In response to the rapid growth in demand for high-precision location-based services driven by the widespread adoption of smart devices, and considering the limited positioning accuracy and stability of global navigation satellite systems (GNSS) in complex environments, this paper proposes a GNSS/fifth-generation (5G) integrated high-precision positioning method designed for smartphone platforms. Specifically, a joint smoothing model is constructed by integrating multi-frequency carrier phase, Doppler shift, and initial GNSS/5G positioning estimates to enhance the continuity and reliability of pseudorange observations in complex environments; inter-satellite and inter-base-station single-differencing techniques are applied to GNSS and 5G observations, respectively, and combined with a non-combined solution model, in order to eliminate receiver clock bias and improve robustness against frequency instability. Results demonstrate that the proposed approach achieves measurable gains in positioning accuracy compared with GNSS-only positioning. In static open-sky experiments, the horizontal RMS error of the Huawei P40 decreased from 0.648 m to 0.385 m, while that of the Xiaomi 11 decreased from 0.692 m to 0.466 m. Under obstructed conditions, 5G integration mitigated GNSS degradation, reducing the vertical RMS error of the Huawei P40 from 2.374 m to 1.762 m and that of the Xiaomi 11 from 2.535 m to 1.900 m. With carrier-phase observations, the inclusion of 5G measurements was still effective in accelerating convergence and enhancing positioning accuracy and stability across both open-sky and obstructed environments. These results validate the feasibility and practical value of GNSS/5G integration for enhancing smartphone positioning accuracy and continuity across diverse environments.

The performance of Global Navigation Satellite Systems (GNSS) in high-latitude marine environments is critical for maritime navigation and scientific research. This study uses dynamic observations. It systematically evaluates GNSS signal quality and precise positioning capabilities in the Southern Hemisphere's high-latitude seas. Results show that the Number of Visible Satellites remains above 11 at a 10 degrees cut-off elevation angle, ensuring sufficient satellite availability. The average Position Dilution of Precision (PDOP) for individual systems is around 2.0, while the combined PDOP across all systems falls below 1.0, indicating optimal satellite geometry. Signal strength is robust, with an average Carrier-to-Noise Ratio exceeding 40 dBHz, and the BeiDou Navigation Satellite System (BDS) demonstrates superior multipath resistance (23 cm) compared to other systems. In Real-Time Kinematic (RTK) positioning, GNSS surpass sub-meter three-dimensional accuracy, with horizontal accuracy better than 2 cm and vertical accuracy better than 8 cm. BDS outperforms Global Positioning System (GPS) in RTK positioning, and the combined GPS/BDS system improves horizontal accuracy by 33.33 %, vertical accuracy by 16.44 %, and fix rate by 1.1 %. For Precise Point Positioning (PPP), GPS achieves 0.124 m three-dimensional accuracy, while multi-system combinations enhance accuracy to centimeter level (horizontal <4 cm, vertical <9 cm) and reduce the convergence time by over 70 %. These findings provide valuable reference for high-precision GNSS applications and marine development in the high-latitude regions of the Southern Hemisphere. (c) 2025 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated navigation is one of the key methods for achieving precise positioning in complex urban environments. However, in some scenarios such as urban canyons, overpasses, and foliage occlusion, GNSS signals are frequently attenuated or interrupted, leading to degraded positioning accuracy when relying solely on INSs. To address this limitation, this study developed an improved GNSS/INS-integrated navigation algorithm based on a hybrid framework that combines a Robust Adaptive Kalman Filter (RAKF) with a Radial Basis Function (RBF) neural network. The RAKF allows a multi-criterion optimization strategy to be created to adaptively adjust the measurement noise covariance matrix according to GNSS data quality indicators such as PDOP, the number of satellites, and signal quality factors. This enhances the filter’s robustness and outlier detection capability under degraded GNSS conditions. Meanwhile, the RBF network is trained to predict pseudo-position increments, which substitute missing GNSS measurements during signal outages to maintain continuous navigation. Real-world vehicular experiments were conducted to evaluate the proposed RBF-aided RAKF (RBF-RAKF) against three other methods: the Extended Kalman Filter (EKF), standard RAKF, and RBF-aided Kalman Filter (RBF-KF). The experimental results demonstrate that during GNSS outages the proposed method achieved root mean square (RMS) positioning errors of 0.94, 1.02, and 0.21 m in the north, east, and down directions, respectively, representing improvements of over 90% compared with conventional filters. Moreover, the algorithm maintained meter-level horizontal accuracy and sub-meter vertical precision under severe GNSS signal degradation. These results confirm that the proposed RBF-RAKF algorithm provides stable and high-precision navigation performance in challenging urban environments.

The economic and strategic value of high-latitude maritime regions is increasingly significant, yet traditional Global Navigation Satellite Systems remain constrained by unfavorable geometric configurations and slow convergence speeds at high latitudes, failing to meet the growing demand for real-time centimeter-level high-precision positioning in these areas. Benefiting from their rapid motion and superior coverage over high-latitude zones, Low Earth Orbit (LEO) satellites offer an effective means to enhance positioning performance in such regions. This paper uses the real BDS data collected by an unmanned surface vessel in the high-latitude waters of the Southern Hemisphere, jointly simulates polar and medium-inclination LEO constellations, and systematically assess the enhancement effects of LEO augmentation on Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) techniques. The results demonstrate that the polar-orbiting constellation markedly improves the observation environment, increasing the number of visible satellites by 70.2% and reducing the Position Dilution of Precision from 2.4 to 1.7, whereas the medium-inclination orbit constellation offered negligible improvement due to insufficient visibility. The rapid geometric change brought by LEO constellations is the core key to achieving fast convergence. Incorporating LEO observations drastically shortened the BDS PPP convergence time from 45.3 min to under 1 min, achieving a reduction of over 97%. Simultaneously, it improved the three-dimensional Root Mean Square accuracy by 54.7%, from 0.086 m to 0.039 m. Convergence within one minute was consistently achieved when at least 5.4 LEO satellites were included in the solution. Moreover, the addition of LEO signals increased the fixed solution rate of short-baseline RTK from 96.5% to 100%, while improving horizontal and vertical accuracy by 31.5% and 12.3%, respectively. This study confirms that LEO constellations, especially those in polar orbits, can substantially enhance BDS precise positioning performance in high-latitude maritime environments, thereby providing critical technical support for related navigation applications.

In the precise point positioning-ambiguity resolution (PPP-AR) method, the wide-lane (WL) and narrow-lane (NL) uncalibrated phase delays (UPDs) are instrumental in resolving the WL and NL ambiguities, respectively, ultimately achieving PPP-AR. In the traditional UPD estimation algorithms, the ionosphere-free (IF) ambiguity is typically employed for estimating NL ambiguities and isolating NL UPDs. However, in the PPP algorithm, IF ambiguities are treated as constant parameters, which necessitates the separation of time-varying UPD products from these constants. This approach inherently results in that the NL UPDs for each satellite being significantly influenced by the cumulative observation data from prior epochs, which might even be from a long time ago. To get the true variation characteristics of the NL UPDs, this paper proposes a real-time NL UPD estimation method based on a sliding time window. Specifically, when the reference station performs PPP calculation with the aim of UPDs estimation, the estimation method based on a sliding time window is adopted. The reliability of this new approach has been thoroughly scrutinized through rigorous experimental comparisons. The findings demonstrate that, compared to NL UPDs calculated using the traditional method, the NL UPDs estimated using the proposed method more accurately reflect the true values of UPDs in the current epoch. Furthermore, the successful fixing rate, the average Time-To-First-Fix (TTFF), and correct fixing rate of PPP-AR results have significantly improved when employing the proposed method.

Since 2020, the BDS-3 has been providing real-time corrections via the B2b signal, enabling users in China and its neighboring regions to achieve kinematic positioning accuracy at the decimeter level. The rapid geometric changes of Low-Earth-Orbit (LEO) satellites facilitate the rapid resolution of phase ambiguities and accelerate the convergence of Precise Point Positioning (PPP). Therefore, this study proposes an LEO-enhanced BDS-3 PPP-B2b positioning model. Firstly, a novel BDS-3 PPP model accounting for satellite clock bias characteristics is proposed, and experimental validation confirms its efficacy. Subsequently, an LEO-enhanced BDS-3 PPP model is developed. Finally, the positioning performance is rigorously evaluated using combined LEO simulation observations and BDS-3 observations. The results indicate that, compared with the traditional PPP model, the new model yields an average convergence time of 25.1 min for experiments where the convergence criterion is jointly satisfied, representing a 35.6% improvement in convergence speed, while maintaining the same positioning accuracy after convergence. When augmented with LEO satellites, the convergence time of the BDS-3 PPP-B2b solution is reduced to less than 2 min. Furthermore, when more than three LEO satellites are available, the mean convergence time is shortened to within 1 min.

The technology of precise point positioning - real time kinematic (PPP - RTK) can realize regional accurate positioning. However, poor quality atmospheric corrections can greatly impact the integer ambiguity resolution. The low reliability of interpolated corrections may arise from blocked transmission of the updated corrections, atmospheric disturbance, and when the user is located outside the service area. Therefore, to maintain a continuous ambiguity-fixed state in an inaccurate correction observation environment, we propose a novel stop-and-go (SAG) kinematic positioning method. Integer ambiguities inherited from the last epoch are used to estimate the ionospheric errors of the current epoch using an inversion calculation method. Unmodeled errors contained in the ionospheric corrections are also considered. We then experimentally compare the proposed method and traditional PPP - RTK and SAG methods with the results of the PPP-ambiguity resolution calculation using geomagnetic storm-influenced data. All indicators, including the number of fixed ambiguities, errors of corrections, successful fix rate, and correct fix rate, confirm the superiority of the proposed method. The proposed method achieves a horizontal correct fix rate of 98% and maintains the vertical correct fix rate above 96% throughout the day. It is proved that for most of the time the novel method can provide continuous ambiguity-fixed solutions for users in an inaccurate correction observation environment.

In this study, 22 maneuvering events of C59 and C60 geostationary equatorial orbit (GEO) satellites of the BeiDou global navigation satellite system (BDS-3) in 2021 were detected and analyzed based on a time-differenced carrier phase velocity measurement algorithm combined with a broadcast ephemeris and station data. We set different empirical thresholds to analyze the effect of threshold selection on the maneuvering detection sensitivity. The sensitivity and consistency of this algorithm for GEO satellite maneuvering detection were analyzed by combining BDS-3 with other Global navigation satellite systems (GNSS) and selecting different geographic stations. The results demonstrate that changing the threshold significantly affects the maneuvering detection of C60, with the optimal maneuvering thresholds of C59 and C60 being 0.045 and 0.02, respectively. A combination of BDS-3 and GPS with equal weights was identified to be most suitable for maneuvering detection of GEO satellites. For any specific maneuver, the difference between the maneuvering time detection of C59 by stations at different geographical locations was no more than 1 min. During the maneuvering detection of C60, the start time of maneuvering detected by African stations was 4.26–8.61 min earlier than that detected by the Chinese and Australian stations, and the end time of maneuvering detected by the African stations was consistent with that detected by the Chinese and Australian stations.

The BeiDou-3 global navigation satellite system (BDS-3) has been widely used in various fields worldwide since its official launch on July 31, 2020. As of August 1, 2021, 33 satellite orbital maneuver events have occurred in BDS-3. The satellite orbits deviate owing to external factors, and orbital maneuvers are required to adjust the orbit to ensure the appropriate operation and service of the system. This study is the first systematic analysis of historical orbital maneuvers since the launch of BDS-3, eight stations that received BDS-3 signals in the Asia-Pacific region and India were selected, and 33 maneuver events of BDS-3 were detected and enumerated using the time-differenced carrier phase velocity measurement algorithm. The results revealed that the method can detect all orbital maneuvers of BDS-3, and the detection results are consistent with the maneuver dates marked by the broadcast ephemeris. In most maneuver events, the detection start and end times were approximately 10–60 min and 30–90 min earlier, respectively, than the marked time in the broadcast ephemeris. The orbital maneuvers of inclined geosynchronous orbit satellites significantly affected the velocity measurements, resulting in a mean error of approximately 0.06–0.73 m/s for each velocity component. Furthermore, the maneuvering of geostationary orbit satellites had a little effect on their velocity, and the mean velocity measurement error was mostly within 0.09 m/s. Among these satellites, the maneuvering of the C60 satellite had a smaller effect on the velocity measurement, and the mean velocity measurement error was within 0.03 m/s. The weak response at the ground level led to the weak detection sensitivity of this method to the maneuver of C60.

The Low Earth Orbit (LEO) satellites can be used to effectively speed up Precise Point Positioning (PPP) convergence. In this study, 180 LEO satellites with a global distribution are simulated to evaluate their contribution to the PPP convergence. LEO satellites can give more redundant observations and improve satellite geometric distributions, particularly for a single Global Navigation Satellite System (GNSS). The convergence speed of the PPP float solution using the Global Positioning System (GPS, G) or BeiDou Navigation Satellite System (BDS, C) single system as well as the G/C/Galileo navigation satellite system (Galileo, E)/GLObal NAvigation Satellite System (GLONASS, R) combined system with LEO satellites added is improved by 90.0%, 91.0%, and 90.7%, respectively, with respect to the system without LEO satellites added. We introduced LEO observations to assist GNSS in PPP-AR (Ambiguity Resolution) and PPP-RTK (Real Time Kinematic). The success fix rate of a single system is significantly improved, and the Time-To-First-Fix (TTFF) of G and G/C/E is reduced by 86.4% and 82.8%, respectively, for the PPP-AR solution. We analyzed the positioning performance of LEO satellite assisted G/C/E PPP-RTK in the reference networks of different scales, namely different atmospheric delay interpolation accuracies. The success fix rate of the G/C/E combined system is improved from 86.8 to 94.9%, and the TTFF is reduced by 36.8%, with the addition of LEO satellites in the 57 km reference network. In the 110 km reference network, the success fix rate of the G/C/E combined system is improved from 64.0 to 88.6%, and the TTFF is reduced by 32.1%. GNSS PPP-RTK with adding the LEO satellites in the reference networks of different scales shows obvious improvement because the atmospheric correlation decreases with increasing distance from the reference networks.

With the addition of multi-frequency and multi-constellation systems, the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm is expected to provide a global vertical and horizontal guidance for the localizer performance of vertical guidance (LPV)-200 approach phase in aeronautical navigation worldwide. Currently, the second and third generations of the BeiDou navigation satellite system (BDS-2 and BDS-3) provide their services to users. We consider ARAIM for dual-frequency iono-free BDS pseudorange combinations. With the aim to improve the service performance of the BDS-2 and BDS-3 systems, the assumed integrity support message (ISM) was used to calculate the vertical protection level (VPL) for the LPV-200 approach. The impact of the different parameters of ISM on the ARAIM availability was evaluated. The results demonstrate that, compared with BDS-3, the global coverage of availability for BDS-2+BDS-3 is slightly higher, mainly due to the increase of the number of visible satellites. The availability of BeiDou in the Americas is affected by user range accuracy (URA). With URA decreasing from 2.0 to 0.5 m, the ARAIM availability of BDS-2+BDS-3 in the Americas increased from 50 to 99.9%.

Precise point positioning (PPP) technology is one of the core technologies in the field of GNSS high-precision positioning. It is used widely because it can realize centimeter-level positioning in outdoor environments by using only a single receiver. However, its convergence is time-consuming, particularly in urban areas where satellite occlusion is more severe. A combined BeiDou Navigation Satellite System (BDS) and fifth generation mobile communication technology (5G) PPP observation model is proposed, in which the two kinds of observations are combined and solved at the original observation level. The impact of different numbers and geometries of 5G base stations on the convergence time of PPP is analyzed from both static and dynamic perspectives. The results confirm that PPP technology combining BDS and 5G can effectively accelerate convergence while improving the accuracy of positioning.

随着全球卫星导航系统(GNSS)的发展和移动通信技术的进步,用户对位置服务(LBS)提出了更高的要求.本文采用市面上常见的两部Android智能手机采集GNSS数据,对Android智能手机伪距单点定位(SPP)和单频精密单点定位(PPP)算法进行研究,分析了在不同条件下智能手机的SPP、单频PPP定位性能.结果表明:在使用多普勒平滑伪距和信噪比随机模型的基础上,Android智能手机GPS单系统的SPP定位精度可达3 m,GPS、Galileo、GLONASS、北斗卫星导航系统(BDS)四系统定位精度可达亚米级.在单频PPP静态定位中,在GPS单系统下,定位精度仅能达到米级,且收敛时间较长;在GPS、Galileo、GLONASS、BDS四系统下,定位精度可达亚米级,且平面方向可在40 min内收敛.在单频PPP动态定位中,手机的定位精度仅能达到米级.

In environments such as urban canyons and indoor environments, an insufficient number of visible satellites can degrade the positioning performance of the BeiDou Navigation Satellite System (BDS). Thus, a positioning algorithm that combines the BDS and 5G technology was developed based on raw observation data. Three different satellite occlusion environments were simulated to compare the effects of factors such as the number of base stations and geometric configurations on the positioning performance. The experimental results revealed that the introduction of 5G base stations effectively increased the positioning accuracy and reliability under different occlusion conditions. Additionally, increasing the number of base stations and optimizing the geometric configuration further improved the accuracy and reliability of fusion localization. Moreover, the positive effects of the introduction of 5G base stations were stronger under more severe satellite occlusion conditions. In the future, this fusion positioning algorithm is expected to facilitate the realization of seamless indoor and outdoor positioning.

In addition to the orbital maneuver information, other satellite anomalies were also marked in the satellite's health status of broadcast ephemeris. For the signal-in-sp ace (SIS) performance evaluation, it is necessary to classify and evaluate the impact of a single fault, as well as the comprehensive impact. Therefore, it remains to identify the satellite orbital maneuver from the broadcast ephemeris and evaluate its impact on the signal-in-space performance. This study proposed an orbit maneuver detection method based on a combination of the square root of the major half-axis of the satellite orbit and the health status of the satellite recorded in broadcast ephemeris. The broadcast ephemerides provided by The Multi-GNSS Experiment (MGEX) from 2016 to 2020 were first used to detect the orbit maneuvers of BeiDou satellites; the orbit maneuvering and recovery periods of GEO and IGSO were detected next. The number of orbital maneuvers of the satellites made each year, and the interval of orbital maneuver of each satellite, was also obtained. The main findings of this study are as follows: (1) the proposed method can detect satellite orbit maneuvers and recovery periods recorded in the broadcast ephemeris; (2) the average orbit maneuvering interval of GEO and IGSO satellites were obtained and found to be approximately 27 days for GEO satellites except C04 and the IGSO, for which they were 45 days and approximately 178 days, respectively; (3) the average recovery time for the two types of satellite orbital maneuvers was about 6.6 h, and generally the same for the BeiDou-3 and BeiDou2 satellites; and (4) using the detected orbital maneuver intervals and recovery periods, its impact on the signal-in-space availability and continuity of the BeiDou satellite was evaluated, which showed that the per-satellite availability of IGSO satellites were approximately 0.998 and 0.9998/h respectively. The per-satellite availability of each GEO satellite was about 0.986-0.996, and the continuity was about 0.9982/h-0.9992/h; therefore, the orbital maneuver reduced the per-satellite availability and continuity of the GEO and IGSO satellites by 0.002-0.014 and approximately 0.0002/h-0.0018/h, respectively. (C)2022 COSPAR. Published by Elsevier B.V. All rights reserved.

不同卫星导航系统之间时差的稳定性分析对时差的建模预报及应用具有重要价值,因此基于由国际GNSS服务(IGS)中心提供的数据和产品从不同测站、不同观测量、不同时间长度三个方面对GPS和北斗三号全球卫星导航系统(BDS-3)的系统时差进行稳定性分析.结果表明:不同测站因接收机、天线、时钟三种设备型号不同,提取的时差值存在差异,但稳定性相当;基于载波相位观测量解算的时差结果稳定性优于伪距观测量解算的时差结果,伪距得到的时差结果万秒频率稳定度在10?12～10?13量级,相位得到的时差结果万秒频率稳定度在10?14量级;通过单天与多天数据的时差解算结果比较,得到不同时长的时差稳定性一致.

地球静止轨道(GEO)卫星为保持地球同步特性,需要频繁进行轨道机动,及时准确的对卫星轨道机动的状态进行动态监测,有助于对卫星真实轨道进行修复,使其在机动过程中仍能提供基本可用的轨道参数.利用基于历元差分测速原理的卫星轨道监测模型,对北斗三号卫星导航系统(BDS-3)的2颗GEO卫星各12次历史机动进行了分析.结果表明:所选不同空间尺度测站网均可以对C59卫星的机动时间与轨道动态变化进行实时监测,且监测结果基本一致.另外,本文所选的不同空间尺度测站网均可对C60卫星机动时间进行精准探测,但在对其轨道状态进行实时监测时,空间尺度较大的测站网监测结果更优.

若全球卫星导航系统(GNSS)观测值域综合改正数中存在粗差或周跳则不可避免地会影响精密单点定位(PPP)增强的定位结果.针对综合改正数中可能存在的异常,对综合改正数质量控制方法开展研究并提出异常识别与控制算法.该算法根据综合改正数特点,利用经过频间和二阶历元间差分后的综合改正数组合值采用中位数法进行异常识别与定位,并对使用该异常值的卫星采用模糊度重新初始化、降权或剔除方法进行控制处理,以减少异常值对结果的影响.以平均边长为26 km的部分香港连续运行参考站(CORS)组成的参考网以及科廷大学提供的零基线数据对该方法验证,结果表明:对30 s采样间隔的数据该方法能够有效探测出差分组合值中大部分1周以上的较大异常和部分1周以内的异常,有效控制部分异常值对定位结果的影响.

In PPP-RTK, obtaining accurate atmospheric delay information for the user through interpolation is one of the keys to achieving high-precision real-time positioning. The ionospheric delay that is extracted by a reference network based on uncalibrated phase delay (UPD) products is often difficult to separate from errors such as receiver code hardware delay and UPD reference error. Inter-satellite single-difference (SD) ionospheric delay information is typically provided to the user. This paper proposes an interpolation model that uses the atmospheric delay coefficient to represent the SD ionospheric delay, based on the mean position of the ionospheric pierce point (IPP) of each satellite pair and the center position of the network, which is called the differenced surface model (DSM). We chose four scenarios to compare the interpolation accuracy of the proposed model with the inverse distance-based linear interpolation method (DIM) and USM based on the difference between the longitude and latitude of the reference and ionospheric pierce point (IPP) of every satellite (here, we call it USM for short). The four scenarios involve a medium-scale reference network with an average distance to the reference station of 41 km, a large-scale reference network with an average distance to the reference station of 98 km, and out-of-network users, and a network with a common minimum of three reference stations. The results show that the root mean square (RMS) of the SD residuals of ionospheric delay for DSM were 1.4, 3.2, 2.2, and 1.4 cm, respectively, for the four scenarios that were considered, which are slightly better delay values than those that were achieved using DIM and USM. For the scenario with three reference stations, the interpolation accuracies of DIM and DSM were no different from those for four reference stations, indicating that the server can still try to provide ionospheric correction service under the condition of fewer reference stations. In contrast, USM could not provide service because it lacked the sufficient number of reference stations. DSM was used as the ionospheric delay interpolation model to analyze GPS and Galileo dual-system PPP-RTK positioning performance. In addition, the atmospheric parameter constraint method of users was used in PPP-RTK in reference networks of different scales. For the 41-km and 98-km reference networks, the time to first fix (TTFF) were 14.5 s and 33.1 s, respectively, and the mean RMS values for the east (E), north (N), and up (U) directions were 0.80, 0.93, and 2.72 cm, respectively, and 1.0, 1.1, and 4.0 cm, respectively, for a period of 5 min after convergence. The fixing rate and positioning accuracy of DSM during the 5-min period were better than those of DIM when the same empirical model was used to determine the mean square error of atmospheric delay.

随着全球卫星导航系统(GNSS)的不断建设,智能手机基于移动位置服务(LBS)得到了迅猛发展.文中选取市面上常见的3种手机机型,包括:三星S9+(Exynos)、华为Mate30和华为P40 Pro作为研究对象,并使用北斗星通UR4B0-D高性能GNSS接收机进行同步静态观测实验,从卫星可见数、载噪比(CNR)、卫星高度角和多路径误差等方面,对手机GNSS数据质量进行分析.结果表明:不同型号手机在观测能力和数据质量方面存在明显差异.Android智能手机的GNSS数据质量较差,CNR较小,且CNR与卫星高度角无明显关系.此外,多路径误差是影响Android智能手机高精度定位的主要误差项之一.