长距离GPS/BDS参考站网多频载波相位整周模糊度解算方法

长距离网络RTK是实现GPS/BDS高精度实时定位的主要手段之一,其核心是长距离参考站网GPS/BDS整周模糊度的快速准确确定。本文提出了一种长距离GPS/BDS参考站网载波相位整周模糊度解算方法,首先利用GPS双频观测数据计算和确定宽巷整周模糊度,同时利用BDS的B2、B3频率观测值确定超宽巷整周模糊度。然后建立GPS载波相位整周模糊度和大气延迟误差的参数估计模型,附加双差宽巷整周模糊度的约束,解算双差载波相位整周模糊度,并建立参考站网大气延迟误差的空间相关模型。根据B2、B3频率的超宽巷整周模糊度建立包含大气误差参数的载波相位整周模糊度解算模型,利用大气延迟误差空间相关模型约束BDS双差载波相位整周模糊度的解算。克服了传统的使用无电离层组合值解算整周模糊度的不利影响。采用实测长距离CORS网GPS、BDS多频观测数据进行算法验证,试验结果证明该方法可实现长距离参考站网GPS/BDS载波相位整周模糊度的准确固定。     

GPS/陀螺组合测姿中整周模糊度的快速解算

采用方向余弦矩阵描述姿态,建立GPS/陀螺组合姿态确定系统模型,由矩阵Kalman滤波方法解算整周模糊度的浮点解,然后再利用MCLambda方法得到整周模糊度固定解。仿真实验结果表明,附加方向余弦矩阵约束的Kalman滤波方法可以有效地提高整周模糊度浮点解的精度,使得整周模糊度的固定成功率和效率均得到提高,尤其是在GPS观测条件较差的情况下。     

综述GPS定位中整周糊度求解问题

GPS定位中确定整周模糊度是关键问题,而在进行短时段的短基线向量的解算时,由于观测值较少以及卫星星座几何形状变化不大等因素,会出现整周模糊度不能固定为整数的现象,本文综述了当前求解整周模糊度的主要方法,并对GPS精密快速定位中整周模糊度定位问题提出了一定看法,可供GPS研究及定位工作者参考。     

姿态测量中GPS双频观测的应用

随着GPS定位技术的发展和完善,利用GPS进行动态载体的姿态测量具有广阔的发展前景.姿态测量问题中,实时、高精度的解算整周模糊度是关键.利用双频观测、RATI0检验等方法进行单历元整周模糊度的解算,得到较好的结果.因此,这一方法可以应用到动态载体姿态测量当中去.     

双移动载体GPS精密相对定位研究

GPS双移动载波相位差分技术的关键,是如何实现可变基线条件下整周模糊度的快速解算。为此,本文详细地讨论了其确定整周模糊度的方法,并设计了检验该技术精度的实验方案;实算结果表明,用该技术获得了厘米级的相对定位精度。     

GPS短基线整周模糊度的直接解法

提出了在位移值较大的情况下(0.7 m),通过多种载波相位组合,解算短基线GPS整周模糊度的方法。导出了在解算过程中保证L1和L2载波的整周模糊度N1和N2为整数的条件,从而将DC(direct calcu-lation)算法[1]不仅推广到大变形的情况,而且推广到短基线GPS整周模糊度的解算,解决了快速准确解算短基线GPS整周模糊度的问题。     

长距离GPS/BDS双系统网络RTK方法

基于区域参考站网的网络实时动态定位(real-time kinematic,RTK)方法是实现全球定位系统(global positioning system,GPS)、北斗卫星导航系统(BeiDou satellite navigation system,BDS)高精度定位的主要手段。研究了一种长距离GPS/BDS双系统网络RTK方法,首先采用长距离参考站网GPS/BDS多频观测数据确定宽巷整周模糊度,利用引入大气误差参数的参数估计模型解算GPS/BDS双差载波相位整周模糊度;然后按照长距离参考站网观测误差特性的不同,分类处理参考站观测误差,利用误差内插法计算流动站观测误差,以改正流动站GPS/BDS双系统载波相位观测值的观测误差;最后使用流动站多频载波相位整周模糊度解算方法确定GPS/BDS载波相位整周模糊度并解算位置参数。使用长距离连续运行参考站(continuously operating reference stations,CORS)网的实测数据进行实验,结果表明,该方法能够利用长距离GPS/BDS参考站网实现流动站的厘米级定位。     

单历元解算整周模糊度及检验方法研究

针对GPS测量中因工作盲区等实际生产因素的影响而造成历元较少的情况,提出在Tikhonov正则化的基础上解算历元较少时方差-协方差阵的病态情况。为提高解算整周模糊度的成功率,提出在Tikhonov正则化的基础上结合阻尼LAMBDA方法固定整周模糊度,同时采用电子总含量(TEC)检验,通过实例证明此方法适用于单历元情况,并能明显提高解算整周模糊度的成功率。     

一种基于双频GPS接收机的精确快速相对定位方法

利用GPS载波相位测量可以精确确定两个载体间的相对距离，其核心问题是整周模糊度的快速求解，通过双频数据可以提高模糊度求解的速度。在推导模糊度组合的一般公式的基础上，研究了一种基于双频GPS接收机模糊度快速求解算法。实验证明该方法正确有效。     

基于卫星高度角的GPS观测量随机模型分析

主要研究了等权法和基于卫星高度角的GPS观测量随机模型确定方法,由此确定权矩阵应用于GPS基线解算中以检验其效果,并通过对模型试验结果的比较,分析说明了采用卫星高度角定权对整周模糊度搜索和基线解算结果的影响。     

基于整数可逆模糊度变换和概率计算的GPS动态数据处理快速算法

在讨论整数可逆模糊度变换对模糊度搜索空间影响及直接取整法成功概率的基础上，结合Kalman滤波技术，提出一种新的GPS动态数据处理快速算法－－基于概率计算的模糊度快速分解技术（Probability Based Fast Ambiguity-resolution Technique,简称PBFAT法）。该算法在取整成功概率大于给定限值时，直接对浮点模糊度取整；若取整概率小于给定的值则进行一定范围的模糊度搜索。试验表明该方法的计算速度高于传统方法，所求的模糊度有一个明确的置信水平。     

Position-domain integrity risk-based ambiguity validation for the integer bootstrap estimator

Integrity monitoring for ambiguity resolution is of significance for utilizing the high-precision carrier phase differential positioning for safety–critical navigational applications. The integer bootstrap estimator can provide an analytical probability density function, which enables the precise evaluation of the integrity risk for ambiguity validation. In order to monitor the effect of unknown ambiguity bias on the integer bootstrap estimator, the position-domain integrity risk of the integer bootstrapped baseline is evaluated under the complete failure modes by using the worst-case protection principle. Furthermore, a partial ambiguity resolution method is developed in order to satisfy the predefined integrity risk requirement. Static and kinematic experiments are carried out to test the proposed method by comparing with the traditional ratio test method and the protection level-based method. The static experimental result has shown that the proposed method can achieve a significant global availability improvement by 51% at most. The kinematic result reveals that the proposed method obtains the best balance between the positioning accuracy and the continuity performance.     

Analysis of the upper bounds for the integer ambiguity validation statistics

Integer ambiguity validation is an essential quality control step for high-precision positioning and navigation with global navigation satellite systems (GNSS). In order to validate the resolved integer ambiguities, statistical tests, such as the R-ratio test, F-ratio test, W-ratio test, difference test, and projector test, have been favored. In practice, the critical values for these statistical tests are determined either empirically or from the assumed distributions. However, previous research has revealed that some of these statistics have upper bounds, which can be obtained from simulations. In this contribution, we find that under the framework of the integer aperture estimation, the upper bounds for these ambiguity validation statistical tests can be derived without actual measurements or simulation. As a result, the assumed distributions for these statistical tests are inappropriate. According to the derivation, it has been concluded that the upper bounds of these ambiguity validation tests depend only on the ambiguity geometry (e.g., the float ambiguity variance–covariance matrix) and can be obtained at the design stage of GNSS positioning. Thus, the critical value for these ambiguity validation statistics has a rigorous range, and it should be chosen to be smaller than a priori derived upper bound. Otherwise, no integer ambiguities can be obtained.     

一种检验GNSS相位模糊度整周解算有效性的方法

模糊度整周解检验是评价模糊度解算正确性的关键,决定着最终定位结果的可靠性。对原有的假设检验存在的缺陷和不足进行了分析,提出了一种更可靠的比值（Ratio）检验方法。理论分析和数值试验结果都显示改进的检验方法更能正确评价模糊度整数解解算的正确性。该新检验方法,又提出了一种最终模糊度整数解确定的新方法即模糊度候选值再分析法。实验表明：应用该方法能提高模糊度整数解确定的成功率。     

On the probability density function of the GNSS ambiguity residuals

Integer GNSS ambiguity resolution involves estimation and validation of the unknown integer carrier phase ambiguities. A problem then is that the classical theory of linear estimation does not apply to the integer GPS model, and hence rigorous validation is not possible when use is made of the classical results. As with the classical theory, a first step for being able to validate the integer GPS model is to make use of the residuals and their probabilistic properties. The residuals quantify the inconsistency between data and model, while their probabilistic properties can be used to measure the significance of the inconsistency. Existing validation methods are often based on incorrect assumptions with respect to the probabilistic properties of the parameters involved. In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GPS carrier phase ambiguity residuals. The residuals and their properties depend on the integer estimation principle used. Since it is known that the integer least-squares estimator is the optimal choice from the class of admissible integer estimators, we will only focus on the PDF of the ambiguity residuals for this estimator. Unfortunately the PDF cannot be evaluated exactly. It will therefore be shown how to obtain a good approximation. The evaluation will be completed by some examples.     

Ambiguity validation with combined ratio test and ellipsoidal integer aperture estimator

To ensure reliable ambiguity resolution, ambiguity validation is an indispensable step. It has been a challenge for many years and is far from being resolved. Over the past years, various ambiguity validation methods have been proposed, such as F-ratio test, R-ratio test, difference test, projector test, ellipsoidal integer aperture (EIA) estimator and penalized integer aperture (PIA) estimator. In this paper, through analysis and testing, we find that, when the aperture region of EIA is not allowed to be overlapped, the efficiency of ambiguity resolution with EIA is low and it is not applicable to fast static positioning or real-time kinematic (RTK) applications. Then EIA with overlapped aperture regions is recommended and the resulted fail-rate becomes upper bound of the actual one. After that, it is suggested that combined use of overlapped EIA and R-ratio test can increase the reliability of ambiguity resolution. Finally, numerical tests are carried out based on practical buoy data and simulated Galileo data.     

基于可靠性指标的Ratio检验模糊度质量方法

整周模糊度估值的可靠性对保障卫星导航定位精度有着至关重要作用,本文针对常规Ratio检验模糊度方法中阈值c难以确定问题,基于模糊度成功率检验理论分析了Ratio检验法的概率特性,推导了模糊度失败率与Ratio检验阈值间的函数关系式,实现利用给定可靠性指标——模糊度失败率确定Ratio检验阈值c,从而保证模糊度固定解的可靠性。算例表明,该方法可解决Ratio检验中阈值c动态取值的关键问题,具有一定的实际意义。     

载波相位差分接收机自主完好性监测研究

首先提出了浮点变换完全去相关法,该方法能够在单历元动态确定整周模糊度。研究了基于载波相位测量的完好性监测方法。利用最小二乘残差构造统计检验量,对整周模糊度进行检测。分析了定位误差保护限与卫星构型、漏警概率的关系。实测数据表明,整周模糊度在单历元动态求解的成功率为100%,增加1颗卫星将使垂直定位误差保护限减少约0.2 m,统计检验量检测周跳的正确率为100%。     

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.     

An optimality property of the integer least-squares estimator

A probabilistic justification is given for using the integer least-squares (LS) estimator. The class of admissible integer estimators is introduced and classical adjustment theory is extended by proving that the integer LS estimator is best in the sense of maximizing the probability of correct integer estimation. For global positioning system ambiguity resolution, this implies that the success rate of any other integer estimator of the carrier phase ambiguities will be smaller than or at the most equal to the ambiguity success rate of the integer LS estimator. The success rates of any one of these estimators may therefore be used to provide lower bounds for the LS success rate. This is particularly useful in case of the bootstrapped estimator. Received: 11 January 1999 / Accepted: 9 July 1999