Taking correlations into account: a diagonal correlation model

GPS Solutions - The true covariance matrix of the GPS phase observations is unknown and has to be assumed or estimated. The variance of the least-squares residuals was empirically shown to have an...     

Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50–70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.     

Kriging方法结合最小二乘配置在GPS高程拟合中的应用

本文利用Kriging方法结合最小二乘配置将GPS高程转换成正常高.研究了将Kriging方法中的变异函数用于计算最小二乘配置中的协方差的方法,并对一局部GPS水准网的高程作了拟合计算.通过将最小二乘配置法与平面拟合模型和多面函数拟合模型等进行比较,其外符合精度从最大的±0.0277m提高到±0.0162m.     

Considered parameters in a least squares adjustment process

Least squares adjustment processes occasionally utilize constants with a known degree of uncertainty. If the covariance matrix of the adjusted parameters is estimated without considering those uncertainties the resulting estimate is invariably too optimistic. A method is proposed by which without altering the values of the adjusted parameters their a posteriori (after the adjustment) covariance matrix can be improved by the inclusion of the effect of uncertainties in the constants.     

粒子群最小二乘支持向量机在GPS高程拟合中的应用

针对传统的GPS高程拟合方法要求有足够多样本数据的缺陷,本文采用粒子群(PSO)算法优化最小二乘支持向量机(LSSVM)参数的方法进行GPS高程拟合。实验表明,在有限样本的情况下,PSO-LSS-VM模型不仅发挥了LSSVM处理小样本数据的能力,而且通过PSO优化后的LSSVM能够选择出合适的参数;与LM-BP神经网络、标准最小二乘支持向量机等方法比较,PSO-LSSVM模型拟合精度较高。     

二次曲面与最小二乘配置的组合模型在GPS高程异常拟合中的应用

在工程实践应用中,为了有效利用GPS高程数据,减少对传统水准测量的依赖,提高GPS高程异常的拟合精度便显得十分重要。为此,本文在介绍二次曲面拟合和最小二乘配置拟合基本原理分析、算法过程推导的基础上,提出了一种新的高程异常拟合方法。首先在二次曲面拟合的基础上,计算得到原始观测数据与拟合数据之间的残差序列,然后采用最小二乘配置模型对包括二次曲面拟合模型误差的综合误差进行优化减弱,最后得到新的高程异常。通过实例,将二次曲面拟合法,最小二乘配置法与文中提出的新方法进行比较分析。结果表明：新的组合方法的拟合预测精度要明显优于最小二乘配置及二次曲面拟合。     

A procedure for testing the assumption of homoscedasticity in least squares residuals: a case study of GPS carrier-phase observations

Due to increased demands on the quality of the results of Global Positioning System (GPS) evaluations, various authors have studied improvements of the stochastic model of GPS carrier-phase observations. These improvements are based on the reasonable assumption that the commonly used stochastic model with independent and homoscedastic (i.e. equal variance) errors is unrealistic. However, this has not been proved rigorously so far. A statistical test procedure based on uncorrelated least–squares residuals, which allows verification of the hypothesis of a heterogeneous variance, is provided. The statistical test procedure is of interest in its own right, and is independent of the practical problem considered. The presented technique is applied to GPS carrier-phase observations. Results show that the variances of the investigated observations are far from homogeneous. It is indicated that the error variances of the presented data increase with decreasing GPS satellite elevation. These results confirm the assumption that the commonly used stochastic model of GPS observations is inadequate and has to be improved.     

A comparison of a Hi/Lo GPS constellation with a populated conventional GPS constellation in support of RTK: A covariance analysis

This study makes an initial comparison of three GPS-like constellations. Starting with a simplified constellation of 25 GPS satellites as a reference, GPS(25), we determine what kinematic positioning improvements would result from a constellation comprising a Hi component of 16 GPS satellites (at roughly 16.8 earth radii) coupled with a Lo component of 49 GPS satellites (at roughly 2.1 earth radii). We also include a GPS constellation of 49 GPS satellites, GPS(49), which comprises orbits like the GPS(25) constellation. The GPS(49) and the Hi(16)/Lo(49) constellations have semi-major axes selected so that they have exactly the same average number of satellites above 7.5 degrees elevation (averaged over 24 hours). What motivated this study was a need to measure the benefits, to precision differential kinematic positioning methods (i.e., RTK), which result from the higher Doppler shifts (hence speedier integrated Doppler) generated by the Lo component. Quicker initial convergence was anticipated, of course.     

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

GBAS testbed development in Taiwan with a prototype GPS/GBAS receiver

In this paper, we present the development of a local area differential GPS testbed of the ground-based augmentation system (GBAS) as the future airport navigation facility in the Taipei Flight Information Region (FIR) in Taiwan. The testbed is mainly a GBAS ground facility, which consists of a ground station, three GBAS receivers, and a VDL (VHF data link) broadcast antenna. We also present an airborne GPS/GBAS prototype receiver in this paper. The airborne subsystem (a GPS/GBAS receiver) receives the correction messages from the ground subsystem to perform a differential GPS (DGPS) positioning. In order to provide an ILS-look-alike approach and landing, the output messages of the airborne receiver are packed in an ARINC 429 format. The proposed airborne system has a software-based global navigation satellite system (GNSS) receiver structure.     

Comparing GPS-only with GPS + GLONASS positioning in a regional permanent GNSS network

Within the regional EUREF Permanent Network (EPN) all positioning is purely based on GPS. This paper investigates, using the Bernese GNSS analysis software, the influence of adding GLONASS observations to the EPN processing using fixed orbits from the International GNSS Service (IGS) as well as from the CODE analysis centre. The GPS-only coordinates and GPS + GLONASS coordinates will be compared and the change in their repeatabilities will be investigated. The influence of the used orbits will also be outlined. The results show that a combined GPS + GLONASS data analysis can be set up without major efforts and that it will not degrade the positions obtained within the EPN.     

大区域似大地水准面模型的建立方法研究

在充分研究现有几何方法确定局域似大地水准面的基础上,根据独立网内点间高程异常差的不变性和独立网间大地高起算基准面与WGS84椭球面的平行性,提出通过两步处理,获得大区域连续似大地水准面的思想和方法,即首先统一相邻两个独立GPS网大地高起算基准面,然后再利用几何方法确定大区域似大地水准面。该方法在长江口北岸得到了很好的验证,并取得了比较理想的精度。     

南极Dome A地区高精度DEM的建立——顾及波形重定、坡度改正及数据融合

介绍了CryoSat-2LRM模式下优化后的OCOG、CFI和LIRT的3种波形重定算法。基于南极Dome-A昆仑站区的实测GPS数据,比较了CryoSat-2LRM模式下的3种波形重定方法,对不同波形重定算法下的测高数据进行了精度评估。结果表明优化后的OCOG算法精度最好,与GPS结果平均差值约为-0.07m,标准差约为0.60m,明显优于其他两种算法。通过比较坡度与卫星数据精度的关系,发现坡度因素对于卫星测高数据精度的影响不可忽视,在Dome A地区验证结果表明,坡度改正可使得卫星测高精度提高约38%。最后联合GPS和CryoSat-2OCOG数据,建立了南极Dome-A地区300m分辨率DEM,其精度约为0.24m。     

Comparing the Kalman filter with a Monte Carlo-based artificial neural network in the INS/GPS vector gravimetric system

Rigorous physical and mathematical analysis has been intensively developed to obtain the gravity disturbance vector from the inertial navigation system and the global positioning system. However, the combination of the observation noise and the systematic INS errors make it very challenging to accurately and efficiently describe the dynamics of the system with rigorous equations. Thus, the accuracy of the gravity disturbance estimates, especially in the horizontal components, is limited by the insufficient error models. To overcome the difficulty of directly modeling the systematic errors with exact mathematical equations, a Monte Carlo based artificial neural network is successfully applied in the moving base gravimetric system. The computation results show significant improvement in the precision of all components of the gravity disturbance estimates.