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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. [ABSTRACT FROM AUTHOR]

Cableways have been widely used in industrial areas, cities, and scenic spots due to their advantages, such as being a convenient mode of transportation, time-saving, labor-saving, and low cost, as well as offering environmental protection. To ensure the safe operation of a cableway, based on the characteristic that the velocity of the cableway bracket is approximately zero in a static deformation monitoring environment, a deformation monitoring method called zero velocity update (ZUPT)-based GNSS/IMU tightly coupled algorithm with the constraint of the Earth's rotation angular velocity was proposed. The proposed method can effectively solve the problem of a single GNSS being unable to output attitude, which is directly related to the status of wire ropes and cable cars. Meanwhile, ZUPT is used to restrain the Kalman filter's divergence when IMU is stationary. However, the improvements of ZUPT on attitude are not obvious, so the constraint of the Earth's rotation angular velocity was applied. The performance of the proposed method was evaluated through monitoring the cableway bracket of the Yimeng Mountain Tourism area in Shandong. Compared with the ZUPT-based GNSS/IMU tightly coupled algorithm (ZUPT-TC), the proposed method can further constrain the error accumulation of IMU while stationary and, therefore, it can provide reliable position and attitude information on cableway brackets. [ABSTRACT FROM AUTHOR]

The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by applying the double difference observation model. In the actual monitoring environment, due to the complexity of the BDS constellation, it is difficult for existing algorithms to consider GEO, IGSO, MEO and other different orbital types of satellites for real-time and efficient multipath error reduction. Therefore, we propose a novel BDS dual-frequency multipath error reduction method for real deformation monitoring for BDS considering various satellite orbit types. This method extracts the single error residual of each satellite based on the assumption of "zero mean" and divides the appropriate grid density of GEO and IGSO/MEO, respectively, to construct a dual-frequency multipath hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multipath error elimination of the observed values of different orbits and different frequencies. The results of simulation experiments and real deformation monitoring data demonstrate that this method can effectively eliminate low-frequency multipath delay errors in the observation domain and coordinate domain. After multipath correction, the precision of the horizontal coordinates and height coordinates are 1.7 mm and 4.6 mm. The precision of the horizontal coordinate and height coordinate is increased by 50% and 60%, respectively. The fixed rate of ambiguity increased by 5–7%. [ABSTRACT FROM AUTHOR]

As a typical application of geodesy, the GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation technique was developed and has been applied for decades. For the integrated systems with multiple sensors, data fusion is one of the key problems. As a well-known data fusion algorithm, the Kalman filter can provide optimal estimates with known parameters of the models and noises. In the literature, however, the data fusion algorithm of the GNSS/INS integrated navigation and positioning systems is performed under a certain norm, and performance of the conventional filtering algorithms are improved only under this fixed and limited frame. The mixed norm-based data fusion algorithm is rarely discussed. In this paper, a mixed norm-based data fusion algorithm is proposed, and the hypothesis test statistics are constructed and adopted based on the chi-square distribution. Using the land vehicle data collected through the multi-GNSS and the IMU (Inertial Measurement Unit), the proposed algorithm is tested and compared with the conventional filtering algorithms. Results show that the influences of the outlying measurements and the uncertain noises are weakened with the proposed data fusion algorithm, and the precision of the estimates is further improved. Meanwhile, the proposed algorithm provides an open issue for geodetic applications with mixed norms. [ABSTRACT FROM AUTHOR]

The accuracy and integrity of structural deformation monitoring can be improved by the GNSS/accelerometer integrated system, and gross error detection is the key to further improving the reliability of GNSS/accelerometer monitoring. Traditional gross error detection methods assume that real-state information is known, and they need to establish state iterators, which leads to low computational efficiency. Meanwhile, in multi-sensor fusion, if the sampling rates are different, the change in the dimension of the observation matrix must be considered, and the calculation is complex. Based on state-domain consistency theory, this paper proposes the State-domain Robust Autonomous Integrity Monitoring by Extrapolation (SRAIME) method for identifying slow-growing gross errors for GNSS/accelerometer integrated deformation monitoring. Compared with the traditional gross error detection method, the proposed method constructs state test statistics based on the state estimated value and the state predicted value, and it directly performs gross error identification in the state domain. This paper deduces the feasibility of the proposed method theoretically and verifies that the proposed method does not need to consider the dimension change of the observation matrix in gross error detection. Meanwhile, in the excitation deformation experiments of the Suntuan River Bridge in Anhui and the Wilford Bridge in the United Kingdom, the slow gradient of the slope was added to the measurement domain, and the traditional AIME method and the method proposed in this paper were adopted for the gross error identification of the GNSS/accelerometer fusion process. The results demonstrate that both methods can effectively detect gross errors, but the proposed method does not need to consider the dimensional change in the observation matrix during the fusion process, which has better applicability to GNSS/accelerometer integrated deformation monitoring. [ABSTRACT FROM AUTHOR]

Although multiple global navigation satellite systems (multi-GNSS) with more visible satellites have a high success rate, they make positioning time-consuming. Partial ambiguity resolution (PAR) can improve the efficiency of multi-GNSS; however, at present PAR cannot simultaneously achieve fast and high-precision positioning with a high success rate. Therefore, PAR based on ambiguity dilution of precision- and convex-hull-based satellite selection is proposed. The experimental results of the proposed PAR, its corresponding satellite selection algorithm, the classical PAR, and the low-cutoff-elevation-angle-based multi-GNSS show that the proposed PAR outperforms the classical PAR, i.e., it achieves fast and high-precision positioning with a success rate of 100⋅0%. Furthermore, in terms of R-ratio-test-based ambiguity validation, it improves the reliability of carrier-phase-based integrity monitoring of multi-GNSS and the corresponding satellite selection algorithms. In addition, its positioning accuracy is close to that of multi-GNSS and higher than that of the classical PAR, with maximum differences of 0⋅3 and 2⋅4 cm, respectively. The proposed single (dual) frequency-based PAR improves single/dual-frequency multi-GNSS efficiency by more than 54⋅9%/80⋅4% (42⋅0%/75⋅8%) when 14⋅4 (13⋅2) out of 24⋅4 satellites are selected. [ABSTRACT FROM AUTHOR]

Aiming at abrupt faults in GNSS/INS integrated systems in complex environments, classical fault detection algorithms are mostly developed from the measurement domain. A robust chi-square test method based on the state domain is proposed in this paper. The fault detection statistic is built based on the difference between the prior state estimation and the posterior state estimation in Kalman filtering. To improve the calculation stability, singular value decomposition (SVD) is used to factor the covariance matrix of the difference. The relevant formulas of the proposed method were theoretically derived, and the relationship between the proposed method and the existing innovation chi-square test method was revealed. The proposed method was compared with state-of-the-art chi-square test methods and verified by GNSS/INS integrated navigation experiments using simulation data and real data. The experimental results show that the proposed method (a) directly works in the state domain, (b) does not require the known real system state, (c) has computational efficiency and good robustness, and (d) accurately detects abrupt faults. [ABSTRACT FROM AUTHOR]

The fast and high-precision positioning with multiple Global Navigation Satellite Systems (multi-GNSS) has been challenging for decades. Although the single-frequency single system (SF-SS), satellite selection for multi-GNSS, and multi-GNSS-based partial ambiguity resolution (PAR) can achieve rapid positioning, the varying theoretical bases of them result in different fixed reliability of ambiguities. Hence, we provide the theory analyzing the ambiguity resolution capabilities of the named systems. By adding satellite observations, the equations giving the variance–covariance matrix variation of the original float parameters are derived. Then, the relationship between the ambiguity dilution of precision (ADOP) values of the original ambiguity vector (OAV) before and after adding observations is obtained. This is followed by the analyses of the changing trends in the OAV’s probability density function, integer least-squares pull-in region, and the R-ratio test-based integer aperture pull-in region. In terms of precision, ADOP, and R-ratio test-based fixed reliability of ambiguities, the analyses indicate that the multi-GNSS can improve the partial ambiguity estimation and validation. Besides, compared to satellite selection and SF-SS, the PAR is optimal. The BeiDou Navigation Satellite System (BDS) and the Global Positioning System (GPS)-based single-epoch positioning experiments showed that both BDS B1 and B1-based PAR outperform GPS L1 and L1-based PAR in terms of ADOP and R-ratio test-based fixed reliability. The ADOP of the former is smaller than 0.14, and both the R-ratio test-based acceptance and success rates are up to 99.64%. Finally, the false alarm, failure, and detection rates are reduced to 0.34%, 0.0%, and 0.02%, respectively. [ABSTRACT FROM AUTHOR]

Low-cost GPS/INS integration system is the ideal combination of navigation and positioning. However, the sensitivity of low-cost INS is not good enough for the initial alignment in statics base before navigation. Considering this problem, this paper presents an arbitrary misalignment angle error propagation model which does not rely on small misalignment angles assumption and two simplified versions. These models are presented in the ECEF frame approach and are suitable to implement the in-motion alignment with GPS aided. Another three error models based on quaternion, Rodrigues parameters and modified Rodrigues parameters were also proposed. Three experiments were designed to verify the accuracy and computational efficiency of these error models. The experiments' results showed that the small misalignment angle model was applicable to the small misalignment angle for higher computational efficiency but without improvement of accuracy. And the large misalignment angle is the best error model for the initial alignment of the arbitrary misalignment angle. [ABSTRACT FROM AUTHOR]

Interferometric phase filtering represents an indispensable step in interferometric synthetic aperture radar (InSAR) data processing. However, conventional filtering methods fail to make a balance between the noise elimination and phase preserving in strong noise environments or dense fringe regions. This in turn leads to an inaccurate interferometric phase. To overcome this problem, the authors introduce the concept of slope‐compensated filter based on the local adaptive frequency estimation. This method uses the estimation of signal parameters via rotational invariance techniques (ESPRITs), based on the singular value decomposition of the correlation matrix and generalised eigenvalue solution for providing an accurate local fringe frequency. Meanwhile, the size of the estimation window is adaptively determined by the coherence coefficient, and the judgement and modification of the invalid frequency estimation are utilised to further improve the accuracy of the local fringe frequency. Moreover, the authors consider a two‐stage with the back projection technique to further eliminate the noise residual and improve the filtering performance. The simulated and TerraSAR‐X add‐on for Digital Elevation Measurements (TanDEM) data sets are used to verify the effectiveness of the proposed method. The experimental results show that this method is capable of efficiently reducing the noise level as well as minimising the loss of the signal, outperforming other conventional methods. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) carrier phase measurement for short baseline meets the requirements of deformation monitoring of large structures. However, the carrier phase multipath effect is the main error source with double difference (DD) processing. There are lots of methods to deal with the multipath errors of Global Position System (GPS) carrier phase data. The BeiDou navigation satellite System (BDS) multipath mitigation is still a research hotspot because the unique constellation design of BDS makes it different to mitigate multipath effects compared to GPS. Multipath error periodically repeats for its strong correlation to geometry of satellites, reflective surface and antenna which is also repetitive. We analyzed the characteristics of orbital periods of BDS satellites which are consistent with multipath repeat periods of corresponding satellites. The results show that the orbital periods and multipath periods for BDS geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites are about one day but the periods of MEO satellites are about seven days. The Kalman filter (KF) and Rauch-Tung-Striebel Smoother (RTSS) was introduced to extract the multipath models from single difference (SD) residuals with traditional sidereal filter (SF). Wavelet filter and Empirical mode decomposition (EMD) were also used to mitigate multipath effects. The experimental results show that the three filters methods all have obvious effect on improvement of baseline accuracy and the performance of KT-RTSS method is slightly better than that of wavelet filter and EMD filter. The baseline vector accuracy on east, north and up (E, N, U) components with KF-RTSS method were improved by 62.8%, 63.6%, 62.5% on day of year 280 and 57.3%, 53.4%, 55.9% on day of year 281, respectively. [ABSTRACT FROM AUTHOR]

Unwrapping high-noise interferograms, particularly those with discontinuous quality maps, can be a challenge when employing the interferometric-synthetic-aperture-radar technique. This letter improves the performance of the cubature-Kalman-filter phase unwrapping method based on a multireference-point strategy, which prevents the propagation of unwrapped errors from low-quality areas to high-quality areas. In applying this strategy, a selection method for reference points is presented, which overcomes the subjectivity and unpredictability in selecting reference points. In order to emphasize the importance of multiple reference points, other steps (including unwrapping model, quality map, etc.) remained the same. Both simulated and real data experiment results validate the feasibility and effectiveness of the proposed multireference-point strategy and reference-point selection method in overcoming error propagation. [ABSTRACT FROM PUBLISHER]

A new nonlinear robust filter is proposed in this paper to deal with the outliers of an integrated Global Positioning System/Strapdown Inertial Navigation System (GPS/SINS) navigation system. The influence of different design parameters for an H∞ cubature Kalman filter is analysed. It is found that when the design parameter is small, the robustness of the filter is stronger. However, the design parameter is easily out of step in the Riccati equation and the filter easily diverges. In this respect, a singular value decomposition algorithm is employed to replace the Cholesky decomposition in the robust cubature Kalman filter. With large conditions for the design parameter, the new filter is more robust. The test results demonstrate that the proposed filter algorithm is more reliable and effective in dealing with the outliers in the data sets produced by the integrated GPS/SINS system. [ABSTRACT FROM AUTHOR]

The estimation of ambiguity in the global navigation satellite system/inertial navigation system (GNSS/INS) tightly coupled system is a key issue for GNSS/INS precise navigation positioning. Only when the ambiguity is solved correctly can the integrated navigation system obtain high-precision positioning results. Aiming at the problem of ambiguity parameter estimation in GNSS/INS tightly coupled system, a new strategy for ambiguity parameter estimation and elimination is proposed in this paper. Here, the ambiguity parameter is first added to the state equations of GNSS/INS in the estimation process. Then, the strategy of eliminating the parameter is used to improve efficiency. A residual test is carried out based on introducing the ambiguity parameter, thereby reducing or avoiding its influence on the filtering estimation process. Two groups of experiments were carried out and compared with GNSS positioning results. The results showed that, in the open sky observation environment, the positioning accuracy of the GNSS/INS tightly coupled method proposed in this paper was within 5 cm, and the ambiguity fixed rate was more than 97%, which is basically consistent. In a GNSS-denied environment, the positioning accuracy of the GNSS/INS tightly coupled method proposed in this paper was obviously better than that of GNSS, and the positioning accuracy in X, Y, and Z directions was improved by 82.46%, 78.87%, and 79.67%, respectively. The fixed rate of ambiguity increased from 73% to 78.57%. Therefore, in a GNSS-challenged environment, the novel strategy of the GNSS/INS tightly coupled system has higher ambiguity fixed rate and significantly improves positioning accuracy and continuity. [ABSTRACT FROM AUTHOR]

Recent study indicates that by using the inertial measurement unit (IMU) sensors inside smartphones, we can obtain similar navigation solutions to the professional ones. However, the sampling rates of the gyros and accelerometers inside some types of smartphones are not set in the same frequencies, i.e., the gyros of "Huawei p40" are in 50 Hz while the accelerometer is 100 Hz. The conventional method is resampling the higher frequency to the lower frequency ones, which means the resampled accelerometer will lose half frequency observations. In this work, a modified Kalman filter was proposed to integrate all these different rate IMU data in the GNSS/IMU-smartphone coupled navigation. To validate the proposed method, a terrestrial test with two different types of android smartphones was done. With the proposed method, a slight improvement of the attitude solutions can be seen in the experiments under the GNSS open-sky condition, and the obvious improvement of the attitude solutions can be witnessed at the simulated GNSS denied situation. The improvements by 45% and 23% of the horizontal position accuracy can be obtained from the experiments under the GNSS outage of 50 s in a straight line and 30 s in a turning line, respectively. [ABSTRACT FROM AUTHOR]

The Single-frequency Single-epoch double-differenced baseline resolution technique of Global Positioning System (GPS) provides a good opportunity for monitoring the displacement or deflection behavior of bridges under different loading conditions in real-time. However, for single GPS, a high success rate baseline solution is difficult to achieve due to the lack of sufficient visible satellites and the low accuracy of float solutions. Galileo Satellite Navigation System (Galileo) has 14 medium earth orbit satellites (as of May 2018) that can be used to supplement GPS. The frequency bands of Galileo overlap with that of GPS on E1/L1 and E5a/L5, which is conducive to the combination of observations in integration positioning. Accordingly, Galileo augmenting GPS is an effective and necessary approach to improve the positioning availability and reliability. Moreover, using the baseline length constraint can improve the accuracy of float solutions, narrow the search space, and finally increase the success rate of ambiguity resolution and positioning. The single-frequency single-epoch double-differenced GPS/Galileo mathematical model with baseline length constraint is deduced in this paper. Two sets of GNSS real bridge data were used for further analysis on the improvement of GPS/Galileo with baseline length constraint when compared to single GPS. Finally, a Fast Fourier Transformation (FFT) algorithm was adopted for precisely detecting the local dominant frequencies of XB, YB, and ZB direction of the two stations. [ABSTRACT FROM AUTHOR]

The Quasi-Zenith Satellite System (QZSS) service area covers the Asia-Pacific region and there are four quasi-zenith satellites (QZS) in orbit with three QZS in operation until March 2018. The QZSS is not required to work in a stand-alone mode, but the system can be used to enhance the Global Positioning System (GPS) or Beidou Satellite Navigation System (BDS). The availability, position dilution of precision (PDOP), ambiguity dilution of precision (ADOP), and success rate of GPS/QZSS and BDS/QZSS under different cut-off elevation angles were compared based on a simulation. Two sets of actual QZSS data were processed and analyzed for single-frequency single-epoch (SFSE) positioning together with GPS/BDS data in this paper. Different combination forms were executed to evaluate the positioning performance of GPS/QZSS and BDS/QZSS for two baseline cases. The results indicate that QZSS is able to increase the SFSE PDOP, ADOP, and success rate of the baseline resolution and decrease the position error for GPS or BDS, especially for longer GPS baseline data. The more QZS are used, the better the enhancement effect. [ABSTRACT FROM AUTHOR]

Persistent Scatterer SAR Interferometry (PSInSAR) is known as one of the most effective technique for monitoring and analyzing ground deformation. It is a key step that how to identify Persistent Scatterers (PS) effectively and automatically from time-series SAR images. In the past research, one pixel will be classified to "PS" set or "no-PS" set clearly by one or more threshold rules for PS features. However, it is easy to fall into the 'either this or that' logical paradox in some cases because the covered objects in study area usually possess ambiguous boundary for interested characteristics. In this paper, a fuzzy PS concept is present and a fuzzy identification method is designed based on fuzzy set theory by taking the fuzzy characteristics of the pixels into account. Two groups of real data tests indicate that the new method can not only recognize more effective and reliable PS, but also can obtain the better quality results of selected PS, which can be used to evaluate the result of deformation and further improve the PSInSAR technology.

Single-Frequency Single-Epoch (SFSE) high-precision positioning has always been the hot spot of Global Navigation Satellite System (GNSS), and ambiguity dilution of precision (ADOP) is a well-known scalar measure for success rate of ambiguity resolution. Traditional ADOP expression is complicated, thus the SFSE extended ADOP (E-ADOP), with the newly defined Summation-Multiplication Ratio of Weight (SMRW) and two theorems for short baseline, was developed. This simplifies the ADOP expression; gives a clearer insight into the influences of SMRW and number of satellites on E-ADOP; and makes theoretical analysis of E-ADOP more convenient than that of ADOP, and through that the E-ADOP value can be predicted more accurately than through the ADOP expression for ADOP value. E-ADOP reveals that number of satellites and SMRW or high-elevation satellite are important for ADOP and, through E-ADOP, we studied which factor is dominant to control ADOP in different conditions and make ADOP different between BeiDou Navigation Satellite System (BDS), Global Positioning System (GPS), and BDS/GPS. Based on experimental results of SFSE positioning with different baselines, some conclusions are made: (1) ADOP decreases when new satellites are added mainly because the number of satellites becomes larger; (2) when the number of satellites is constant, ADOP is mainly affected by SMRW; (3) in contrast to systems where the satellites with low-elevation are the majority or where low- and high-elevation satellites are equally distributed, in systems where the high-elevation satellites are the majority, the SMRW mainly makes ADOP smaller, even if there are fewer satellites than in the two previous cases, and the difference in numbers of satellites can be expanded as the proportion of high-elevation satellites becomes larger; and (4) ADOP of BDS is smaller than ADOP of GPS mainly because of its SMRW., Competing Interests: The authors declare no conflicts of interest.

Differential interferometric synthetic aperture radar has been shown to be effective for monitoring subsidence in coal mining areas. Phase unwrapping can have a dramatic influence on the monitoring result. In this paper, a filtering-based phase unwrapping algorithm in combination with path-following is introduced to unwrap differential interferograms with high noise in mining areas. It can perform simultaneous noise filtering and phase unwrapping so that the pre-filtering steps can be omitted, thus usually retaining more details and improving the detectable deformation. For the method, the nonlinear measurement model of phase unwrapping is processed using a simplified Cubature Kalman filtering, which is an effective and efficient tool used in many nonlinear fields. Three case studies are designed to evaluate the performance of the method. In Case 1, two tests are designed to evaluate the performance of the method under different factors including the number of multi-looks and path-guiding indexes. The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study. Two case studies are then designed to evaluate the feasibility of the proposed phase unwrapping method based on Cubature Kalman filtering. The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.