BDS载波相位历元间差分测速方法研究

针对载波相位历元间差分测速前后历元选取不同广播星历计算时,卫星钟差跳变导致测速结果错误突变的问题,提出前后历元仍采用相同的广播星历来计算卫星位置和钟差的改进方法。用北斗实测数据验证了方法的正确性,并评估了北斗测速的精度。实验结果表明:静态条件下,北斗载波相位历元间差分测速精度可达mm/s级;动态条件下,采样率1Hz,测速结果与高精度组合导航测速结果符合精度为cm/s级;并且测速精度与物体的动态条件(如加速度)有一定的相关性。     

GNSS载波相位整数等变估计及其PPP性能提升算法

精密单点定位技术能够提供全球高精度定位结果,其主要技术瓶颈在于定位收敛时间长,载波相位模糊度固定技术是加快PPP收敛速度、改善定位精度的主要手段之一。模糊度固定的可靠性问题在PPP定位中尤为突出,因为模糊度浮点解质量取决于服务端产品质量、接收机噪声特性和观测环境等多种因素,所以高可靠PPP模糊度固定技术仍然充满巨大挑战。为了保障PPP定位的可靠性,本文将最优整数等变估计(best integer equivariant,BIE)引入PPP模糊度估计过程中。BIE法利用GNSS模糊度整数解加权融合以获得最优的浮点模糊度估计值,可有效降低模糊度错误固定风险,同时又利用了模糊度整数解信息来提升模糊度估值精度,从而提升PPP定位精度,缩短模糊度收敛时间。本文选取了105个全球分布的MGEX测站对BIE估计PPP模糊度的性能进行验证,试验结果表明,与模糊度固定解相比,采用BIE估计PPP模糊度能够进一步改善坐标三分量(东、北、垂向)定位性能,收敛时间分别减少了37%、28%与31%,收敛后定位精度分别提高了9%、8%和3%。此外,BIE估计PPP模糊度定位结果的毛刺和阶跃现象更少。     

Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.     

The total optimal search criterion in solving the mixed integer linear model with GNSS carrier phase observations

Existing algorithms for GPS ambiguity determination can be classified into three categories, i.e. ambiguity resolution in the measurement domain, the coordinate domain and the ambiguity domain. There are many techniques available for searching the ambiguity domain, such as FARA (Frei and Beutler in Manuscr Geod 15(4):325–356, 1990), LSAST (Hatch in Proceedings of KIS’90, Banff, Canada, pp 299–308, 1990), the modified Cholesky decomposition method (Euler and Landau in Proceedings of the sixth international geodetic symposium on satellite positioning, Columbus, Ohio, pp 650–659, 1992), LAMBDA (Teunissen in Invited lecture, section IV theory and methodology, IAG general meeting, Beijing, China, 1993), FASF (Chen and Lachapelle in J Inst Navig 42(2):371–390, 1995) and modified LLL Algorithm (Grafarend in GPS Solut 4(2):31–44, 2000; Lou and Grafarend in Zeitschrift für Vermessungswesen 3:203–210, 2003). The widely applied LAMBDA method is based on the Least Squares Ambiguity Search (LSAS) criterion and employs an effective decorrelation technique in addition. G. Xu (J Glob Position Syst 1(2):121–131, 2002) proposed also a new general criterion together with its equivalent objective function for ambiguity searching that can be carried out in the coordinate domain, the ambiguity domain or both. Xu’s objective function differs from the LSAS function, leading to different numerical results. The cause of this difference is identified in this contribution and corrected. After correction, the Xu’s approach and the one implied in LAMBDA are identical. We have developed a total optimal search criterion for the mixed integer linear model resolving integer ambiguities in both coordinate and ambiguity domain, and derived the orthogonal decomposition of the objective function and the related minimum expressions algebraically and geometrically. This criterion is verified with real GPS phase data. The theoretical and numerical results show that (1) the LSAS objective function can be derived from the total optimal search criterion with the constraint on the fixed integer ambiguity parameters, and (2) Xu’s derivation of the equivalent objective function was incorrect, leading to an incorrect search procedure. The effects of the total optimal criterion on GPS carrier phase data processing are discussed and its practical implementation is also proposed.     

载波相位约束整周模糊度在短基线RTK中的应用

针对单历元RTK定位中受到卫星升起、周跳频发等外界条件干扰时,整周模糊度长时间不能固定,严重影响RTK定位实时精度的问题。文中提出一种用载波相位约束整周模糊度的方法来提高模糊度固定率、Ratio值和解算精度,并且结合GPS单系统、GPS/GLONASS双系统两组实测数据进行未加入和加入载波相位约束整周模糊度的比较实验。结果表明该方法可行。     

Theory of integer equivariant estimation with application to GNSS

Carrier phase ambiguity resolution is the key to high-precision global navigation satellite system (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. The so-called fixed baseline estimator is known to be superior to its float counterpart in the sense that its probability of being close to the unknown but true baseline is larger than that of the float baseline, provided that the ambiguity success rate is sufficiently close to its maximum value of one. Although this is a strong result, the necessary condition on the success rate does not make it hold for all measurement scenarios. It is discussed whether or not it is possible to take advantage of the integer nature of the ambiguities so as to come up with a baseline estimator that is always superior to both its float and its fixed counterparts. It is shown that this is indeed possible, be it that the result comes at the price of having to use a weaker performance criterion. The main result of this work is a Gauss–Markov-like theorem which introduces a new minimum variance unbiased estimator that is always superior to the well-known best linear unbiased (BLU) estimator of the Gauss–Markov theorem. This result is made possible by introducing a new class of estimators. This class of integer equivariant estimators obeys the integer remove–restore principle and is shown to be larger than the class of integer estimators as well as larger than the class of linear unbiased estimators. The minimum variance unbiased estimator within this larger class is referred to as the best integer equivariant (BIE) estimator. The theory presented applies to any model of observation equations having both integer and real-valued parameters, as well as for any probability density function the data might have. AcknowledgementsThis contribution was finalized during the authors stay, as a Tan Chin Tuan Professor, at the Nanyang Technological Universitys GPS Centre (GPSC) in Singapore. The hospitality of the GPSCs director Prof Law Choi Look and his colleagues is greatly appreciated.     

不同采样率对GPS原始相位观测值周跳探测方法的影响及其效果比较

在GPS精密定位中，载波相位观测值周跳探测和修复的好坏程度将直接影响定位结果的精度，特别是实时动态定位（RTK）。当接收机采用不同采样率时，由于相位观测值所组成的序列函数收敛性将发生变化，各种周跳探测方法的能力也将发生改变。综述了几种常规的周跳探测方法，并对其特点与局限性进行了分析，然后对构造出的周跳检验量进行了比较，在此基础上通过大量算例探讨了在不同采样率下其探测周跳的能力和适用度，最后得出了一些有益的结论。     

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。     

Ionospheric TEC estimation with the signals of various geostationary navigational satellites

GPS Solutions - With the development of receiver equipment and GNSS and SBAS constellations, the coherent dual-frequency L-band transmissions are now available from a number of geostationary...     

电离层延迟变化自模型化的载波相位平滑伪距算法

传统的单频载波相位平滑伪距算法因受到电离层延迟变化的影响,容易出现平滑结果发散和精度下降的问题,而现有的解决方案对精度提高有限或需要外部精密电离层改正数据的支持。本文研究了电离层的变化规律并建立回归模型,在此基础上提出了一种自模型化电离层延迟变化的单频载波相位平滑伪距算法。此算法利用伪距和载波观测量中含有的电离层延迟信息进行电离层延迟建模,从平滑伪距中扣除了历元间电离层延迟变化值,有效避免了平滑伪距的发散问题。利用自编软件GNSSer实现了电离层自模型化的载波平滑伪距算法,并采用静态与动态实测观测数据进行了定位试验和精度分析。算例结果表明:①长时段常规Hatch滤波受电离层影响非常严重;②自模型化电离层延迟可达厘米级的精度,在30 min窗口内,使用线性移动开窗拟合法效果最佳;③自模型化电离层改正可以有效消除平滑伪距电离层影响,随着时段窗口的增加,精度没有降低;④利用本文提出的算法进行逐历元单频平滑伪距单点定位,在静态与动态的NEU方向都达到了亚分米级别的定位精度,其中,动态定位测试中水平和高程方向精度为6.25和10.4 cm,比原始伪距分别提高了5.4倍和3.3倍。     

短基线GPS定向系统及搜索模糊度优化算法的研究

GPS载波相位测量相对定位可以达到毫米级精度,利用GPS载波相位测量方向可以达到2密位的精度。研究了载波相位双差测量方向的原理和应用最小二乘法解算基线矢量的算法,详细讨论快速解算整周模糊度的优化算法。实验结果表明,应用双GPS测量方向的原理和搜索模糊度优化算法正确,其定向精度达2密位,解算时间小于0.3秒,并运用于产品中。     

GPS载波相位观测值中周跳探测与修复的研究

针对GPS载波相位定位中出现的周跳问题,提出一种新的周跳探测方法。基于非差相位观测值线性组合模式,以相位与伪距差法和电离层残差法相结合来探测与修复周跳。通过对同一组无周跳的数据采取人为加入周跳,比较两种周跳探测与修复方法的优缺点,以相位与伪距之差组合为辅助,检查大周跳,用电离层残差组合方法再对双频GPS数据进行进一步的周跳探测和修复。根据实例分析,验证该方法能够快速有效地探测并修复周跳,使双频载波相位法更具有实用性。     

一种双频载波相位周跳探测与修复方法

针对相位减伪距法只能探测出大周跳而对小周跳无能为力的问题,提出将相位减伪距法应用于双频载波相位周跳的探测与修复中。对采样率为1s、15s和30s不含周跳的观测值分别加入1周到40周不等大小的周跳,采用相位减伪距法分别对加入周跳的观测值进行处理。结果表明,该方法对于采样率为15s和30s的观测值仍然保持其优秀的大周跳探测能力,对采样率为1s的载波相位观测值则能够探测出小于1周的周跳,且其周跳探测分辨率能达到0.3周的高周跳分辨率。与其他周跳探测方法相比,该方法需要的信息量和计算量更小,效率高,算法易于计算机实现,且具有很强的实用性。     

星载GPS载波相位周跳探测方法

在星载GPS载波相位测量中,周跳的探测与修复对最后的定位精度起着至关重要的作用。本文根据在星载条件下GPS载波相位测量的观测时间短、环境变化复杂、所得历元少和基本不受对流层延迟影响等特点,论述了适用于星载高动态环境GPS载波相位周跳探测和修复的方法,并指出各种方法的特点和适用要求。     

一种改进的载波相位周跳探测与修复方法

本文提出了一种改进的探测和修复小周跳的方法。根据电离层残差值在短周期内的连续性,可以比较准确地用函数来拟合的特点,再根据L1和L2载波相位观测值之间小数部分应该满足的函数关系,来探测和修复第二个载波的周跳。该方法仅使用单星双频载波相位数据,而且每颗卫星之间的数据是独立处理的。由于载波的小数部分不受周跳的影响,所以该方法的有效性能够不受周跳类型的影响。试验表明该方法对于L1上小于9周、L2上小于7周的周跳很有效。     

Unbiased vs biased estimation of GPS phase ambiguities from dual-frequency code and phase observables

With access to dual-frequency pseudorange and phase Global Positioning System (GPS) data, the wide-lane ambiguity can easily be fixed. Advantage is taken of this information in the linear combination of the above four observables for base ambiguity estimation (i.e. of N ₁ and N ₂). Starting points for our analysis are the Best Linear Unbiased Estimators BLUE₁ and BLUE₂. BLUE₁ is the best one (with minimum mean square error, MSE) if the ionosphere effect is negligible. If this is not the case, BLUE₂ has the smallest variance, but not necessarily the least mean square error. Hence, both estimators may suffer from a non-optimal treatment of the ionosphere bias. BLUE₁ ignores possible ionosphere bias, while BLUE₂ compensates for this bias in a less favourable way by eliminating it at the price of increased noise. As an alternative, linear estimators are derived, which make a compromise between the ionosphere bias and the random observation errors. This leads to the derivation of the Best Linear Estimator (BLE) and the Restricted Best Linear Estimator (RBLE) with minimum MSE. The former is generally not very useful, while the RBLE is recommended for practical use. It is shown that the MSE of the RBLE is limited by the variances of BLUE₁ and BLUE₂, i.e.

Cycle slip detection and repair of undifferenced single-frequency GPS carrier phase observations

Cycle slip detection and repair is an important issue in the GPS data processing. Different methods have been developed to detect and repair cycle slips on undifferenced , single- or double-differenced observations. The issue is still crucial for high-precision GPS positioning, especially for the undifferenced GPS observations. A method is proposed to fix cycle slips based on the generalized likelihood ratio (GLR) test. The method has a good performance on cycle slip fixing of undifferenced carrier phase observations on individual frequencies, either on L1 or on L2, without making a linear combination among the observables. The functional model is a piecewise cubic curve fitted to a number of consecutive data using the least squares cubic spline approximation (LS-CSA). For fixing the cycle slips, an integer estimation technique is employed to determine the integer values from the float solution. The performance of the proposed method is then compared with the existing two methods using simulated data. The results on a few GPS data sets with sampling rate of 1 Hz or higher confirm that this method can detect and correct all simulated cycle slips regardless of the size of the cycle slip or the satellite elevation angle. The efficacy of the method is then investigated on the GPS data sets with lower sampling rates of 5, 10, and 30 s. The results indicate that the proposed method always performs the best for the data sets considered. This is thus an appropriate method for cycle slip detection and repair of single-frequency GPS observations.