An EMD—Based Fast Algorithm for INS Aided BDS Ambiguity Resolution

Under the high dynamic conditions, Global Navigation Satellite System (GNSS) signals produce great Doppler frequency shifts, which hinders the fast acquisition of signals. Inertial Navigation System (INS)-aided acquisition can improve the acquisition performance, whereas the accuracy of Doppler shift and code phase estimation are mainly determined by the INS precision. The relation between the INS accuracy and Doppler shift estimation error has been derived, while the relation between the INS accuracy and code phase estimation error has not been deduced. In this paper, in order to theoretically analyze the effects of INS errors on the performance of Doppler shift and code phase estimations, the connections between them are re-deduced. Moreover, the curves of the corresponding relations are given for the first time. Then, in order to have a better verification of the INS-aided acquisition, a high dynamic scenario is designed. Furthermore, by using the deduced mathematical relation, the effects of different grade INS on the GNSS (including Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)) signal acquisition are analyzed. Experimental results demonstrate that the INS-aided acquisition can reduce the search range of local frequency and code phase, and achieve fast acquisition. According to the experimental results, a suitable INS can be chosen for the deeply coupled integration.

A novel method of ambiguity resolution and cycle slip processing for single-frequency GNSS/INS tightly coupled integration system

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.

Vehicular dynamic positioning based on tightly coupled (TC) Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integration in urban areas is due to either low accuracy of pseudorange or poor continuity of carrier phase, resulting in insufficient positioning performance. To enhance the stability while ensuring positioning accuracy, this paper proposed a tightly coupled Beidou Navigation Satellite System (BDS)/INS integration scheme by improving measurement modelling with triple-frequency observations: first, a stepwise single-epoch ambiguity resolution of extra-wide-lane (EWL)/wide-lane (WL) combined observations and then modelling the measurement equation with fixed WL observation instead of conventional pseudorange or carrier phase. Experiments were carried out for verification with data collected in real traffic by a measurement vehicle. The proposed method achieved single-epoch output with an RMS statistical accuracy of decimetre level of 0.152 m horizontally and 0.196 m vertically. The signal outage experiment verified that the proposed algorithm is restoring high-accuracy positioning output in single-epoch once the signal is recaptured. The proposed method obtained a positioning accuracy improvement of 43.6% horizontally and 6.2% vertically in signal outage sections compared to the conventional method. This avoids the multiepoch ambiguity searching to fix with conventional carrier-phase processing, thereby improving the positioning stability.

Precise Point Positioning (PPP) is an increasingly recognized precisely the GPS/GNSS positioning technique. In order to improve the accuracy of PPP, the error sources in PPP measurements should be reduced as much as possible and the ambiguities should be correctly resolved. The correct ambiguity resolution requires a careful control of residual errors that are normally categorized into random and systematic errors. To understand effects from two categorized errors on the PPP ambiguity resolution, those two GPS datasets are simulated by generating in locations in South Korea (denoted as SUWN) and Hong Kong (PolyU). Both simulation cases are studied for each dataset; the first case is that all the satellites are affected by systematic and random errors, and the second case is that only a few satellites are affected. In the first case with random errors only, when the magnitude of random errors is increased, L1 ambiguities have a much higher chance to be incorrectly fixed. However, the size of ambiguity error is not exactly proportional to the magnitude of random error. Satellite geometry has more impacts on the L1 ambiguity resolution than the magnitude of random errors. In the first case when all the satellites have both random and systematic errors, the accuracy of fixed ambiguities is considerably affected by the systematic error. A pseudorange systematic error of 5 cm is the much more detrimental to ambiguity resolutions than carrier phase systematic error of 2 mm. In the 2 nd case when only a portion of satellites have systematic and random errors, the L1 ambiguity resolution in PPP can be still corrected. The number of allowable satellites varies from stations to stations, depending on the geometry of satellites. Through extensive simulation tests under different schemes, this paper sheds light on how the PPP ambiguity resolution (more precisely L1 ambiguity resolution) is affected by the characteristics of the residual errors in PPP observations. The numerical examples recall the PPP data analysts that how accurate the error correction models must achieve in order to get all the ambiguities resolved correctly.

The current positioning accuracy of the BeiDou Navigation Satellite System (BDS) Single Point Positioning (SPP) with code measurement is in the order of several metres due to systematic errors. To further reduce the systematic errors in SPP, this contribution develops a new strategy to BDS SPP with a sparse reference network, named Augmented SPP (A-SPP). In this method, the Combined Residual Errors (CRE) products of BDS B1I measurement are integrated with three optional base stations that are close to the rover station. Based on the Satellite Elevation Angle Weighted (SEAW) average technique, the code residual errors of each BDS satellite observed by the rover station can be acquired epoch-by-epoch. Finally, the corrected code observations for the rover station can be utilised to achieve an A-SPP solution. The validation of this method is confirmed by both static and kinematic tests. Results clearly show that the accuracies of the A-SPP solution for horizontal and vertical directions are better than 0·5 m and 1·0 m. This study suggests that the proposed A-SPP solution is a good option for single-frequency GNSS users to improve their positioning performance.

The regional constellation of BeiDou navigation satellite system (BDS) has been officially in operation since December 27, 2012, and real-time kinematic positioning using BDS and GPS multi-frequency observations is feasible. A heavy computational problem arises when resolving ambiguities in the case of multi-system with multi-frequency observations. A multi-carrier fast partial ambiguity resolution strategy is developed with the property that the extra-wide-lane and wide-lane ambiguities in the multi-frequency case can be resolved reliably in advance. Consequently, the technique resolves ambiguities sequentially instead of the usual batch ambiguity resolution (AR) mode so as to improve the computational efficiency of AR significantly. The strategy is demonstrated with real BDS/GPS dual- and triple-frequency observations. The results have shown that the probability of correct AR by the proposed method is comparable to that of the batch AR. Experimentally, the new method is about 2.5 times as fast as the batch AR in the dual-frequency case, 3 times in the mixed dual- and triple-frequency case and 3.5 times in the triple-frequency case.

The BeiDou Navigation Satellite System (BDS) offers orbit and clock corrections through the B2b signal, enabling Precise Point Positioning (PPP) without relying on ground communication networks. This capability supports applications such as aerial and maritime mapping. However, achieving high precision during the convergence period remains challenging, particularly for missions with short observation durations. To address this, we analyze the performance of PPP over short periods using PPP-B2b products and propose using the backward smoothing method to enhance the accuracy during the convergence period. Evaluation of the accuracy of PPP-B2b products shows that the orbit and clock accuracy of the BDS surpass those of GPS. Specifically, the BDS achieves orbit accuracies of 0.059 m, 0.178 m, and 0.186 m in the radial, along-track, and cross-track components, respectively, with a clock accuracy within 0.13 ns. The hourly static PPP achieves 0.5 m and 0.1 m accuracies with convergence times of 4.5 and 25 min at a 50% proportion, respectively. Nonetheless, 7.07% to 23.79% of sessions fail to converge to 0.1 m due to the limited availability of GPS and BDS corrections at certain stations. Simulated kinematic PPP requires an additional 1–4 min to reach the same accuracy as the static PPP. Using the backward smoothing method significantly enhances accuracy, achieving 0.024 m, 0.046 m, and 0.053 m in the north, east, and up directions, respectively. For vehicle-based positioning, forward PPP can achieve a horizontal accuracy better than 0.5 m within 4 min; however, during the convergence period, positioning errors may exceed 1.5 m and 3.0 m in the east and up direction. By applying the smoothing method, horizontal accuracy can reach better than 0.2 m, while the vertical accuracy can improve to better than 0.3 m.

High precision positioning using carrier phase observations is the main method and approach of Beidou navigation satellite system (BDS) positioning. Especially, the ambiguity fixing has always been the focus, and it is always the key problem of the related research. In the medium/long baseline, the ionospheric delay error will affect the efficiency of ambiguity resolution seriously, and then affect the precision and efficiency of precise positioning. To solve this problem, this paper put forward a method of medium/long baseline ambiguity resolution based on the classical three-carrier ambiguity resolution (TCAR) model. To improve the reliability of wide-lane (WL) ambiguity fixing, a factor is introduced into the optimal linear combination for reducing noise, and the ionospheric priori standard deviation is used to minimize the effect of the length of the baseline. In order to verify the feasibility and effectiveness of the algorithm, the proposed algorithm is compared with the classical TCAR algorithm in several aspects such as the ambiguity fixed success rate. The results show that the proposed algorithm has the highest success rate in the case of medium/long baseline, and can fix the ambiguity instantly.

GNSS observation outage occurs inevitably in various situations, e.g., automobile driving in urban environments. Although the ambiguity resolution (AR) significantly shortens the initialization time of precise point positioning (PPP), frequent re-initialization of PPP AR may be needed due to outages. The inertial navigation system (INS) can be used for acquiring highly accurate position information during GNSS outages. In the previous studies, the GPS PPP/INS with the ambiguity resolution model is proposed, and the experimental results confirm that the INS could facilitate the re-fixing of the interrupted GNSS ambiguity. Multiple GNSS can also be used to shorten the PPP convergence time. We compare the contribution of multi-GNSS and the INS to the ambiguity re-fixing during GNSS outage. Results show that the multi-GNSS, e.g., Galileo, GLONASS and BDS, without ambiguity resolution has little contribution to the re-fixing of GPS ambiguity in PPP/INS, while INS can provide highly accurate positioning results during the GNSS outages. The higher the accuracy of the predicted INS positioning, the lower the contribution of multi-GNSS to the re-fixing of the ambiguity in the PPP/INS. The finding is verified by a theoretical analysis, carborne experiment and shipborne experiment. Experiment results show that the re-fixing time is 43 s for GPS PPP and MEMS-grade INS coupled system in GNSS outage of 1 s. The re-fixing time of GPS is slightly changed when adding the multi-GNSS, e.g., Galileo, GLONASS and BDS, without the ambiguity resolution. However, by performing ambiguity resolution to the added GNSS system, the re-fixing time of PPP/INS is significantly reduced from 43 to 4 s. The reason is that, although the multi-GNSS provides little improvement on the accuracy of the ambiguity, it enlarges the number of the ambiguity parameter. The possibility of ambiguity resolution is increased due to the large candidate set of the ambiguity, which reduces re-fixing time.

Traditional single positioning system (such as GPS PPP) can not deal with some complex environment (such as urban canyon). In some complex environments, the distribution of satellite is poor and the number of available satellites is relatively small. The accuracy, availability and reliability of satellite navigation and positioning are directly related to the number of satellites tracked. Therefore, in the harsh environment such as urban canyon, the positioning accuracy has to be improved greatly. Currently the Beidou navigation satellite system (BDS) has been developed, and can solve these problems combined with other GNSS. Based on this, this paper implements GPS/BDS dynamic precise point positioning using Square Root Information Filtering method as parameter estimation method, evaluates the dynamic positioning performance in complex environment, and compares it with a single GPS or Beidou system, including static simulation of dynamic (different satellite cut-off angle), short distance walking gradually from open ground to indoor, vehicle urban environment (under trees, high-rise block road and relatively open road section) .The results show that with the increase of the satellite cut-off angle, the GPS/BDS positioning advantage is more obvious. When the satellite cut-off angle is 40°, it is difficult for a single GPS or Beidou system to maintain high precision positioning, while the GPS/BDS combined system can still maintain the positioning accuracy within 0.2m; In the walking PPP experiment, the GPS / BDS combined system has better positioning stability than GPS and Beidou single system, and the positioning result does not fluctuate much even when it approaches the indoor quickly; In the vehicle PPP experiment, the 3D position error of GPS/BDS combined system is improved by 31.8% and 42.6% compared with a single GPS or Beidou system in relatively open road section, and 68.4% and 73.6% respectively in the section with a signal occlusion. Compared with a single GPS or Beidou system, the GPS/BDS combined system can improve the positioning accuracy greatly when the vehicle is driving on the road with the signal occlusion than on the road without occlusion, which indicates that the combined system PPP is very suitable for solving the problem of poor positioning accuracy of the single system PPP when the vehicle is driving in the area with the signal occlusion.

Temperature variation is an important factor affecting the performance of Quartz flexible accelerometer (QFA). Performance deterioration of QFA degrades the navigation accuracy of inertial navigation system (INS). Normally dramatic change in temperature causes both thermal effect and severe creep effect on the performance of QFA. Previous papers have proved that part of errors caused by thermal effect can be restrained through simple temperature compensation. However, error caused by severe creep effect is seldom considered. In this paper, creep effect and thermal effect in QFA are detailed analyzed, respectively. Furthermore, based on the analysis of thermal effect and creep effect, the novel temperature model based on nonlinear auto-regressive with external input (NARX) improved by wavelet transform (WT) is proposed to address the retardation problem caused by thermal effect. Creep error causing the ruleless deformation of QFA’s structure is separated from overall errors, and only the thermal error whose effect has strong relationship with temperature is compensated by proposed model. Moreover, a 4-point dumpling experiment in temperature control oven is conducted to train and verify the proposed temperature model. The result of the comparative experiments shows that the performance of proposed method is the best among the comparative models. The compensation result based on proposed method improves stability of 1 g output from 776 to 14.6 µg. The proposed temperature compensation method improves the performance of QFA effectively and feasibly, which could be promoted to other applications of INS in temperature changing environment.

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR.

: This report presents the results of investigations in using a medium-to-high accuracy inertial navigation system (INS) and a geodetic quality Global Positioning System (GPS) receiver on an airborne platform to determine the gravity disturbance vector along the trajectory of an aircraft. The main products of these investigations consist of derivations of alternative algorithms to estimate the horizontal gravity vector components given that the INS's under consideration have different types of available output data, either time-integrated accelerations and direction cosines or raw accelerometer and gyro data. In addition, two distinct data processing methodologies are elucidated to combine the GPS and INS data. The first is based on a traditional Kalman filter approach that treats the gravity disturbance vector as a stochastic process, and the second is an extension of the scalar airborne gravimetry concept. also, the configuration details of a loosely coupled INS/GPS system for airborne application are given, with particular emphasis on time synchronization. A limited number of field tests (ground and airborne) with the LN93 and LN100 were performed. Results from these tests verity the specified accuracy of the INS and yield initial attempted estimations of the vertical deflection using the Kalman filter approach. While the latter are inconclusive in assessing the precision level achievable with this method and instrumentation (due to unexpectedly poor gyro performance), they do indicate the feasibility of the approach provided the INS gyros perform at the specified level.

Zero velocity update (ZUPT) is an inexpensive and effective method for error control of inertial navigation system (INS). Detecting the stopping time interval is important for ZUPT methods. The ZUPT method based on Kalman filter has a higher degree of precision compared with the ZUPT method based on curve fitting and the ZUPT method based on maximum likelihood estimation, but the modeling of Kalman filter is critical for the performance of INS. In this paper, three kinds of zero-velocity detectors and a linear discrete Kalman filter model are applied in ZUPT for INS. Simulation results show that the three kinds of zero-velocity detectors are effective, and the ZUPT method based on the linear discrete Kalman filter model makes the positioning accuracy of INS significantly improved.