GNSS双频整周关系约束模糊度算法研究

根据GNSS双频载波相位观测值间的特定关系,提出了一种基于双频整周关系约束的模糊度解算方法(FirCAR)。该方法在局部整数范围内可将载波相位的等效波长增长,以利于整周模糊度的快速解算。不同长度的基线数据实验证明了该算法的正确性和有效性,并分析了卫星截止高度角对解算结果的影响。     

基于梯级递推的无模糊度GPS基线解算方法研究

通过考虑模糊度的整数特性及相位波长与基线非参考站坐标误差之间的约束条件,提出了一种基于梯级递推的无模糊度GPS基线解算方法。该方法不受周跳的影响,并且在基线求解过程中不用考虑模糊度参数。分别以单个历元和移动窗口的多历元两种求解方案验证了该方法的正确性和可行性,并且基线解算结果具有较高的精度。     

基于搜索空间构造模糊度搜索方法的可靠性

整周模糊度的正确求解关系到GPS精密定位结果的正确性,搜索法解算整周模糊度的原则是获得目标函数的整数解作为模糊度参数的解,文中分析了各种不同搜索方法构造搜索空间的特性,比较了不同搜索方法对模糊度解算可靠性的影响,即通过搜索,不同的方法能否获得满足目标函数的一组整数解.     

基于搜索空间构造模糊度搜索方法的可靠性

整周模糊度的正确求解关系到GPS精密定位结果的正确性，搜索法解算整周模糊度的原则是获得目标函数的整数解作为模糊度参数的解，文中分析了各种不同搜索方法构造搜索空间的特性，比较了不同搜索方法对模糊度解算可靠性的影响，即通过搜索，不同的方法能否获得满足目标函数的一组整数解。     

混合整数线性模型的最小二乘解及其应用分析

全球卫星导航系统整周模糊度解算最终归结为一个混合整数线性模型的求解问题。给出了求解混合整数线性模型最小二乘解的基本过程和由整体最优搜索准则推导出最小二乘模糊度搜索准则的简化过程,讨论了整数解的验证及其在实际应用中存在的问题。最后结合GPS实测数据的处理结果,分析了降相关变换和ratio检验在模糊度解算过程中所起的作用。     

一种用于GPS整周模糊度OTF求解的整数白化滤波改进算法

提出一种用于整周模糊度OTF求解的整数白化滤波改进算法。该算法首先对整周模糊度的协方差矩阵进行整数白化滤波处理 ,以降低整周模糊度间的相关性 ,然后构造搜索空间来判定是否需要进行搜索。如果需要 ,则通过搜索来确定变换后的整周模糊度 ;如果不需要 ,则通过直接取整来确定整周模糊度 ,进而得到原始的整周模糊度和基线分量的固定解。初步试验结果显示 ,采用改进方法解算整周模糊度可以提高成功率和解算效率     

附有基线长度约束的模糊度快速解算方法

在超短基线数据处理中,基线长度可以通过钢尺精确测量,把基线长度作为约束条件,提出了一种附有基线长度约束的快速解算模糊度的搜索新方法.根据双差观测方程得出模糊度浮点解,在浮点解周围建立模糊度搜索空间,利用基线长度约束条件搜索模糊度整数解,进而快速确定基线解.通过一个算例展示该方法的效果.     

网络RTK参考站间模糊度固定新方法

针对当前网络RTK参考站间模糊度解算时模糊度检验的Ratio值较小、固定时间较长的局限性,提出了一种新的模糊度解算方法用于网络RTK参考站间模糊度的固定.首先在模糊度区域内对原始的模糊度通过整数变换,形成宽巷与L2模糊度及其对应的方差协方差阵,然后采用LAMBDA方法对转换后的模糊度分块序贯固定.实验结果表明,与现有的模糊度解算方法相比,本文方法不但可以快速可靠地固定宽巷整周模糊度,而且提高了L2模糊度正确固定时的Ratio值,便于模糊度的正确检验,减少了模糊度的初始化时间,提高了模糊度解算的成功率.     

整数相位钟法精密单点定位模糊度固定模型及效果分析

精密单点定位(PPP)模糊度固定方法有3种:星间单差法、整数相位钟法和钟差解耦法,但目前仅法国CNES公开发布用于整数相位钟法PPP模糊度固定的产品,因此研究基于整数相位钟法的用户端PPP模糊度固定模型很有必要.本文分析了整数相位钟法PPP模糊度固定模型,着重指出该模型与传统浮点解PPP模型的区别;提出一种顾及质量控制的逐级模糊度固定策略用于具体实施PPP模糊度固定.大量动态PPP解算试验表明:与浮点解PPP相比,固定解PPP具有更快的收敛速度且定位精度和稳定性更好.     

基于LAMBDA方法的模糊度解算研究

高精度GNSS定位需要解算双差模糊度值,经典最小二乘求解的模糊度一般为浮点解,浮点解丢失了模糊度的整数性,不利于提高未知参数的精度。本文讨论了LAMBDA方法的原理及其算法,对模糊度整数变换前后LAMBDA方法的执行结果进行了比较,讨论了联合去相关法和迭代法两种整数Z变换算法的基本原理,对LAMBDA整周模糊度解算方法中的两种整数Z变换算法进行了比较。结果表明LAMBDA方法模糊度效率较高,联合去相关法的处理成功率高于迭代法。     

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to real-time kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution, an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance–covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.     

Short baseline GPS multi-frequency single-epoch precise positioning: utilizing a new carrier phase combination method

Traditional carrier phase combinations are linear functions of the original carrier phases. We develop a new way of carrier phase combination that regards carrier phases of different frequencies as the basis of the carrier phase space. The combined carrier phase is a point of this space. Then, this point, i.e., the combined carrier phase, is mapped back to a single-dimensional carrier phase by a bidirectional mapping. The new single-dimensional carrier phase is called mapped carrier phase. The advantages of this combination approach are a long wavelength and small noise of the mapped carrier phase, which make ambiguity resolution easy. Unfortunately, the mapped carrier phase value is not well determined due to the noise in the observed phases. On the contrary, a set of possible mapped carrier phase values are attained; however, only one value is correct. To reduce the number of candidates and fix the correct value of the mapped carrier phase, the following steps are discussed: (1) The integer nature of the original carrier ambiguity is used to attain an initial set of possible mapped carrier phase values; (2) the distribution of the mapped carrier phase ambiguity is included to reduce the possible values; and (3) the Gaussian least-squares objective function is introduced to fix the correct value. As a result of these steps, a single-epoch positioning algorithm is established. Two experiments are carried out to preliminarily compare the new algorithm with LAMBDA. The results show that the new algorithm is slightly below LAMBDA in resolution success rate, but computationally more efficient than LAMBDA.     

基于整周模糊度概率特性的有效性检验

准确确定载波相位整周模糊度是快速高精度GPS定位的关键,已有的检验GPS整周模糊度有效性的方法几乎均是基于其为非随机常量建立的,因而都存在一定的缺陷。本文在研究整周模糊度概率特性的基础上,提出一种基于LABMBAD算法的整周模糊度概率分布函数的检验方法。实际演算表明该方法简单有效,统计概念明确。     

BDS/GPS组合单历元基线解算方法

阐述了BDS/GPS单历元解算函数模型的相关理论,并进行了相应的公式推导。在此基础上,利用基于正则化的载波相位解算模型,解算宽巷模糊度。首先将BDS卫星宽巷模糊度值作为约束固定出IGSO和MEO卫星的模糊度;然后再将IGSO和MEO卫星模糊度值作为约束来固定GEO卫星模糊度。通过实测数据对该方法进行测试和分析,结果表明:BDS/GPS组合系统单历元宽巷模糊度成功率为100%;基频模糊度成功率90%以上;N、E、U方向定位精度达到了毫米至厘米级。     

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     

一种改进的宽巷引导整周模糊度固定算法

一般卫星导航接收机的伪距测量误差大于宽巷波长。根据宽巷引导模型,直接使用双差伪距取整固定双差宽巷整周模糊度有很大概率会产生一周固定错误。基于此,提出了一种改进的宽巷引导整周模糊度固定算法,针对宽巷整周模糊度一周固定错误进行探测和修复。利用整周模糊度为整数的特质构造理论探测量,并将该探测量与载噪比所确定的门限相比较,判断是否出现宽巷整周模糊度一周固定错误;利用双差整周模糊度自由度为3的特点,修复错误宽巷整周模糊度。对该算法在高斯噪声条件下的可行性进行了理论分析,结果表明正常载噪比的观测数据均可分辨出一周宽巷整周模糊度的估计错误。同时,分析了考虑多径等误差后该算法所能接受的载波相位最大误差。计算了不同伪距误差下宽巷整周模糊度一周固定错误出现的概率。使用GPS实测短基线数据对算法进行验证,该算法可将基于宽巷引导的整周模糊度固定算法的固定率从原来的只有不到1/3提升至接近100%。     

整周模糊度解正确性的评价方法

首先指出了基于传统的假设检验理论的三步法在评价模糊度整数解正确性时存在的理论缺陷，然后介绍了模糊度归整域的概念和可容许整数估计的定义，并在可容许整数估计原定义的基础上给出了更为严密的新定义。最后，基于这个可容许整数估计的新定义，讨论了模糊度成功率的概念及其计算公式。从理论上讲，只有模糊度的成功率才是评价模糊度整数解正确性的严密尺度。     

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%。     

Integer estimation in the presence of biases

 Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate, are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution. Received: 28 September 2000 / Accepted: 29 March 2001     

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.