Ionospheric correction using NTCM driven by GPS Klobuchar coefficients for GNSS applications

Global Navigation Satellite Systems (GNSS) require mitigation of ionospheric propagation errors because the ionospheric range errors might be larger than tens of meters at the zenith direction. Taking advantage of the frequency-dispersive property of ionospheric refractivity, the ionospheric range errors can be mitigated in dual-frequency applications to a great extent by a linear combination of carrier phases or pseudoranges. However, single-frequency GNSS operations require additional ionospheric information to apply signal delay or range error corrections. To aid single-frequency operations, the global positioning system (GPS) broadcasts 8 coefficients as part of the navigation message to drive the ionospheric correction algorithm (ICA) also known as Klobuchar model. We presented here an ionospheric correction algorithm called Neustrelitz TEC model (NTCM) which can be used as complementary to the GPS ICA. Our investigation shows that the NTCM can be driven by Klobuchar model parameters to achieve a significantly better performance than obtained by the mother ICA algorithm. Our research, using post-processed reference total electron content (TEC) data from more than one solar cycle, shows that on average the RMS modeled TEC errors are up to 40% less for the proposed NTCM model compared to the Klobuchar model during high solar activity period, and about 10% less during low solar activity period. Such an approach does not require major technology changes for GPS users rather requires only introducing the NTCM approach a complement to the existing ICA algorithm while maintaining the simplicity of ionospheric range error mitigation with an improved model performance.     

Ionospheric tomography using GNSS: multiplicative algebraic reconstruction technique applied to the area of Brazil

Experimental analysis was performed using multiplicative algebraic reconstruction technique (MART) to map the ionosphere over Brazil. Code and phase observations from the global navigation satellite system (GNSS) together with the international reference ionosphere (IRI) enabled the estimation of ionospheric profiles and total electron content (TEC) over the entire region. Twenty-four days of data collected from existing ground-based GNSS receivers during the recent solar maximum period were used to analyze the performance of the MART algorithm. The results were compared with four ionosondes. It was demonstrated that MART estimated the electron density peak with the same degree of accuracy as the IRI model in regions with appropriate geometrical coverage by GNSS receivers for tomographic reconstruction. In addition, the slant TEC, as estimated with MART, presented lower root-mean-square error than the TEC calculated by ionospheric maps available from the International GNSS Service (IGS). Furthermore, the daily variations of the ionosphere were better represented with the algebraic techniques, compared to the IRI model and IGS maps, enabling a correlation of the elevation of the ionosphere at higher altitudes with the equatorial ionization anomaly intensification. The tomographic representations also enabled the detection of high vertical gradients at the same instants in which ionospheric irregularities were evident.     

GNSS电离层TEC和闪烁接收机监测

GAMIT／GLOBK是全球应用最广泛的高精度GPS数据处理软件之一,不仅在高精度定位方面得到应用,而且在全球地壳板块运动监测、电离层监测和GPS气象学等领域也得到广泛应用。本文介绍了在Windows7系统下实现Ubunru Kylin16.04桌面版系统的安装,并在Ubuntu Kylin系统平台下安装、更新最新版GAMIT／GLOBK10.60,并利用中国及其周边IGS站观测数据进行基线解算和网平差,验证了软件安装的正确性。      

Weighted discriminators for GNSS BOC signal tracking

Modern Global Navigation Satellite System including Galileo and GPS III will employ multiplexed binary offset carrier (MBOC) modulation to achieve spectrum separation and enhanced tracking performance. A challenge of the MBOC or BOC signal tracking is the presence of ambiguities due to multiple sidepeaks of the autocorrelation functions. Several different techniques including multi-correlator and double estimator schemes have been proposed to address the ambiguity issue. We propose a class of ambiguity-free code tracking techniques by exploiting the unique features of the BOC modulation. In the proposed architecture, the incoming BOC-modulated signals are correlated with BOC-modulated replica and the spreading codes, respectively. Through a multiplicative combination strategy of the two correlator outputs, a noncoherent weighted discriminator is formed and shown to possess the ambiguity-free property. The multipath effect is assessed and compared with existing early-minus-late power and autocorrelation sidepeak cancellation technique discriminators. The noise effects of the theory and simulation are also discussed. In order to further verify the proposed scheme, a set of field data of a Galileo in-orbit validation satellite is collected and processed. It is demonstrated that the proposed method is simple to implement, free from ambiguities, and yields acceptable performance in the presence of multipath and noise.     

CAPS信号模拟器研究与实现

CAPS信号模拟器,是模拟CAPS接收机在各种运动环境中接收到的CAPS信号,用于实验室条件下测试接收机在各种环境下的性能。本文通过对CAPS系统数学模型的研究,结合CAPS系统特有的虚拟星上原子钟概念,分析了模拟器实现的核心技术——信号延迟表达式,及其基于FPGA实现的关键技术,并给出了模拟器的软硬件实现方法。最后的测试结果表明模拟器可以按设计要求输出精确的仿真信号,可应用于工程实践。     

Ionospheric error contribution to GNSS single-frequency navigation at the 2014 solar maximum

For single-frequency users of the global satellite navigation system (GNSS), one of the main error contributors is the ionospheric delay, which impacts the received signals. As is well-known, GPS and Galileo transmit global models to correct the ionospheric delay, while the international GNSS service (IGS) computes precise post-process global ionospheric maps (GIM) that are considered reference ionospheres. Moreover, accurate ionospheric maps have been recently introduced, which allow for the fast convergence of the real-time precise point position (PPP) globally. Therefore, testing of the ionospheric models is a key issue for code-based single-frequency users, which constitute the main user segment. Therefore, the testing proposed in this paper is straightforward and uses the PPP modeling applied to single- and dual-frequency code observations worldwide for 2014. The usage of PPP modeling allows us to quantify—for dual-frequency users—the degradation of the navigation solutions caused by noise and multipath with respect to the different ionospheric modeling solutions, and allows us, in turn, to obtain an independent assessment of the ionospheric models. Compared to the dual-frequency solutions, the GPS and Galileo ionospheric models present worse global performance, with horizontal root mean square (RMS) differences of 1.04 and 0.49 m and vertical RMS differences of 0.83 and 0.40 m, respectively. While very precise global ionospheric models can improve the dual-frequency solution globally, resulting in a horizontal RMS difference of 0.60 m and a vertical RMS difference of 0.74 m, they exhibit a strong dependence on the geographical location and ionospheric activity.     

BP神经网络辅助的GNSS反射信号土壤湿度反演

针对如何快速准确地估算区域尺度上的土壤湿度问题,该文首先从高质量GPS接收机接收的信噪比观测值中,提取L2C反射信号的振幅和相位作为输入,并采用Noah陆面模型计算土壤湿度值作为期望值,构建基于BP神经网络算法的GNSS卫星反射信号土壤湿度反演模型。实验结果表明:基于BP神经网络算法的GNSS卫星反射信号土壤湿度反演方法获取的土壤湿度结果与土壤湿度参考值误差较小,线性回归的决定系数R2为0.909 1,均方根误差为0.028 7;进一步与线性回归统计模型比较发现,利用BP神经网络模型定量估测土壤湿度明显优于线性回归统计模型,证明了该方法的可靠性。     

Ionospheric tomography based on GNSS observations of the CMONOC: performance in the topside ionosphere

This study carries out a quantitative analysis of the performance of ionospheric tomography in the topside ionosphere, utilizing data of October 2011 collected from 260 Global Navigation Satellite System (GNSS) stations in the Crustal Movement Observation Network of China. This tomographic reconstruction with a resolution of 2° in latitude, 2° in longitude and 20 km in altitude has more than 70 % of voxels traversed by GPS raypaths and is able to provide reliable bottom parts of ionospheric profiles. Compared with the observations measured by the Defense Meteorological Satellite Program (DMSP) satellites (F16, F17 and F18) at an altitude of 830–880 km, the results show that there is an overestimation in the reconstructed plasma density at the DMSP altitude, and the reconstruction is better during daytime than nighttime. In addition, the reconstruction at nighttime also indicates a solar activity and latitudinal dependence. In summary, with respect to DMSP measurements, the daytime bias is on average from ?0.32 × 10⁵/cm³ to ?0.28 × 10⁵/cm³, while the nighttime bias is between ?0.37 × 10⁵/cm³ and ?0.24 × 10⁵/cm³, and the standard deviation at daytime and at nighttime is, respectively, 0.082 × 10⁵/cm³ to 0.244 × 10⁵/cm³ and 0.086 × 10⁵/cm³ to 0.428 × 10⁵/cm³. This study suggests that vertical ionospheric profiles from other sources, such as ionosondes or GNSS occultation satellites, should be incorporated into ground-based GNSS topside tomographic studies.     

近年来我国GNSS电离层延迟精确建模及修正研究进展

空间电离层是影响全球卫星导航系统(GNSS)应用服务性能最棘手的误差源之一。近几十年来,随着地基/空基GNSS数据的日益丰富,国内外学者发展并提出了多种重要技术措施修正、削弱电离层延迟对各类GNSS用户导航定位的影响,取得了重要进展和成果。本文在系统总结GNSS空间电离层延迟影响修正研究成果的基础上,从电离层延迟信息精确提取、建模及误差分析、实时改正方法等几个方面,重点介绍了近年来我国在这一领域的主要研究进展情况。     

Modified compressive sensing approach for GNSS signal reception in the presence of interference

Pre-processing traditional navigation signals in global navigation satellite system (GNSS) receivers includes the conversion of an analog-to-digital sample and acquisition following the basic principle of Nyquist sampling theory. This condition inevitably increases the system computation time and cost of a modern wideband receiver. In recent years, the compressive sensing (CS) approach has been proven to effectively reduce the number of measurement samples required for digital signal acquisition systems. This method gives new potential to this modern design. In this study, a modified compressive sensing algorithm for the acquisition of a GNSS signal that is contaminated by an interfering signal is presented. The proposed method attempts to combine CS demodulation and the subspace projecting method to enhance GNSS signal acquisition performance with interference present. First, the received signal is sub-sampled and aliased from a compressive sampling process. This operation maintains the restricted isometry property (RIP) condition of the second sampling process using a Toeplitz-structured sensing matrix, which replaces a conventional random sensing matrix. The matrix ensures that distances between desired signals on the set of sparse space are not influenced by the sampling process. Next, the interference is eliminated through the orthogonal feature between the interference signal and the desired signal using the subspace projecting method. This also preserves the RIP of the projecting matrix to ensure that the original structure of the linear projection of the signal is preserved. After this, an iterative least-square method is utilized to recover the correlator output from the reception samples taken by the CS demodulator. In addition, the signal detection performance in the presence of co-channel interference using a CS demodulator is analyzed and evaluated. Finally, the relationships between signal detection probability, compressive factor and signal bandwidth are also illustrated. Several numerical results are presented to verify the theory.     

高频GNSS信号去噪的小波和多方向主成分分析

针对传统主成分分析(PCA)忽视测站各坐标分量之间相关性的问题,提出了一种小波去噪和多方向主成分分析(WD-MPCA)组合的方法. 该方法弥补了传统PCA的缺陷,与经验模态分解和主成分分析(EMD-PCA)组合方法及小波去噪和主成分分析(WD-PCA)组合方法相比,WD-MPCA组合方法精度最高. 经WD-MPCA组合方法去噪后,其平均中误差分别为0.83 mm、0.85 mm和8.30 mm,比原始坐标残差时间序列的平均中误差分别降低了81.14%、81.91%和40.37%. WD-MPCA组合方法充分考虑了各测站不同分量之间的相关性,可以有效去除信号中的高频随机白噪声(WN)和低频有色噪声(CN),这对高频全球卫星导航系统(GNSS)技术的实际应用和理论发展具有重要的意义.      

A grid-based tropospheric product for China using a GNSS network

Tropospheric delay accounts for one source of error in global navigation satellite systems (GNSS). To better characterize the tropospheric delays in the temporal and spatial domain and facilitate the safety-critical use of GNSS across China, a method is proposed to generate a grid-based tropospheric product (GTP) using the GNSS network with an empirical tropospheric model, known as IGGtrop. The prototype system generates the GTPs in post-processing and real-time modes and is based on the undifferenced and uncombined precise point positioning (UU-PPP) technique. GTPs are constructed for a grid form (\(2.0{^{\circ }}\times 2.5{^{\circ }}\) latitude–longitude) over China with a time resolution of 5 min. The real-time GTP messages are encoded in a self-defined RTCM3 format and broadcast to users using NTRIP (networked transport of RTCM via internet protocol), which enables efficient and safe transmission to real-time users. Our approach for GTP generation consists of three sequential steps. In the first step, GNSS-derived zenith tropospheric delays (ZTDs) for a network of GNSS stations are estimated using UU-PPP. In the second step, vertical adjustments for the GNSS-derived ZTDs are applied to address the height differences between the GNSS stations and grid points. The ZTD height corrections are provided by the IGGtrop model. Finally, an inverse distance weighting method is used to interpolate the GNSS-derived ZTDs from the surrounding GNSS stations to the location of the grid point. A total of 210 global positioning system (GPS) stations from the crustal movement observation network of China are used to generate the GTPs in both post-processing and real-time modes. The accuracies of the GTPs are assessed against with ERA-Interim-derived ZTDs and the GPS-derived ZTDs at 12 test GPS stations, respectively. The results show that the post-processing and real-time GTPs can provide the ZTDs with accuracies of 1.4 and 1.8 cm, respectively. We also apply the GTPs in real-time kinematic GPS PPP, and the results show that the convergence time of the PPP solutions is shortened. These results confirm that the GTPs can act as an efficient information source to augment GNSS positioning over China.     

组合GNSS观测值反演海面高度EI北大核心CSCD

与验潮站技术相比,岸基全球导航卫星定位系统干涉反射技术(GNSS-IR)海面测高成本较低,且其观测量不受地壳沉降的影响,并可利用目前已有的沿海岸GNSS固定站提供的数据反演海面高度。目前常用观测量为大地测量型GNSS接收机给出的信噪比(SNR)值,然而,早期很多GNSS设备的输出文件中都不包含该值,导致无法利用它们研究海面高度长期变化趋势。但经典的码伪距和载波相位观测值中,同样包含着GNSS-IR测高信息。本文分别引入单频码伪距和单频载波相位的组合,以及单频码伪距和双频载波相位的组合GNSS两种观测值的组合实现了岸基海面测高。本文采用模拟数据证明了基于前一组合的GNSS-IR测高精度受到电离层延迟残差的影响,而后一种组合可避免该误差项的影响。为验证两种组合方法的有效性,在山东威海一海上栈桥上开展了试验,采集了全球定位系统(GPS)和北斗卫星导航系统(BDS)的观测数据,并处理得到了海面测高信息。最后,将反演结果与26 GHz雷达高度计的观测值进行了比较分析,发现二者具有较好的一致性,相关系数均优于85%。试验结果表明:两种码伪距和载波相位组合法均可用于GNSS-IR测高。另外,由于当前GNSS-IR测高受多种误差项影响,导致反演精度较低,使得后一种组合在避免电离层延迟残差方面的优越性并没有明显体现。本文组合方法的引入,增加了海面高度反演方法的多样性,提升了GNSS-IR测高技术的应用空间。     

Ionospheric delay corrections for single-frequency GPS receivers over Europe using tomographic mapping

The majority of navigation satellites receivers operate on a single frequency and experience a positioning error due to the ionospheric delay. This can be compensated for using a variety of approaches that are compared in this paper. The study focuses on the last solar maximum. A 4D tomographic imaging technique is used to map the ionospheric electron density over the European region during 2002 and 2003. The electron density maps are then used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across Europe. The excess delay is applied to correct the pseudo-range single frequency observations at each location and the improvements to the resulting positioning are calculated. The real-time tomographic technique is shown to give navigation solutions that are better than empirical modelling methods and approach the accuracy of the full dual-frequency solution. The improvements in positioning accuracy vary from day to day depending on ionospheric conditions but can be up to 25 m during mid-day during these solar maximum conditions at European mid-latitudes.

Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory

GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications. It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares (ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr–Euchner enumeration (M-SE) and modification of Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension 45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application of the proposed algorithms to the real GPS data.     

Ionospheric super-bubble effects on the GPS positioning relative to the orientation of signal path and geomagnetic field direction

Using GPS data of the Japanese network GEONET, we analyze occurrence of GPS-phase slips and positioning errors during the geomagnetic storm of February 12, 2000. Although the storm was not intensive, registering a minimum Dst excursion of −133 nT and a maximum Kp = 6.7 value, it attracted the attention of researchers because of the appearance of a super-bubble at mid-latitudes. We identified numerous GPS-phase slips in the area of the super-bubble. By the time of the bubble’s appearance, a total of 33% of GPS receivers experienced positioning errors of more than 500 m. Around 13:00 UT, the positioning quality was worse than 100 m almost all of Japan. We also found that the occurrence of phase slips of the satellite signals depends on the angle γ between the receiver-satellite line of sight and geomagnetic field lines. The maximum value of GPS-phase slips corresponds to γ = 0° and 90°. For the satellites positioned close to the magnetic zenith region, the density of phase slips reached 32%. In addition to carrier-phase slips, the super-bubble caused sharp increases in positioning errors of several hundred meters at receiver locations below 38°N latitude. As a result, precise positioning was not possible for about 2 h.     

Integer least-squares theory for the GNSS compass

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the measurement scenarios (e.g. single-epoch vs. multi-epoch, or single-frequency vs. multi-frequency). In particular it is applicable to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance of the different methods is also illustrated.     

Improved vessel squat modeling for hydrographic and navigation applications using kinematic GNSS positioning

The squat phenomenon, that is, the sinkage of a vessel due to its motion can affect the safety of navigation and reduce the accuracy of hydrographic bathymetry. Therefore, it is necessary to model and predict the squat of vessels as a function of cruise speed. We present a Global Navigation Satellite Systems–based squat modeling method for both hydrographic and navigation applications. For implementation of the proposed method, onboard GPS antennae configurations are offered to model bow squat for full-form ships such as supertankers or ore–bulk–oil carriers as well as stern squat for fine-form vessels such as passenger liners or container ships. In the proposed methodology, the onboard GPS observations are used to determine cruise ground speed, heave, attitude, and controlling the quality of kinematic positioning via fixed baselines. The vessel squat is computed from ellipsoidal height differences of the onboard antennae with respect to a reference state, after removal of all disturbing effects due to roll, pitch, heave, tide, vessel load, and geoidal height variations. The final products of the proposed approach are the analytical squat models usable for hydrographic and navigation applications. As the case study, the method is applied to a survey vessel in the offshore waters of Kish harbor. Numerical results indicate that the experimental precision of the derived analytical squat models is in the range of 0.003–0.028 m. The computed navigation squat of the test vessel at a speed of 12.64 knots is 30 % of the vessel draft and about twice its hydrographic squat. Although the field test was performed on a survey vessel, the method can be applied to any ship at any waterway. The proposed method can address the inevitable demand of reliable squat models for delicate hydrographic projects and high-speed marine traffic.     

Sensing strides using EMG signal for pedestrian navigation

Navigation applications and location-based services are now becoming standard features in smart phones. However, locating a mobile user anytime anywhere is still a challenging task, especially in GNSS (Global Navigation Satellite System) degraded and denied environments, such as urban canyons and indoor environments. To approach a seamless indoor/outdoor positioning solution, Micro-Electro-Mechanical System sensors such as accelerometers, digital compasses, gyros and pressure sensors are being adopted as augmentation technologies for a GNSS receiver. However, the GNSS degraded and denied environments are typically contaminated with significant sources of error, which disturb the measurements of these sensors. We introduce a new sensor, the electromyography (EMG) sensor, for stride detection and stride length estimation and apply these measurements, together with a digital compass, to a simple pedestrian dead reckoning (PDR) solution. Unlike the accelerometer, which senses the earth gravity field and the kinematic acceleration of the sensor, the EMG sensor senses action potentials generated by the muscle contractions of the human body. The EMG signal is independent of the ambient environment and its disturbance sources. Therefore, it is a good alternative sensor for stride detection and stride length estimation. For evaluating the performance of the EMG sensor, we carried out several field tests at a sports field and along a pedestrian path. The test results demonstrated that the accuracy of stride detection was better than 99.5%, the errors of the EMG-derived travelled distances were less than 1.5%, and the performance of the corresponding PDR solutions was comparable to that of the global positioning system solutions.