid-latitude region in 2016–2020 to establish a novel MF model. First, we retrieve the mapping coefficient \(\alpha_{h}\) for different LT and DOY, where the results show significant correlation with LT and DOY, and other periodic variations. Then, we use the empirical orthogonal functions (EOF) to decompose the time series, and the first four order EOF components can describe 98.31% of the total variability. Finally, the periodic function is used to fit the time series of EOF, and a small number of model coefficients are obtained. This work employs the differential STEC of 28 IGS tracking stations in the mid-latitudes of the northern hemisphere in 2020 to verify the accuracy of the new MF and compare it with the widely used modified single-layer model (MSLM) MF. The results show that the accuracy of the new MF is higher than the existing MSLM MF when using JPLG (Jet Propulsion Laboratory’s final Global Ionospheric Maps) to convert VTEC to STEC. Compared with MSLM MF, the RMS of the new MF is reduced by 0.24 TECU on average, and the maximum reduction is close to 0.4 TECU (~ 25%). Among the 28 tracking stations that participated in the verification, the new MF is better than MSLM MF on most days, with 7 stations reaching 100% and 20 stations exceeding 95%. For nearly 60% of the days in 2020, the accuracy of the new MF for all tracking stations is better than that of MSLM MF. PubDate: 2022-04-30

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Abstract: Abstract Among the continuous (CONT) campaigns of very long baseline interferometry (VLBI), CONT17 is a special CONT campaign which comprises three independent networks: two legacy networks, and one VGOS network to mainly check possible biases in network geometry. In this study, we estimate all types of geodetic parameters (station and source coordinates, and Earth orientation parameters (EOP)) within the single networks and compare them to investigate potential network dependent biases. Since the separate networks are technically linked to each other by common parameters, i.e. EOP and common radio source coordinates, they can be regarded as a single network on the Earth and integrated in one common adjustment. Thus, we also estimate the station and source coordinates, and the EOP from the integrated networks and compare them with those of the single networks to check the impact on the geodetic parameters. There are both subtle and large biases (up to 7.1 mm between the legacy networks in the Ty component and 23.3 mm between the legacy and VGOS networks in the \(D_3\) component on the surface of the Earth) between the single networks depending on parameter types. The integrated network eventually compensates those differences. Adding the VGOS network to the legacy networks does not show any significant improvement for the latter. However, the integration can provide the VGOS network with better parameter estimates which is important for the new stations. PubDate: 2022-04-27

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Abstract: Abstract Tropospheric delay modeling is challenging in high-precision Very Long Baseline Interferometry (VLBI) analysis due to the rapid water vapor variation and imperfect observation geometry, where observations from Global Navigation Satellite Systems (GNSS) co-locations can enhance the VLBI analysis. We investigate the impact of tropospheric ties in the VLBI and GNSS integrated processing during the CONT05–CONT17 campaigns, and present a method that automatically handles the systematic tropospheric tie biases. Applying tropospheric ties at VLBI–GNSS co-locations enhances the observation geometry and improves the solution reliability. The VLBI network is stabilized, with station coordinate repeatability improved by 12% horizontally and by 28% vertically, and the network scale improved by 32%. The Earth Orientation Parameters (EOP) improve by up to 20%. Both zenith delay and gradient ties contribute to the improvement of EOP, whereas the gradient ties contribute mainly to the improvement of length of day and celestial pole offsets. PubDate: 2022-04-26

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Abstract: Abstract Seasonal deformation related to mass redistribution on the Earth’s surface can be recorded by continuous global navigation satellite system (GNSS) and simulated by surface loading models. It has been reported that obvious discrepancies exist in the seasonal deformation between GNSS estimates and modeled loading displacements, especially in the horizontal components. The three-dimensional seasonal deformation of 900 GNSS stations derived from the International GNSS Service (IGS) second reprocessing are compared with those obtained from geophysical loading models. The reduction ratio of the weighted mean amplitude of GNSS seasonal signals induced by loading deformation correction is adopted to evaluate the consistency of seasonal deformation between them. Results demonstrate that about 43% of GNSS-derived vertical annual deformation can be explained by the loading models, while in the horizontal components, it is less than 20%. To explore the remaining GNSS seasonal variations unexplained by loading models, the potential contributions from Inter-AC disagreement, GNSS draconitic errors, regional/local-scale loading and loading model errors are investigated also using the reduction ratio metric. Comparison of GNSS annual signals between each IGS analysis center (AC) and the IGS combined solutions indicate that more than 25% (horizontal) and 10% (vertical) of the annual discrepancies between GNSS and loading models can be attributed to Inter-AC disagreement caused by different data processing software implementations and/or choices of the analysis strategies. Removing the draconitic errors shows an improvement of about ~ 3% in the annual vertical reduction ratio for the stations with more than fifteen years observations. Moreover, significant horizontal discrepancies between GNSS and loading models are found for the stations located in Continental Europe, which may be dominated by the regional/local-scale loading. The loading model errors can explain at least 6% of the remaining GNSS annual variations in the East and Up components. It has been verified that the contribution of thermoelastic deformation to the GNSS seasonal variations is about 9% and 7% for the horizontal and vertical directions, respectively. Apart from these contributors, there are still ~ 50% (horizontal) and ~ 30% (vertical) of the GNSS annual variations that need to be explained. PubDate: 2022-04-25

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Abstract: Abstract The marine gravity field model is mainly derived from nadir satellite altimetry measurements. However, the accuracy of the east component of the vertical deflection is significantly lower than that of the north component in most areas due to the orbital inclination of altimetry satellites. As a novel altimetry technique, wide-swath altimeters are expected to simultaneously obtain high-precision and high-resolution two-dimensional sea surface height measurements and hence to improve the accuracy and resolution of the recovered marine gravity field model. Here, taking the Surface Water and Ocean Topography (SWOT) wide-swath altimeter mission as an example, based on the proposed nadir ground tracks and swath width, one cycle of SWOT sea surface height measurements is simulated and compared with one year of the simulated sea surface height measurements from the nadir altimeter missions of Jason-1/GM (Geodetic Mission), Cryosat-2/LRM (Low Rate Mode) and SARAL/GM. Then, the vertical deflections are determined in the South China Sea and part of the Indian Ocean. Compared with the EGM2008 gravity field model, the vertical deflections determined by one cycle of SWOT data are better than the results determined by the combined dataset of Jason-1/GM, Cryosat-2/LRM and SARAL/GM data and can significantly improve the accuracy of east vertical deflection. It is determined that the SWOT random and systematic errors have certain effects on the accuracy of the vertical deflection, but these can be reduced by filtering. In addition, under the premise of the expected accuracy and spatial resolution of the SWOT mission, vertical deflections with grid spacing smaller than 1 arcmin and comparable accuracy could be derived. PubDate: 2022-04-21

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Abstract: Abstract Ionospheric models are applied for computing the Total Electron Content (TEC) in ionosphere to reduce its effects on the Global Navigation Satellite System (GNSS)-based Standard Point Positioning (SPP) applications. However, the accuracy of these models is limited due to the simplified model structures and their dependency on the calibration period. In this study, we present a sequential Calibration approach based on the Ensemble Kalman Filter (C-EnKF) to improve TEC estimations. The advantage of C-EnKF, over the frequently implemented state-of-the-art, is that a short period of GNSS network measurements is needed to calibrate model parameters. To demonstrate the results, the International Reference Ionosphere (IRI)-2016 model is used as reference and the Vertical TEC (VTEC) estimates from 53 IGS (the International GNSS Service) stations in Europe are applied as observation. The C-EnKF is applied to calibrate four selected model parameters (i.e., \(IG_{12}\) , URSI(771), URSI(1327) and URSI(1752) related to the ionospheric activity as well as height and density peak-modelling in the F2 layer), which are identified by performing a sensitivity analysis. The calibrated model, called ‘C-EnKF-IRI’, is localized within Europe and can be used for near-real time TEC estimations and forecasting of the next day (at least). Validation against the dual frequency GNSS measurements of three IGS stations indicates that during September 2017, the accuracy of forecasting VTECs is improved up to 64.87% compared to IRI-2016. The electron density (Ne) profiles of C-EnKF-IRI are validated against those of COSMIC products, which indicates \(\sim \) 38.1% improvement during days with low ( \(Kp=3\) ) and high ( \(Kp=8\) ) geomagnetic activity. Applying the forecasts of VTECs in SPP experiments shows similar performance as the 11-days delayed IONEX data, i.e., 51%, 52% and 79%, improvements in estimating ionospheric contributions compared to the usage of the original IRI-2016, Klobuchar and NeQuick-G models, respectively. The TEC forecasts of C-EnKF-IRI are found to be of the same quality of the IONEX final TEC products in SPP applications. PubDate: 2022-04-20

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Abstract: Abstract Sentinel-3 (S3) satellites are equipped with microwave radiometers that perform brightness temperature (TB) measurements at 23.8 and 36.5 GHz to determine the wet tropospheric correction (WTC). The analysis of the two MWR-derived WTC present in S3 products, retrieved from three- and five-input neural network (NN) algorithms, suggest the need for their improvement. Focusing on the inputs and physical component, this paper aims at improving the WTC retrieval for open ocean, considering a suitable learning for S3 and a better accounting for the surface contribution to the WTC retrieval. Adopting a purely empirical approach, the learning database has been built using 1 year (2017) of valid S3A measurements, ERA5-derived WTC, and dynamic sea surface temperature (SST) from ERA5. The proposed approach is a similar NN with four inputs: TB at 23.8 and 36.5 GHz, altimeter backscattering coefficient and SST. Results show that the use of a dynamic SST, instead of static tables as currently adopted in S3, makes the fifth input (vertical temperature decrease) redundant. Comparisons with reference and independent WTC sources show that the WTC derived from this algorithm, when compared with those available in the S3 products, leads to a decrease in the RMS values of WTC differences, with respect to these independent WTC, by about 1 mm globally, that locally can reach almost 1 cm. This study proposes a new approach for the WTC of Sentinel-3 by considering a suitable set of dynamic inputs that better characterize the atmosphere, which is a significant enhancement over the current algorithms. PubDate: 2022-04-19

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Abstract: Abstract GNSS tropospheric tomography is one of the applications of the Global Navigation Satellite Systems (GNSS) signals which attracts more and more interest in the field of meteorology. This method can reconstruct the water vapour of the atmosphere, which has a considerable effect on weather forecasting and early warning systems of severe weather. In GNSS tomography, traditionally, a regular spaced 3D grid stretches from the GNSS network to the effective height of the troposphere in the area of interest. Therefore, this method can offer a permanent monitoring service for water vapour and wet refractivity fields at a low cost and a reasonable spatial resolution compared to conventional observations, like radiosonde and radio occultation profiles. Nevertheless, the quality of the reconstructed field is still one of the challenges in the GNSS tomography. In this research, we propose the concept of spread as a mathematical tool to provide a quality measure without using the reference field and calculating statistical measures like RMSE and Bias. Thereby, two synthetic and one real datasets (part of Germany and Czechia) covering overlapping periods between 29 May and 14 Jun of the year 2013 (DoY 149–165; DoY 160–165; DoY 160–165, 2013) have been tested to investigate the proposed method. According to the obtained results, the proposed tool shows a strong correlation (up to 0.81 for synthetic and 0.72 for real observations) with the standard deviation of the reconstructed wet refractivity with respect to the radiosonde profile reference. The correlation between spread and the Bias of the retrieved wet refractivity field is also significant. However, there is no clear picture depending on the applied spread computation models. Therefore, the spread of the resolution matrix can be used as a proxy for the accuracy of the tomography reconstruction field based on the quality of the observations, the initial field, and the design matrix. PubDate: 2022-04-19

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Abstract: Abstract One of the core products of VLBI is the rapid determination of the Earth rotation parameter, expressed through dUT1. Multiple so-called Intensive observing programs exist that are observing dUT1 on a regular basis. Within this work, a detailed overview over the last five years of the VLBI Intensive observing programs INT2 and INT3 is provided. INT2 sessions are typically observed with a single baseline using a recording rate of \({256}\,\hbox {Mbps}\) while INT3 sessions are multi-baseline Intensives with up to five stations and a recording rate of \({1}\,\hbox {Gbps}\) . The median dUT1 precision estimated from INT2 sessions is \({10.5}\,{\mu }\hbox {s}\) while it is \({5.9}\,\mu \hbox {s}\) for INT3 sessions. The best performing INT2 baseline is between station MK-VLBA and WETTZELL with a median dUT1 formal error of \({6.4}\,\mu \hbox {s}\) and showing only a small bias of \({-2.5}\,\mu \hbox {s}\) w.r.t. the JPL EOP2 series. Starting in 2019, the scheduling strategy of the INT3 sessions was significantly changed, leading to a reduction in the estimated average dUT1 formal errors by 25 % for 4-station sessions and 45 % for 5-stations sessions. Mid-2020, the same change was performed for INT2 sessions, leading to a reduction in the average dUT1 mean formal error of up to 44 % for the baseline between MK-VLBA and WETTZELL. It is further revealed that the precision of single-baseline INT3 analysis is not significantly better than its INT2 counterpart, although a four-times higher data-rate is used. The reason for this is differences in scheduling optimization. On average, the mean formal error of the best single-baseline INT3 analysis is 50 % higher compared to utilizing the whole network. Besides analyzing dUT1 formal errors, the latency of the dUT1 results is compared for three analysis centers. For INT3 sessions, results are typically available within 24 hours, while it takes two to three days for INT2 sessions, due to observations occurring on weekends. Overall, this work provides detailed insight into the INT2 and INT3 session performances while revealing a strong positive trend in the precision of dUT1 measurements over the last years due to changes in the scheduling strategy. PubDate: 2022-04-15

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Abstract: Abstract Every three years, the International VLBI Service for Geodesy and Astrometry (IVS) has carried out a continuous observing campaign (CONT) with the goal of demonstrating state-of-the art Very Long Baseline Interferometry (VLBI) observing since 2002. In 2017, the campaign was unique in two respects: three independent networks ran simultaneously and one of the networks was a demonstration of new VLBI Global Observing System (VGOS) technology. Two 14-station legacy station networks, CONT17-L1 and CONT17-L2 observed in S/X mode and the third network, CONT17-VGOS, consisted of five stations observing in VGOS broadband mode. We investigated the differences between Earth Orientation Parameters (EOPs) and scale parameters estimated from the simultaneous observing sessions of the three networks. Prior studies could not determine VLBI EOP precision or VLBI network biases within the VLBI technique. For CONT17, EOP (X-pole, Y-pole, and UT1) biases between the CONT17-L2 and CONT17-L1 networks were \(-11\pm 12\) \(\mu \) as, \(-19\pm 13\) \(\mu \) as, \(-1.1\pm 1.0\) \(\mu \) s, which are at the 1-sigma level. X-pole, Y-pole, and UT1 biases between the CONT17-VGOS and CONT17-L1 networks were \(-108\pm 24\) \(\mu \) as, \(-17\pm 23\) \(\mu \) as, \(1.4\pm 0.6\) \(\mu \) s. Three corner hat analysis of the CONT17-L1, CONT17-L2, and Global Navigation Satellite System (GNSS) series yielded X and Y polar motion precisions of CONT17-L1: 19.8 \(\mu \) as, 22.4 \(\mu \) as; CONT17-L2: 41.0 \(\mu \) as, 35.2 \(\mu \) as; GNSS: 19.8 \(\mu \) as, 15.0 \(\mu \) as. Session scale parameter precisions of the CONT17-L1 and CONT17-L2 networks based on the standard deviation of their respective scale series are 0.45 ppb and 0.30 ppb. Baseline length repeatabilities for each of the networks indicate that the length precision versus length of the VGOS network is about 0.4 ppb compared to 0.5 ppb for the CONT17-L2 network and 0.6 ppb for the CONT17-L1 network for baselines of length less than 10,000 km. PubDate: 2022-04-09

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Abstract: Abstract Satellite-borne microwave radiometers provide wet tropospheric correction (WTC) for altimetry observations, which is critical to high-accuracy sea surface height (SSH) measurements. However, it was reported that the Haiyang-2A (HY-2A) calibration microwave radiometer (CMR) experienced abrupt 18.7 GHz band failure. The global navigation satellite system (GNSS) can provide (near) real-time accurate WTC with high temporal resolutions. In this study, GNSS observations of 132 global coastal sites from January 2017 to February 2018 are used for CMR validation and calibration. In addition, the European Centre for Medium-Range Weather Forecasts (ECMWF) products during the same period are also used for comparison. After calibration with GNSS observations, the root-mean-square (RMS) of the WTC differences between CMR and ECMWF decreases from 2.53 to 1.66 cm. After calibration with ECMWF products, the RMS of the WTC differences between ECMWF-calibrated CMR and ECMWF is 1.54 cm. Moreover, different processing strategies of WTC are applied to SSH measurements. The mean sea level anomaly (SLA) values of SSH obtained with ECMWF-calibrated CMR are comparable to those obtained with GNSS-calibrated CMR WTC and with ECMWF WTC. In addition, compared to the SLAs of Jason-3, the SLAs of HY-2A obtained with ECMWF WTC show the smallest differences of 7.79 cm in RMS, which are 0.1 cm smaller than those obtained with ECMWF-calibrated CMR WTC and 0.23 cm smaller than those obtained with GNSS-calibrated CMR WTC. The SLAs obtained with original CMR WTC are reduced by approximately 0.8 cm in RMS after using GNSS-calibrated CMR WTC. Therefore, even with the known limitations of ground-based GNSS (non-collocated measurements over land instead of over ocean), it can indeed serve as a valuable WTC source for radiometer calibration due to the lower latency of GNSS observations. PubDate: 2022-04-09

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Abstract: Abstract Prevalent north–south striping (NSS) noise in the spherical harmonic coefficient products of the satellite missions gravity recovery and climate experiment greatly impedes the interpretation of signals. The overwhelming NSS noise always leads to excessive smoothing of the data, allowing a large room for improvement in the spatial resolution if this particular NSS noise can be mitigated beforehand. Here, we put forward a new spatial filter that can effectively remove NSS noise while remaining orthogonal to physical signals. This new approach overcomes the limitations of the previous method proposed by Swenson and Wahr (2006), where signal distortion was large and high-order coefficients were uncorrectable. The filter is based on autocorrelation in the longitude direction and cross-correlation in the latitude direction. The NSS-type noise identified by our method is mainly located in coefficients of spherical harmonic order larger than about 20 and degree beyond 30, spatially between latitudes ± 60°. After removing the dominating NSS noise with our method, a weaker filter than before is added to handle the residual noise. Thereby, the spatial resolution can be increased and the amplitude damping can be reduced. Our method can coincidentally reduce outliers in time series without significant trend bias, which underpins its effectiveness and reliability. PubDate: 2022-04-04

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Abstract: Abstract The strength of the GNSS precise positioning model degrades in cases of a lack of visible satellites, poor satellite geometry or uneliminated atmospheric delays. The least-squares solution to a weak GNSS model may be unreliable due to a large mean squared error (MSE). Recent studies have reported that Tikhonov’s regularization can decrease the solution’s MSE and improve the success rate of integer ambiguity resolution (IAR), as long as the regularization matrix (or parameter) is properly selected. However, there are two aspects that remain unclear: (i) the optimal regularization matrix to minimize the MSE and (ii) the IAR performance of the regularization method. This contribution focuses on these two issues. First, the “optimal” Tikhonov’s regularization matrix is derived conditioned on an assumption of prior information of the ambiguity. Second, the regularized integer least-squares (regularized ILS) method is compared with the integer least-squares (ILS) method in view of lattice theory. Theoretical analysis shows that regularized ILS can increase the upper and lower bounds of the success rate and reduce the upper bound of the LLL reduction complexity and the upper bound of the search complexity. Experimental assessment based on real observed GPS data further demonstrates that regularized ILS (i) alleviates the LLL reduction complexity, (ii) reduces the computational complexity of determinate-region ambiguity search, and (iii) improves the ambiguity fixing success rate. PubDate: 2022-03-28

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Abstract: Abstract We propose a novel dictionary learning add-on for the Inverse Problem Matching Pursuit (IPMP) algorithms for approximating spherical inverse problems such as the downward continuation of the gravitational potential. With the add-on, we aim to automatize the choice of dictionary and simultaneously reduce the computational costs. The IPMP algorithms iteratively minimize the Tikhonov–Phillips functional in order to construct a weighted linear combination of so-called dictionary elements as a regularized approximation. A dictionary is an intentionally redundant set of trial functions such as spherical harmonics (SHs), Slepian functions (SLs) as well as radial basis functions (RBFs) and wavelets (RBWs). In previous works, this dictionary was chosen manually which resulted in high runtimes and storage demand. Moreover, a possible bias could also not be ruled out. The additional learning technique we present here allows us to work with infinitely many trial functions while reducing the computational costs. This approach may enable a quantification of a possible bias in future research. We explain the general mechanism and provide numerical results that prove its applicability and efficiency. PubDate: 2022-03-24

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Abstract: Abstract The paper presents a coherent, original theory and an effective algorithm to calculate the surface area of a geodesic polygon, i.e. the area on an ellipsoid of revolution limited by geodesics, connecting pairs of subsequent vertices of known geographical coordinates. Using the cylindrical coordinate system and introducing an equatorial geodesic triangle, the novel strict recursive formulas were derived for the longitude on the ellipsoid and the distance along the geodesic and the area of a geodesic polygon. The area is determined by constant coefficients, not the values of finite series. The orthodromic properties of geodesics, which led to the detection of bifurcation lines composed of the double solutions of the inverse geodetic problem were analysed. The novel algorithm presented, integrating the problem with geodesic polygon area calculation, is based on the newly proposed parameterisation with two alternative working unknowns and a new formula to obtain the initial value of the geodesic C parameter. It allows solutions for all cases, including near-antipodal or near-vertices, and offers two solutions if bifurcation occurs. The algorithm presented was tested and verified using numerical examples from known publications. The numerical tests proved the accuracy of 1m2 of the computed geodesic area using standard IEEE 754 Double Floating Point PC arithmetic, for geodesic lengths up to ten thousand km. PubDate: 2022-03-24

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