BDS Dual-Frequency Carrier Phase Multipath Hemispherical Map Model and Its Application in Real-Time Deformation Monitoring.

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%.

Zero-Velocity Update-Based GNSS/IMU Tightly Coupled Algorithm with the Constraint of the Earth's Rotation Angular Velocity for Cableway Bracket Deformation Monitoring.

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.

A Modified Kalman Filter for Integrating the Different Rate Data of Gyros and Accelerometers Retrieved from Android Smartphones in the GNSS/IMU Coupled Navigation.

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.

Characteristics of BeiDou Navigation Satellite System Multipath and Its Mitigation Method Based on Kalman Filter and Rauch-Tung-Striebel Smoother.

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.

Adaptive Estimation of Multiple Fading Factors for GPS/INS Integrated Navigation Systems.

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.

An Extended ADOP for Performance Evaluation of Single-Frequency Single-Epoch Positioning by BDS/GPS in Asia-Pacific Region.

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.

A New Adaptive H-Infinity Filtering Algorithm for the GPS/INS Integrated Navigation.

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.

Evaluation of a Cubature Kalman Filtering-Based Phase Unwrapping Method for Differential Interferograms with High Noise in Coal Mining Areas.

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.

A fuzzy identification method for persistent scatterers in PSInSAR technology.

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.