Ambiguity Recovery Using the Triple-Differenced Carrier Phase Type Approach for Long-Range GPS Kinematic Positioning

Precise, long-range GPS kinematic positioning to centimeter accuracy requires that carrier phase ambiguities be resolved correctly during an initialization period, and subsequently to recover the “lost" ambiguities in the event of a cycle slip. Furthermore, to maximize navigational efficiency, ambiguity resolution and carrier phase-based positioning need to be carried out in real-time. Due to the presence of the ionospheric signal delay, satellite orbit errors, and the tropospheric delay, so-called absolute ambiguity resolution “on-the-fly” for long-range applications becomes very difficult, and largely impossible. However, all of these errors exhibit a high degree of spatial and temporal correlation. In the case of short-range ambiguity resolution, because of the high spatial correlation, their effect can be neglected, but their influence will dramatically increase as the baseline length increases. On the other hand, between discrete trajectory epochs, they will still exhibit a large degree of similarity for short time spans. In this article, a method is described in which similar triple-differenced observables formed between one epoch with unknown ambiguities and another epoch with fixed ambiguities can be used to derive relative ambiguity values, which are ordinarily equal to zero (or to the number of cycles that have slipped when loss-of-lock occurred). Because of the temporal correlation characteristics of the error sources, the cycle slips can be recovered using the proposed methodology. In order to test the performance of this algorithm an experiment involving the precise positioning of an aircraft, over distances ranging from a few hundred meters up to 700 kilometres, was carried out. The results indicate that the proposed technique can successfully resolve relative ambiguities (or cycle slips) over long distances in an efficient manner that can be implemented in real-time.     

Cycle Slip Detection and Ambiguity Resolution Algorithms for Dual-Frequency GPS Data Processing

This article investigates the problem of cycle slip detection and ambiguity resolution using dual-frequency GPS data. Several algorithms are proposed and described. F or cycle slip detection, three L1/L2 observable combinations have been integrated to formulate a new algorithm for cycle slip detection. For ambiguity resolution, both widelane and narrowlane ambiguity resolution algorithms are presented, but the focus is on the narrowlane ambiguity resolution. Numerical results are included to evaluate the performance of the proposed algorithms, which have shown that cycle slips can be effectively detected and the narrowlane ambiguities can be resolved almost instantaneously after successful determination of the widelane ambiguities.     

Sea Surface Determination Using Long-Range Kinematic GPS Positioning and Laser Airborne Depth Sounder Techniques

Precise long-range kinematic GPS positioning requires the use of carrier phase measurements, the data processing of which suffers from the technical challenges of ambiguity resolution and cycle slip repair. In this paper, the combination of an ambiguity recovery technique and a linear bias correction method has been used to overcome such problems. An experiment was conducted to test the utility of this technique to determine aircraft height to high accuracy, over very long baselines (of the order of one thousand kilometres), in support of the Laser Airborne Depth Sounder (LADS). From a comparison of four independently derived trajectories, this airborne GPS kinematic positioning experiment has confirmed that the sea surface can be determined to centimetre accuracy. The sea surface profiles thus obtained can be used to correct the errors introduced by long period ocean swells.     

Sea Surface Determination Using Long-Range Kinematic GPS Positioning and Laser Airborne Depth Sounder Techniques

Precise long-range kinematic GPS positioning requires the use of carrier phase measurements, the data processing of which suffers from the technical challenges of ambiguity resolution and cycle slip repair. In this paper, the combination of an ambiguity recovery technique and a linear bias correction method has been used to overcome such problems. An experiment was conducted to test the utility of this technique to determine aircraft height to high accuracy, over very long baselines (of the order of one thousand kilometres), in support of the Laser Airborne Depth Sounder (LADS). From a comparison of four independently derived trajectories, this airborne GPS kinematic positioning experiment has confirmed that the sea surface can be determined to centimetre accuracy. The sea surface profiles thus obtained can be used to correct the errors introduced by long period ocean swells.     

Improved Method to Detect and Repair Cycle Slip for GNSS Medium–Long Baseline in Real-Time Marine Surveys

Distance-related errors complicate the resolution of real-time ambiguity in medium–long baseline marine surveys. Therefore, detection and recovery of cycle slips in real time is required to ensure high accuracy of global navigation satellite system positioning and navigation in marine surveys. To resolve this, an improved method was presented, where linear combinations of the triple-differenced (TD) between carriers L₁ and L₂ were formed for a wide lane and free ionosphere. To overcome severe ill-conditioned problems of the normal equation, the Tikhonov regularization method was used. The construction of a regularized matrix by combining a priori information of known coordinates of reference stations, followed by the determination of the corresponding regularized parameter are suggested. A float solution was calculated for the TD ambiguity. The search cycle slip (TD integer ambiguity) was obtained using the least-squares ambiguity decorrelation adjustment (LAMBDA) method. Using our method, cycle slips of several reference station baselines with lengths of a few hundred to one thousand kilometers were detected in real time. The results were consistent with professional software, with a success rate of 100%.     

短基线北斗三频数据模糊度解算方法的比较

首先分析了矩阵变换、无几何CIR、几何CIR、组合观测量PAR、原始观测量PAR五种模糊度解算方法的原理;然后采用短基线北斗三频实测数据对每种方法进行测试和分析比较。结果表明:短基线条件下,无几何CIR算法和矩阵变换算法受电离层延迟和观测噪声的影响较大,模糊度固定成功率比较低,不适用于北斗实测数据;几何CIR算法和组合观测量PAR算法采用组合观测量会放大噪声水平,部分历元的模糊度固定出现错误;原始观测量PAR模糊度固定成功率最高,在本次算例中达到100%。     

三种GNSS模糊度解算方法成功率比较

介绍了在航模糊度求解的模型。在航模型每个历元均需要多估计一组坐标矢量,因而降低模糊度求解的精度。用取整法、引导取整法和整数最小二乘法三种模糊度固定方法,比较了在静态模型和在航模型下整周模糊度求解的成功率和需要的初始化时间,为动态平台的糊度解算提供参考。     

Real‐time failure detection in the carrier phase measurements of GPS by robust and conventional kalman state estimates

Among the fastest‐growing applications of high‐precision GPS positioning are those which are kinematic in nature. Carrier phase‐based GPS positioning of a moving antenna—for example, attached to a ship, an aircraft, or a land vehicle—is now commonplace. Recent software innovations make use of advanced ambiguity resolution “on the fly” and real‐time kinematic data processing algorithms to emulate the ease of operation of conventional differential GPS (DGPS) based on transmitted pseudo‐range corrections. However, as much higher accuracy must now be assured compared to DGPS, greater attention must be focused on the quality control aspects of GPS positioning. This study describes two methods for detecting failures or changes of small magnitude in real time in GPS measurements. Examination of the overlap or disjointedness of robust and conventional confidence intervals and studentized normal variates have been used as failure detection tools. These methods are based on testing the performance of the differences between the conventional (nonrobust) Kalman state estimates and the robust Kalman filler estimates. Detection of cycle slips in carrier phase data, outliers in phase rate or in code ranges, or any other type of disorder in the measurements of the GPS system can be addressed with these failure detection methods. Application and evaluation of the algorithms has been carried out using raw carrier‐phase and phase‐rate GPS measurements. It has been demonstrated that these failure detection tools provide powerful and efficient diagnostics for detecting small changes in the measurements of the GPS system.     

Undifferenced Cycle Slip Estimation of Triple-Frequency BeiDou Signals with Ionosphere Prediction

With the rapid development of BeiDou satellite navigation system (BDS), high-quality service has been provided in the Asia-Pacific region currently, which will be extended to the whole world very soon. BDS is the first Global Navigation Satellite System that all satellites broadcast the triple-frequency signals. The triple-frequency signals in theory can improve the cycle slip detection that is one of the preconditions in precise positioning by making use of carrier phase. This paper discusses the development of a cycle slip detection method for undifferenced BDS triple-frequency observations in kinematic scenario. In this method, two geometry-free extra-wide-lane combinations and one geometry-free narrow-lane (NL) combinations are employed. The key is to mitigate the between-epoch ionospheric biases in the geometry-free NL combinations. We propose to predict the ionospheric biases of current epoch by using those from its consecutive foregoing epochs. The method is tested with extensive experiments in varying observation scenarios. The results show that in case of sampling interval as small as 5 s, the between-epoch ionospheric biases can be ignored and the correct cycle slips can be determined. Meanwhile in case of lower sampling frequency, one needs to compensate the ionospheric biases of current epoch by using the predicted ionospheric biases. The presented method can correctly detect all cycle slips even if they are as small as 1 cycle.     

伪距单点定位的精度分析及改进

GPS伪距单点定位速度快、不存在整周模糊度,因此具有很大的应用价值。分析了电离层延迟、对流层延迟、相对论效应、地球自转改正对伪距单点定位结果的影响,介绍了两种多历元求解时处理接收机钟差的方法,最后讨论了如何以大地坐标和高斯坐标为参数进行定位求解。     

The Effects of GPS Carrier Phase Ambiguity Resolution on Jason-1

We have used GPS carrier phase integer ambiguity resolution to investigate improvements in the orbit determination for the Jason-1 satellite altimeter mission. The technique has been implemented in the GIPSY orbit determination software developed by JPL. The radial accuracy of the Jason-1 orbits is already near 1 cm, and thus it is difficult to detect the improvements gained when the carrier phase ambiguities are resolved. Nevertheless, each of the metrics we use to evaluate the orbit accuracy (orbit overlaps, orbit comparisons, satellite laser ranging residuals, altimeter crossover residuals, orbit centering) show modest improvement when the ambiguities are resolved. We conservatively estimate the improvement in the radial orbit accuracy is at the 10–20% level.     

实时GPS精密卫星钟差估计及实时精密单点定位

研究了GPS实时精密卫星钟差的估计方法,并将实时钟差应用于实时精密单点定位。采用自编软件,依据全球均匀分布的IGS参考站实测数据,基于非差消电离层组合载波和伪距观测量实现了GPS实时精密卫星钟差估计。试验结果表明,自主估计的实时卫星钟差与IGS发布的最终精密钟差具有较好一致性,互差优于0.2ns;用于实时精密单点定位,能够获得静态定位1~2cm、仿动态定位厘米级精度。     

精密单点定位中双频GPS数据的周跳探测与修复

周跳的探测与修复，特别是小周跳的探测是实现GPS高精度实时定位的关键技术基础之一。分析了非差相位观测值线性组合模式，比较了几种周跳修复的方法，得出宽巷和电离层组合方法更适用于精密单点定位中双频GPS数据的周跳探测和修复。通过实例分析，证明该方法能够有效地探测并修复周跳。     

一种双频数据的周跳探测和修复方法的研究

研究了伪距／载波组合和电离层残差探测和修复周跳。利用伪距／载波组合探测和修复6—8周以上的周跳，对修复后的数据进行电离层残差探测，分离发生周跳历元的电离层残差跳变量，得到8周以内的周跳量并修复，实现了30s以内采样间隔任意整周周跳的探测和修复。实验证明此方法是可行的。     

GPS网络RTK内插算法分析与比较

在GPS网络RTK中,利用不同的内插算法,生成的流动站误差改正数不同,它们对定位结果的影响也不同。通过算例分析表明,选择合理的内插算法,不仅可以生成与流动站真实误差较为接近的误差改正数,还可以提高整周模糊度的解算成功率和导航定位的精度。     

Determination of instantaneous sea surface,wave heights,and ocean currents using satellite observations of the global positioning system

Abstract

Using GPS phase observations in the kinematic mode, we are able to achieve centimeter accuracy in relative three‐dimensional coordinates. This could be verified even for fast‐moving sensors in aircraft, such as airborne photogrammetric cameras, at the time of exposure. Sophisticated kinematic software has been developed resolving cycle slips and carrier‐phase ambiguities during motion. To determine the instantaneous sea surface, the GPS receiver is placed in a free‐drifting buoy with the antenna on top. Differencing the 1‐Hz observations, wave heights can be determined as well as velocity and direction of ocean (tidal) currents.

This article deals with the experiences from a test for the practical realization of this proposal. Hardware installation, software, and data analysis are described. Plans to use such an observational scenario of a GPS buoy array in the North Sea for the calibration of the radar altimeter of the European satellite ERS‐1 are presented.     

实时GPS姿态测量中整周模糊度的快速解算方法

姿态测量核心问题是整周模糊度解算.提出了一种适合实时姿态测量的模糊度解算方法,利用单差平滑伪距进行解算,与传统的模糊度解算方法相比具有许多优点.通过仿真实验验证了该方法的有效性和实用性.     

STPIR和MW组合的北斗三频周跳探测与修复

针对载波相位观测值中出现周跳的问题及北斗卫星导航系统全星座播发三频信号的现状,提出一种三频相位电离层残差二阶历元差分(STPIR)的算法,克服了传统电离层残差法受观测数据采样间隔影响较大的问题,联合MW组合观测量进行周跳探测又可避免各自的探测盲区。两种组合观测量均很好地削弱了电离层延迟项的影响,联立方程组进行周跳求解时,直接取整即可得到周跳值。通过北斗三频实测数据验证,提出的组合方法在观测数据采样间隔较大时,可以准确探测出所有周跳,并有效修复。     

一种超短基线定位系统阵型的改进方法

超短基线随着作用距离增加,其定位误差也增大.为了满足远距离作业需要,提高超短基线远距离的定位精度,文中提出通过改进超短基线基阵阵型的方法来提高定位精度,但同时会带来相位模糊的问题,因此进一步提出一种利用双脉冲信号相位抗模糊的方法以保证在改进的阵型条件下能够正确地定位.仿真和实验结果证明通过阵型改进后的超短基线系统定位精度得到了很大的提高.     

Fast BDS Positioning Convergence Based on the Contribution of GPS Observations

Comparing to single BeiDou Navigation Satellite System (BDS) Precise Point Positioning (PPP), a method which can more quicklydetermine the ambiguity parameters of BDS through applying the contribution of GPS observations is proposed and analyzed in this article. The numerical examples and analysis show that the ionosphere-free ambiguities of BDS satellites can be determined and converged more quickly because of the contribution of GPS observations. The average improvement of the convergent speed of positioning is 18.5% and its positioning accuracy in N, E, and U components are improved by 29.4, 30.3, and 34.4%, respectively, with the contribution of the a priori coordinates obtained from GPS observations. This method is useful for single BDS system positioning when there is a priori information provided by GPS or other sensors which be replaced by and can be applied at the beginning of the computation.