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The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by establishing 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, this paper proposes 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 the dual-frequency multi-path hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multi-path 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 is 1.7mm and 4.6mm. 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%.

The monitoring of bridges is a crucial operation for their structural health examination and maintenance. GNSS technology is one of the methods which are applied with the main advantage that the direct measurement of the bridge displacement is conducted in an independent global coordinate system. However, the high cost of the GNSS stations, which are consisted of dual-frequency receivers and geodetic GNSS antennas, is the main reason of the limited application of GNSS for bridge monitoring. In this study, we assessed the performance of low-cost multi-GNSS receivers in monitoring dynamic motion, similar to that of bridge response. The performance of the low-cost GNSS receivers was assessed based on controlled experiments of horizontal and vertical motion. For the horizontal motion, controlled experiments of circular motion of various predefined radius between 5 and 50 cm were executed where the low-cost GNSS receivers were assessed against dual-frequency geodetic receivers. For the vertical motion, manually controlled experiments of vertical oscillations of amplitude 8 and 15 mm were executed where the low-cost GNSS receivers were assessed against the Robotic Total Station (RTS). Finally, a low-cost monitoring system formed by two closely spaced low-cost GNSS receivers was applied in dynamic displacement monitoring of the Wilford Suspension Bridge. The analysis of the low-cost GNSS data revealed the beneficial contribution of (i) the multi-constellation on the accuracy and precision of the GNSS solution and (ii) the combination of closely spaced low-cost GNSS receivers, to limit potential cycle slips and the low-cost GNSS noise level and reach accuracy and precision similar to that of geodetic-grade GNSS receivers. This was confirmed in the bridge monitoring application, where the main modal frequency and the response amplitude of the bridge were identified successfully by the low-cost GNSS receivers’ data analysis.

The issue of non‐linear robust state estimation in the integration of a strapdown inertial navigation system and global positioning system is addressed in this study. Based on the cubature Kalman filtering frame, a non‐linear robust filter called a robust cubature Kalman filter (RCKF) was introduced to address the outliers and the inaccurate model. It has been found that the determination of an optimal restriction parameter is crucial for maintaining the robustness and accuracy of the non‐linear robust filter. Unfortunately, the value of this restriction parameter is always determined by experience. In this study, an iterative strategy was proposed to adaptively attain the optimal restriction parameter without much previous experience. To improve the computational stability of the iterative non‐linear robust filter, a singular value decomposition strategy was adopted simultaneously. Two case studies indicate that the iterative RCKF can achieve greater robustness and accuracy using the methodology discussed in this study.

The recent advances of low-cost GNSS receivers have broadened their application field not only in positioning and navigation, but also in deformation monitoring of civil engineering structures and geohazards. Even though some consumer-grade low-cost GNSS receivers can achieve cm-level accuracy, their lower performance compared to the dual-frequency high-end GNSS receivers restricts its systematic application of GNSS technology in monitoring projects. In this study, the noise level and performance of the low-cost GNSS receivers are assessed against geodetic receivers in terms of precision and availability when subjected to different measurements conditions, such as antenna grade, satellite constellation, and base station (antenna-receiver), based on zero- and short-baseline measurements. Furthermore, a new method is developed where a dual low-cost GNSS rover-system is formed by deploying two closely spaced low-cost GNSS receivers (30 cm apart), aiming to model their common error (multipath, satellite constellation, etc.) and reduce their noise level. The analysis of the zero- and short-baseline measurements reveals the potential improvement of the precision of the low-cost receiver by using multi-GNSS measurements and the importance of using a GNSS base station with geodetic antenna. However, development of a methodology which is based on adopting the sidereal filtering and the common mode error technique for the two closely spaced low-cost GNSS receivers may lead to precision of mm-level. The proposed methodology may broaden the application of low-cost GNSS receivers in monitoring networks and mainly for slowly developed deformations.

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.

With the Global Navigation Satellite System (GNSS) developing, the single-frequency single-epoch multiple GNSSs (multi-GNSS) relative positioning has become feasible. Since a larger number of the observed satellites make the instantaneous (single-epoch) positioning time-consuming, a proper satellite selection is necessary. Among the present methods, the satellite selection with a fixed high cut-off elevation angle (CEA) is least time-consuming. However, there is no criterion how large a fixed high CEA should be to achieve a high success rate and less time consumption. Besides, a fixed high CEA makes the number of visible satellites largely variable, which affects the success rate. Hence, a satellite selection strategy based on ambiguity dilution of precision (ADOP) is proposed. Firstly, the theoretical proof that the ADOP increases the least when removing satellites are all low-elevation-angle satellites is given, which is important to achieve the fast positioning with a high success rate. Then, the threshold β is calculated for a different number of satellites and a given ADOP. The satellites are selected based on their elevation angles from high to low until β of the selected satellites becomes smaller than the corresponding threshold; this method is called the extended floating CEA multi-GNSS (EF-multi-GNSS). The comparison of the single-frequency single-epoch positioning performance of the EF-multi-GNSS with the satellite selections based on a fixed low CEA (L-multi-GNSS) and a fixed high CEA (H-multi-GNSS) via the relative positioning experiments shows that: (1) the EF-multi-GNSS with a minimal number of satellites can achieve the fast positioning and a high success rate close to 100%. It can greatly reduce the time consumption of the L-multi-GNSS, by about 64.0%, by selecting 12.6 satellites of 23.4 satellites; (2) the floating CEA of EF-multi-GNSS eliminates the consideration how large a fixed high CEA should be, and a CEA larger than the fixed high CEA of the H-multi-GNSS makes it more suitable for different conditions.

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.

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.

A new single-epoch single-frequency algorithm based on partial least-squares ambiguity decorrelation adjustment (Par Lambda) that employs baseline constraints is developed for BeiDou Navigation Satellite System (BDS) called Improved Par Lambda, based on the characteristics of building deformation monitoring. The floating solution of double-difference ambiguities is obtained by means of double-difference observations and least-squares method. The double-difference observation equations with baseline length constraint are composed of the equations of BDS single-frequency pseudo-range observations and carrier phase observations and the baseline length constraint equation. The least-squares principle is used to compute floating solution of double-difference ambiguities and the corresponding cofactor matrix. Based on the precision of double-difference ambiguities, the ambiguities will be divided into different levels (2, 1, 1,..., 1) and then be fixed based on the Lambda method progressively. The 1, 5 and 10 s short baseline data of BDS single-epoch single-frequency based on B 1 band carrier phase were computed through this method. The results showed that, for BDS single-epoch single-frequency, the success rate and the search efficiency of fixing ambiguities of Improved Par Lambda were all better than the traditional methods and the success rate was more than 98%.

Water vapor is the basic parameter used to describe atmospheric conditions. It is rarely contained in the atmosphere during the water cycle, but it is the most active element in rapid space–time changes. Measuring and monitoring the distribution and quantity of water vapor is a necessary task. GPS tomography is a powerful means of providing high spatiotemporal resolution of water vapor density. In this paper, a spatial structure model of a humidity field is constructed using voxel nodes, and new parameterizations for acquiring data about water vapor in the troposphere via GPS are proposed based on inverse distance weighted (IDW) interpolation. Unlike the density of water vapor that is constant within a voxel, the density at a certain point is determined by IDW interpolation. This algorithm avoids the use of horizontal constraints to smooth voxels that are not crossed by satellite rays. A prime number decomposition (PND) access order scheme is introduced to minimize correlation between slant wet delay (SWD) observations. Four experimental schemes for GPS tomography are carried out in dry weather from 2 to 8 August 2015 and rainy days from 9 to 15 August 2015. Using 14 days of data from the Hong Kong Satellite Positioning Reference Station Network (SatRef), the results indicate that water vapor density derived from 4-node methods is more robust than that derived from that of 8 nodes or 12 nodes, or that derived from constant refractivity schemes and the new method has better performance under stable weather conditions than unstable weather (e.g., rainy days). The results also indicate that an excessive number of interpolations in each layer reduce accuracy. However, the accuracy of the tomography results is gradually reduced with increases in altitude below 7000 m. Moreover, in the case of altitudes between 7000 m and the upper boundary layer, the accuracy can be improved by a boundary constraint.

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.

The Smart City concept requires new, fast methods for collection of 3-D data representing features of urban landscape. Laser scanning technology (LiDAR - Light Detection and Ranging) enables such approach producing dense 3-D point clouds of millions of points, which, however, contain noise. Therefore, we developed a new approach allowing for a semi-automatic elimination of data noise resulting from motion of objects within the scanned scene such as persons. We used a connected-component labelling method to filter out the noise points from terrestrial laser scanning point clouds. Our approach was based on a step-by-step object classification with a proper parameterisation. In the first step, all points located close to the predicted terrain were selected. In the second step, the points representing the terrain and floor were classified using the surface filter tool implemented in the RiScan Pro software by RIEGL. The rest of points were classified using point cloud clustering via the connected-component labelling method implemented in the CloudCompare software. In the final step, the operator manually decides whether the point cluster represents the noise. The method was applied to the Cathedral of Saint Elizabeth, a sacral object located in the historical centre of the city of Košice in Slovakia during normal operating hours. We managed to capture approximately 80% of the data noise in total. The method provides a better flexibility in surveying overcrowded city locations using the laser scanning technology. URL:https://www.gcass.science.upjs.sk/&nbsp

Phase unwrapping is one of the most critical steps in InSAR data processing. Filter-based phase unwrapping methods can perform phase unwrapping and noise removal simultaneously, and show a clear advantage in dealing with high noise and density fringe interferograms. Based on the precision estimation theory of nonlinear functions in Extended Kalman Filter (EKF) and Cubature Kalman Filter (CKF) algorithms, we derive and analyze in detail the estimated precision of the EKF and the CKF on nonlinear observation equations in the phase unwrapping model. Results show that both EKF and CKF algorithms have similar precision in areas with better phase quality. However, in poorer quality areas, the precision of the two shows a certain difference and there is no consistent superiority for each algorithm. Experiments using simulated and measurement data confirm the validity of our theoretical analysis.

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.

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.

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.

The Kalman filter has been widely applied in the field of dynamic navigation and positioning. However, its performance will be degraded in the presence of significant model errors and uncertain interferences. In the literature, the fading filter was proposed to control the influences of the model errors, and the H-infinity filter can be adopted to address the uncertainties by minimizing the estimation error in the worst case. In this paper, a new multiple fading factor, suitable for the Global Positioning System (GPS) and the Inertial Navigation System (INS) integrated navigation system, is proposed based on the optimization of the filter, and a comprehensive filtering algorithm is constructed by integrating the advantages of the H-infinity filter and the proposed multiple fading filter. Measurement data of the GPS/INS integrated navigation system are collected under actual conditions. Stability and robustness of the proposed filtering algorithm are tested with various experiments and contrastive analysis are performed with the measurement data. Results demonstrate that both the filter divergence and the influences of outliers are restrained effectively with the proposed filtering algorithm, and precision of the filtering results are improved simultaneously.

The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms.

Kalman filter is widely applied in data fusion of dynamic systems under the assumption that the system and measurement noises are Gaussian distributed. In literature, the interval Kalman filter was proposed aiming at controlling the influences of the system model uncertainties. The robust Kalman filter has also been proposed to control the effects of outliers. In this paper, a new interval Kalman filter algorithm is proposed by integrating the robust estimation and the interval Kalman filter in which the system noise and the observation noise terms are considered simultaneously. The noise data reduction and the robust estimation methods are both introduced into the proposed interval Kalman filter algorithm. The new algorithm is equal to the standard Kalman filter in terms of computation, but superior for managing with outliers. The advantage of the proposed algorithm is demonstrated experimentally using the integrated navigation of Global Positioning System (GPS) and the Inertial Navigation System (INS).

Fuzzy integrals are commonly used as aggregation operators. In this paper, we present a new model based on fuzzy integrals with \(\mathfrak{T}\)-norms and \(\mathfrak{T}\)-conorms before obtaining some basic properties. This model can act as an aggregation tool to deal with many information fusing and data mining problems such as programming and classification.

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.