A procedure for the significance testing of unmodeled errors in GNSS observations

It is a crucial task to establish a precise mathematical model for global navigation satellite system (GNSS) observations in precise positioning. Due to the spatiotemporal complexity of, and limited knowledge on, systematic errors in GNSS observations, some residual systematic errors would inevitably remain even after corrected with empirical model and parameterization. These residual systematic errors are referred to as unmodeled errors. However, most of the existing studies mainly focus on handling the systematic errors that can be properly modeled and then simply ignore the unmodeled errors that may actually exist. To further improve the accuracy and reliability of GNSS applications, such unmodeled errors must be handled especially when they are significant. Therefore, a very first question is how to statistically validate the significance of unmodeled errors. In this research, we will propose a procedure to examine the significance of these unmodeled errors by the combined use of the hypothesis tests. With this testing procedure, three components of unmodeled errors, i.e., the nonstationary signal, stationary signal and white noise, are identified. The procedure is tested by using simulated data and real BeiDou datasets with varying error sources. The results show that the unmodeled errors can be discriminated by our procedure with approximately 90% confidence. The efficiency of the proposed procedure is further reassured by applying the time-domain Allan variance analysis and frequency-domain fast Fourier transform. In summary, the spatiotemporally correlated unmodeled errors are commonly existent in GNSS observations and mainly governed by the residual atmospheric biases and multipath. Their patterns may also be impacted by the receiver.     

利用Allan方差分析GPS非差随机模型特性

非差GPS定位中,通常采用以观测值服从高斯白噪声条件的估计准则进行参数求解。研究表明卫星端误差、传播路径误差、测站环境误差等会破坏观测值的白噪声特性,并且未模型化误差同样具有不利影响。这不仅破坏了估计准则的假设条件,而且部分非白噪声有可能被状态参数吸收,影响估计的准确性。本文将观测值白噪声、有色噪声和未模型化误差一同纳入GPS非差随机模型,以验后残差来表征GPS数据的随机特性,进行Allan方差分析,研究噪声成分及其参数。结果表明,GPS非差噪声组合主要为WN+GM,相位白噪声为2.392mm,GM过程噪声为4.450mm/s,相关时间为52.074s,伪距白噪声为0.936m,GM过程噪声为0.833m/s,相关时间为14.737s,相位的GM过程噪声与卫星相关性较大,而其余噪声则与测站相关性较大,大量分析结果表明GPS非差随机模型并不服从高斯白噪声假设,有待精化。     

顾及有色噪声的卡尔曼滤波在多路径误差削弱中的应用

多路径误差为一时空环境效应,难以构建准确数学模型消除其影响,且该误差在基线两端不具有空间相关性,运用现有差分技术也无法很好消除,是高精度短基线测量中主要误差之一.为进一步削弱多路径误差,本文以监测站坐标时间序列中多路径误差为研究对象,根据多路径误差在历元间的时变特性,建立多路径误差状态空间模型,采用标准卡尔曼滤波和顾及有色噪声的卡尔曼滤波从监测站第一天双差固定解坐标残差序列中估计多路径误差改正序列,并根据多路径误差的周日重复特性,利用第一天得到的多路径误差改正序列对之后各天坐标序列进行改正.最后通过实验分析,得出顾及有色噪声的卡尔曼滤波估计方法优于标准卡尔曼滤波的结论.研究方法对提高GNSS定位精度具有重要实用价值.     

Using Allan variance to improve stochastic modeling for accurate GNSS/INS integrated navigation

MEMS-based integrated system of a global navigation satellite system (GNSS) and an inertial navigation system (INS) has been widely used in various navigation applications. However, such integration encounters some major limitations. On the one hand, the noisy MEMS-based INS undermines the accuracy with time during the frequently occurring GNSS outages caused by signal blockage or attenuation in certain situations such as urban canyon, tunnels, and high trees. On the other hand, the model mismatch between actual GNSS error and the assumed one would also degrade the obtained accuracy even with continuous GNSS aiding. To improve the overall performance for GNSS/MEMS-INS, better error models can be obtained using Allan variance (AV) analysis technique for modeling inertial sensor errors instead of the commonly recommended auto-regressive processes, and on the other hand, the measurement update in Kalman filter is improved using innovation filtering and AV calculation. The performance of each method and the combined algorithm is evaluated by a field test with either differential GNSS (DGNSS) or single-point positioning (SPP) as external aid. In addition to the considerable navigation enhancement brought by each method, the experimental results show the combined algorithm accomplishes overall accuracy improvements by about 18% (position), 8% (velocity), and 38% (attitude) for integration with DGNSS, and by about 15% (position), 75% (velocity), and 77% (attitude) for that with SPP, compared with corresponding traditional counterparts.     

利用接收机钟差实时滤波提高GNSS精度

建立接收机钟差的高斯马尔可夫模型,通过自相关函数估计接收机钟差的时间常数,利用Allan方差确定模型谱密度参数,将滤波后的接收机钟差返回补偿至GNSS观测方程,重新进行导航解算。实验结果表明,对接收机钟差进行滤波,可有效提高钟差估计精度,提高GNSS的精度。     

基于微惯性技术的室内定位理论及应用

室内定位方法的可行性及准确性成为位置信息服务体系的研究热点,针对移动智能终端普及率的提高,提出了基于内置微惯性传感器的定位理念。通过采用Allan方差分析惯性器件误差参数,并基于频谱分析采用滤波降噪方案提高器件输出信噪比,结合人体运动特征准确判定步态,为零速修正算法的实现提供依据,通过建立局部区域的地磁信息数据库,实现磁匹配零速修正卡尔曼组合误差修正。实验结果验证了基于微惯性技术的室内定位方法的可行性。     

Systematic error mitigation in multi-GNSS positioning based on semiparametric estimation

Joint use of observations from multiple global navigation satellite systems (GNSS) is advantageous in high-accuracy positioning. However, systematic errors in the observations can significantly impact on the positioning accuracy if such errors cannot be properly mitigated. The errors can distort least squares estimations and also affect the results of variance component estimation that is frequently used to determine the stochastic model when observations from multiple GNSS are used. We present an approach that is based on the concept of semiparametric estimation for mitigating the effects of the systematic errors. Experimental results based on both simulated and real GNSS datasets show that the approach is effective, especially when applied before carrying out variance component estimation.     

Android智能手机GNSS高精度实时动态定位

本文基于智能手机GNSS观测值的质量和性质,利用手机载波相位观测值不确定度进行粗差处理,使用星间单差法消除智能手机伪距和载波相位观测值之间差值不固定特性的影响,针对手机观测值修改滤波过程中的观测值噪声方差数值,采用不固定载波相位整周模糊度的常加速度动态单频Kalman滤波模型实现实时PPP和RTK两种定位方法,提高手机实时GNSS定位精度。使用某智能手机进行验证,单频实时动态PPP定位在99s内达到稳定状态,平面定位精度为1.51 m,高程精度为2.79 m;RTK定位在27 s内达到稳定状态,平面定位精度为0.73 m,高程精度为0.78 m。测试结果表明目前智能手机的GNSS定位模块具有提供更加精准的位置服务能力,甚至在某些特定场景下具有实施测绘作业的潜能。     

eLoran噪声误差模型及产生方法研究

增强罗兰(eLoran)系统具备与全球卫星导航系统(GNSS)的互补性,使其成为最佳备份系统. 接收机通过测量到达时间(TOA)进行定时与定位,噪声是影响eLoran信号TOA精度的重要因素,而噪声中高斯白噪声(WGN)又是普遍存在的. 本文首先基于最大似然估计(MLE)方法推导了WGN下的TOA误差模型,其次采用线性同余法与Box-Muller变换对法相结合生成WGN,仿真分析了WGN的时、频域特性,最后利用产生的噪声模拟出TOA测量误差,并与理论TOA模型进行比较. 结果表明:理论误差模型与仿真TOA值误差吻合,验证该研究的TOA测量误差模型和产生噪声的正确性,研究成果可为eLoran信号的TOA误差模型和模拟器中噪声产生提供参考,促进eLoran系统应用发展.      

高性能原子钟钟差建模及其在精密单点定位中的应用

鉴于当前许多IGS跟踪站均配置有高性能原子钟的现状,本文首先采用修正Allan方差法分析了不同IGS跟踪站的接收机钟随机噪声的时域特性,进而评估了不同类型接收机的短期稳定度及钟差建模的可行性,然后利用IGS站配有氢原子钟的观测数据,在精密单点定位算法中,通过对钟差参数进行短时建模约束接收机钟差的随机变化,进而改进精密单点定位(PPP)的定位性能。试验结果表明钟差建模方法显著降低了高程分量参数、天顶对流层延迟参数与接收机钟差参数之间的相关性,GNSS高程分量的精度可提高50%。该方法对于提升PPP技术在地壳形变监测、低轨卫星定轨、水汽监测及预报等高精度GNSS地学领域的应用水平具有一定意义。     

Estimation and exclusion of multipath range error for robust positioning

In integrated systems for accurate positioning, which consist of GNSS, INS, and other sensors, the GNSS positioning accuracy has a decisive influence on the performance of the entire system and thus is very important. However, GNSS usually exhibits poor positioning results in urban canyon environments due to pseudorange measurement errors caused by multipath creation, which leads to performance degradation of the entire positioning system. For this reason, in order to maintain the accuracy of an integrated positioning system, it is necessary to determine when the GNSS positioning is accurate and which satellites can have their pseudorange measured accurately without multipath errors. Thus, the objective of our work is to detect the multipath errors in the satellite signals and exclude these signals to improve the positioning accuracy of GNSS, especially in an urban canyon environment. One of the previous technologies for tackling this problem is RAIM, which checks the residual of the least square and identifies the suspicious satellites. However, it presumes a Gaussian measurement error that is more common in an open-sky environment than in the urban canyon environment. On the other hand, our proposed method can estimate the size of the pseudorange error directly from the information of altitude positioning error, which is available with an altitude map. This method can estimate even the size of non-Gaussian error due to multipath in the urban canyon environment. Then, the estimated pseudorange error is utilized to weight satellite signals and improve the positioning accuracy. The proposed method was tested with a low-cost GNSS receiver mounted on a test vehicle in a test drive in Nagoya, Japan, which is a typical urban canyon environment. The experimental result shows that the estimated pseudorange error is accurate enough to exclude erroneous satellites and improve the GNSS positioning accuracy.     

基于RWTLS的Allan方差算法简化

Allan方差是现在应用最广泛的随机误差辨识方法之一。大量的试验表明Allan方差可有效地分离出导航过程中的多项随机误差,但是Allan方差也有自身的局限性。针对Allan方差在处理大数据量时计算效率低下、辨识度受粗差的影响较大的问题,本文提出了简化Allan方差算法的方案。首先,在确保Allan方差计算准确的前提下,以提高Allan方差计算效率为目的,对Allan方差算法进行简化;然后,利用抗差加权整体最小二乘（RWTLS）模型的迭代算法对简化后的Allan方差辨识结果进行抗差拟合处理;最后,以光纤式惯性测量单元（IMU）为分析对象,设计试验方案对简化后的Allan方差进行验证。     

双目视觉辅助GNSS在恶劣环境下导航定位

视觉里程计能够在复杂环境下提供短时间的高精度导航定位,全球卫星导航系统（GNSS）具有全天候、全球性和误差不随时间积累的特性,但是在恶劣环境多路径效应下,GNSS定位精度会变差甚至不可用. 为了研究在复杂环境下视觉里程计辅助GNSS导航定位技术,首先介绍了视觉里程计的导航定位原理;然后在卡尔曼滤波器中将GNSS定位结果和视觉里程计定位结果进行了松组合处理;并利用视觉里程计定位结果和预测的视觉里程计误差实现了GNSS在恶劣环境下的导航定位. 基于KITTI数据集的模拟验证结果表明,设计的组合方案能够在恶劣环境下持续提供可靠的导航定位.      

基于三频SNR数据探测北斗GEO卫星多径效应

多径误差是全球卫星导航系统（global navigation satellite system,GNSS）高精度实时定位的主要误差源。由于多径效应具有时变特性且与观测环境有关,难以有效探测与剔除,尤其是动态定位领域。鉴于多径效应对于同颗卫星不同频率观测值影响不同,本文采用三频信噪比（signal-noise ratio,SNR）频率间差分数据,设计算法探测北斗对地静止卫星（geostationary orbit satellite,GEO）多径误差,并依据开阔环境SNR频间差分数据序列进行统计分析,确定其探测阈值。实验结果表明,北斗GEO卫星易受多径误差影响,传统方法难以实时有效探测,本文提出的新方法可有效探测GEO多径误差,并基于设定的阈值对其数据进行降权或剔除,可应用于GNSS数据质量控制。     

Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modelling

Multipath is one of the most important error sources in Global Navigation Satellite System (GNSS) carrier-phase-based precise relative positioning. Its theoretical maximum is a quarter of the carrier wavelength (about 4.8 cm for the Global Positioning System (GPS) L1 carrier) and, although it rarely reaches this size, it must clearly be mitigated if millimetre-accuracy positioning is to be achieved. In most static applications, this may be accomplished by averaging over a sufficiently long period of observation, but in kinematic applications, a modelling approach must be used. This paper is concerned with one such approach: the use of ray-tracing to reconstruct the error and therefore remove it. In order to apply such an approach, it is necessary to have a detailed understanding of the signal transmitted from the satellite, the reflection process, the antenna characteristics and the way that the reflected and direct signal are processed within the receiver. This paper reviews all of these and introduces a formal ray-tracing method for multipath estimation based on precise knowledge of the satellite–reflector–antenna geometry and of the reflector material and antenna characteristics. It is validated experimentally using GPS signals reflected from metal, water and a brick building, and is shown to be able to model most of the main multipath characteristics. The method will have important practical applications for correcting for multipath in well-constrained environments (such as at base stations for local area GPS networks, at International GNSS Service (IGS) reference stations, and on spacecraft), and it can be used to simulate realistic multipath errors for various performance analyses in high-precision positioning.     

基于功率谱和小波谱在GNSS时间序列信号探测分析中的应用

GNSS坐标在观测过程中受多方面因素影响,产生各种误差,存在一些波动变化,根据波动变化特征可以分析探测存在的信号。本文主要利用功率谱、小波谱和小波熵对GNSS原始、去趋势项、差分处理3种情况下时间序列进行分析,通过对比显示,小波谱和小波熵对于非平稳信号探测比功率谱分析能力强,GNSS时间序列存在一个趋势项和一个年周期信号。     

GNSS坐标时间序列噪声特征分析

为了研究我国目前建立的连续运行参考网络（CORS）GNSS基准站的坐标时间序列噪声特征是否与国际领域研究的成果相符合,对江苏CORS网连续3年24个分布均匀的GNSS基准站的数据进行处理,利用GAMIT软件获取了各基准站的坐标时间序列,并利用CATS软件采用最大似然估计法对坐标时间序列的噪声特征进行了分析,结果表明：GNSS基准站坐标时间序列不仅包含白噪声,还包含有色噪声;GNSS基准站坐标时间序列在N、E、U方向的噪声类型并不完全一致,其中N、E方向的最佳噪声模型为“WH＋FN＋RWN”,U方向的最佳噪声模型为“WH＋FN”.     

顾及有色噪声的光纤陀螺随机噪声自适应滤波方法

作为光纤陀螺误差的重要组成部分,随机噪声严重影响着光纤陀螺的精度,对光纤陀螺随机噪声进行准确建模和补偿是提升陀螺精度的有效方式。本文针对光纤陀螺随机噪声的复杂性,难以对其进行精确分析,ARIMA （auto-regressive moving average）模型Kalman滤波中有色噪声不能使用状态扩充法建模的问题,扩展了Harvey方程,实现有色噪声白化。同时,考虑先验噪声的不确定性以及模型参数在线更新导致的参数与状态噪声相互耦合,分析了动态Allan方差估计量测噪声的不足,使用VBAKF （variational Bayesian adaptive Kalman filter）实时修正滤波状态噪声与量测噪声。试验表明,Harvey法较传统滤波建模方式,随机噪声序列方差降低40%,Harvey法结合VBAKF使序列方差降低了54%;VBAKF较动态Allan方差,可以更好地估计量测噪声。结果表明,此方法可有效抑制随机噪声Kalman滤波中有色噪声和随机模型不准确的影响,提高随机误差补偿精度。     

面向北斗单历元分米级定位的ARAIM保护水平计算方法CSCD

精密定位的质量控制和完好性评估是实时全球卫星导航系统(GNSS)导航应用不可或缺的环节,尤其是在GNSS易受损害的城市峡谷等场景下,这种需求更加迫切.广域精密单点定位(PPP)瞬时分米级定位,利用GNSS三频信号形成的两个宽巷观测值可以实现单点单历元分米级定位.然而,在城市复杂环境中,反射信号、严重多路径以及其他信号干扰对定位造成的影响无法准确评估与识别,限制了PPP瞬时分米级单点定位的应用.完好性概念中的高级接收机自主完好性监测(ARAIM)可以计算用户定位误差最小置信区间的上限保护水平(PL)以评估定位有效性,可经过一定改进用于PPP瞬时定位的质量控制.针对当前ARAIM中计算PL的误差模型难以适应高精度定位需求的问题,提出了一种改进的ARAIM PL算法,称其为BARAIM(Back Advanced Receiver Autonomous Integrity Monitoring).使用PPP三频组合观测值残差对ARAIM权与误差模型进行修正以计算PL.基于不同复杂程度的环境下采集的车载数据对算法进行了验证,对PL的改进情况以及导航的可用性提升情况进行评估.结果表明:在不同环境下,基于改进的B-ARAIM算法得到的PL,相比传统方法得到的PL更符合城市定位的需要,将PL降低了30%~70%.此方法有助于将ARAIM算法应用在高精度GNSS定位领域.     

伪距单点定位两域联合平差解的等价性分析

针线性观测模型观测值域联合平差解和平差值域联合平差解完全等价,但实际中联合平差的观测模型多为非线性模型,参数估计时常常需要进行线性化处理,存在线性化引起的模型误差,该误差对两域平差解的等价性影响值得探讨. 以伪距单点定位(SPP)为例,论文推导了其平差值域联合平差求解公式,分析了两域联合平差不能完全等价的原因,并用实例进行了数值对比. 研究表明:在配置相同的情况下,不同全球卫星导航系统(GNSS)组合SPP的两域平差位置解在毫米量级上数值相同,就SPP应用而言,两域平差解可认为相同. 论文内容对于一些GNSS其他应用也具有一定的参考意义.