GPS数据处理中基准站的加权及其影响

将Bayes估计中的全部参数加权扩展为部分参数加权，从Bayes定理出发导出了参数估值公式和精度估计公式；推导了GPS数据处理中基准站加权不当对平差值的影响公式；证明了基准站加权不当时将影响参数估值的最优性，使估值精度降低，并用算例估计了基准站加权不当对框架参数影响的大小。     

Least squares adjustment and collocation

Summary For the estimation of parameters in linear models best linear unbiased estimates are derived in case the parameters are random variables. If their expected values are unknown, the well known formulas of least squares adjustment are obtained. If the expected values of the parameters are known, least squares collocation, prediction and filtering are derived. Hence in case of the determination of parameters, a least squares adjustment must precede a collocation because otherwise the collocation gives biased estimates. Since the collocation can be shown to be equivalent to a special case of the least squares adjustment, the variance of unit weight can be estimated for the collocation also. This estimate gives the scale factor for the covariance matrices being used in the collocation. In addition, the methods of testing hypotheses and establishing confidence intervals for the parameters of the least squares adjustment may be applied to the collocation.     

香港地区大气加权平均温度建模与研究

在地基GPS水汽反演过程中,针对因大气加权平均温度的精度而影响大气可降水量计算结果精度的问题,文中采用回归分析方法对香港地区2006-2016年的探空数据进行研究,构建适用于香港地区的单因子以及多因子两种大气加权平均温度计算模型.并使用两种模型分别预测2017年加权平均温度,与多种经验公式结果以及真值进行对比,单因子和多因子模型与真值的偏差在-5～5K范围内分别占比80.72%和85.26%,明显优于其他经验公式;且按季节分别建模对大气加权平均温度计算结果的精度并没有明显提高,但按昼夜分别建模能够使计算结果的精度得到明显的提高.因此为了能够使水汽反演计算时的精度得到提升,应当使用当地多年的探空气象资料构建适用于当地的加权平均温度计算模型,对于提高GPS反演大气水汽总量的精度具有重要意义.     

Partial EIV模型的非负最小二乘方差分量估计

Partial Errors-in-Variables(Partial EIV)模型是EIV模型的扩展形式,权阵构造简单,当系数矩阵中存在非随机元素和随机元素时,Partial EIV模型的适用性更强。针对Partial EIV模型中随机模型不准确的情况,将系数矩阵和观测向量分别作为一类数据,本文在该模型的基础上,使用最小二乘方差分量估计方法,推导相关计算公式及迭代算法,分别估计出相应的方差分量估值。并对出现的负方差使用非负最小二乘理论,增加约束条件,对随机模型进行修正,得到更加合理的参数估值。试实验结果表明,本文的方法与其他方差分量估计方法等价。     

顾及截断偏差影响的TSVD截断参数确定方法

TSVD通过截断参数截掉较小的奇异值来改善病态性对估计的影响,其本质是通过引入少量偏差来降低方差,以提高估值的稳定性和可靠性。截断参数是影响TSVD解算效果的关键因素,常用的广义交叉核实法(GCV法)和L曲线法未从TSVD改善模型参数估值质量的角度确定截断参数,稳定性和可靠性不足,而最小MSE法理论依据充分但受限于MSE计算的准确性。通过分析TSVD由小到大截掉奇异值后,相应的估值方差与偏差变化,本文提出了引入偏差量小于降低方差量来确定截断参数的思想,并通过估计出较大奇异值截掉后的偏差引入量建立偏差估值可信区间,利用可信区间内偏差估值与方差下降量进行比较,避免较小奇异值截掉后的方差下降量与偏差引入量的直接比较,从而解决参数真值未知截掉较小奇异值引入偏差量难以准确计算的问题。最后通过试验验证了新方法的可行性和有效性,相比于GCV法和L曲线法,新方法确定的截断参数稳定性和可靠性更高,可有效提高TSVD的解算效果。     

顾及起始数据误差的双点测边交会的精度计算

推导了起始数据误差对双点测边交会定点精度影响的估算式，并依此给出顾及起始数据误差的点位精度计算公式。     

Stochastic significance of peaks in the least-squares spectrum

The least-squares spectral analysis method is reviewed, with emphasis on its remarkable property to accept time series with an associated, fully populated covariance matrix. Two distinct cases for the input covariance matrix are examined: (a) it is known absolutely (a-priori variance factor known); and (b) it is known up to a scale factor (a-priori variance factor unknown), thus the estimated covariance matrix is used. For each case, the probability density function that underlines the least-squares spectrum is derived and criteria for the statistical significance of the least-squares spectral peaks are formulated. It is shown that for short series (up to about 150 values) with an estimated covariance matrix (case b), the spectral peaks must be stronger to be statistically significant than in the case of a known covariance matrix (case a): the shorter the series and the lower the significance level, the higher the difference becomes. For long series (more than about 150 values), case (b) converges to case (a) and the least-squares spectrum follows the beta distribution. The results of this investigation are formulated in two new theorems. Received: 27 May 1997/Accepted: 30 September 1998     

Improving the modeling of the atmospheric delay in the data analysis of the Intensive VLBI sessions and the impact on the UT1 estimates

The very long baseline interferometry (VLBI) Intensive sessions are typically 1-h and single-baseline VLBI sessions, specifically designed to yield low-latency estimates of UT1-UTC. In this work, we investigate what accuracy is obtained from these sessions and how it can be improved. In particular, we study the modeling of the troposphere in the data analysis. The impact of including external information on the zenith wet delays (ZWD) and tropospheric gradients from GPS or numerical weather prediction models is studied. Additionally, we test estimating tropospheric gradients in the data analysis, which is normally not done. To evaluate the results, we compared the UT1-UTC values from the Intensives to those from simultaneous 24-h VLBI session. Furthermore, we calculated length of day (LOD) estimates using the UT1-UTC values from consecutive Intensives and compared these to the LOD estimated by GPS. We find that there is not much benefit in using external ZWD; however, including external information on the gradients improves the agreement with the reference data. If gradients are estimated in the data analysis, and appropriate constraints are applied, the WRMS difference w.r.t. UT1-UTC from 24-h sessions is reduced by 5% and the WRMS difference w.r.t. the LOD from GPS by up to 12%. The best agreement between Intensives and the reference time series is obtained when using both external gradients from GPS and additionally estimating gradients in the data analysis.     

起算数据误差对平差值及其精度的影响

讨论了起算数据误差对平差值和平差值精度的影响,给出了计算各种影响值的公式和应用实例,并对实例计算结果进行了分析和讨论。     

方差分量估计在机载InSAR区域网平差中的应用

基于验后方差分量估计的思想,针对观测值中各类观测分量的方差难以直接估计的问题,研究了机载InSAR区域网平差干涉参数定标权值确定理论,设计了利用Helmert方差分量估计扩展模型的机载InSAR区域网平差干涉参数定标权值确定方法。采用我国机载双天线InSAR数据进行相关试验,表明验后估计定权能合理地顾及DEM的生成精度和拼接精度。     

北斗/GPS抗差移动窗口定权位移探测

蠕变状态下Kalman定位精度通常与观测值方差有极大关系,BDS(BeiDou Navigation Satellite System)/GPS组合观测值方差易受观测值权比精确度的影响。为了提高位移探测精度、缩短初始坐标收敛时间及降低监测成本,本文采用时钟同步双天线BDS/GPS接收机,在构建单频单差组合定位模型基础上,分别对GPS和BDS观测值等价权进行抗差处理,利用引入时间相关遗忘因子的Helmert方差估计,精确确定GPS与BDS观测值权比,最后通过实时更新观测值方差,实现扩展Kalman滤波的逐历元定位。试验结果表明,针对短基线(1km),BDS/GPS抗差精密定权Kalman方法可显著缩短初始坐标收敛时间,位移探测精度可达到亚毫米级,位移收敛速率与移动窗口参数基本成反比关系,适用于具有蠕变特征形变体的监测。     

Evaluating Errors in a Digital Vegetation Map with Forest Inventory Data and Accuracy Assessment Using Fuzzy Sets

In large-area mapping projects, existing reference data, often collected for a different purpose, are increasingly being used for map accuracy assessment. Multi-attribute digital vegetation maps have been developed for all National Forest lands in California (8.1 million ha). We developed decision rules that could be applied to quantitative Forest Inventory and Analysis (FIA) plot data in order to score the fuzzy membership of plot locations in all possible map classes. We compare the accuracy of the vegetation map attributes estimated using this method to accuracy estimated from fuzzy class membership scores assigned by experts (inventory crews) during field work. Accuracy of the vegetation life form attribute was estimated to be higher when expert label assignments were used as reference data (76–87%), instead of FIA plot data (62–79%). This suggests that automated decision rules applied to detailed data from FIA plots, which have smaller area than map polygons, may systematically underestimate map accuracy. However, assignment of the actual map labels to FIA plot locations by inventory crews appears to be a robust method for using the FIA data for accuracy assessment.     

精密重力测量中相对重力仪格值系数的贝叶斯估计方法

相对重力仪的格值系数随时间会发生微小的变化,是影响精密重力测量精度的重要因素。通常需定期对相对重力仪进行专门的基线标定来评估仪器格值系数的变化。本文提出了一种利用重力观测数据进行格值系数评估的新方法,原理是利用测网中已知的多个绝对重力基准点作为先验约束,同时考虑仪器的非线性漂移变化,将格值系数作为超参数,基于贝叶斯原理和赤池贝叶斯信息准则（ABIC）估计最优值。通过对模拟数据的测试,该方法在高斯噪声和仪器非线性漂移等不确定性存在的情况下,可以获得格值系数的准确估计结果。对实测重力数据的测试表明：估计的格值系数与测量前在基线场标定的格值系数差值在5×10^-5以内;而且相较于采用标定不准确的格值系数,该方法可以获得与绝对重力测量结果差异更小的平差重力值。本文研究结果为有效提高精密重力测量的效率和精度提供了方法保障。     

Adaptive Kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of GNSS triple-frequency signals

In order to incorporate the time smoothness of ionospheric delay to aid the cycle slip detection, an adaptive Kalman filter is developed based on variance component estimation. The correlations between measurements at neighboring epochs are fully considered in developing a filtering algorithm for colored measurement noise. Within this filtering framework, epoch-differenced ionospheric delays are predicted. Using this prediction, the potential cycle slips are repaired for triple-frequency signals of global navigation satellite systems. Cycle slips are repaired in a stepwise manner; i.e., for two extra wide lane combinations firstly and then for the third frequency. In the estimation for the third frequency, a stochastic model is followed in which the correlations between the ionospheric delay prediction errors and the errors in the epoch-differenced phase measurements are considered. The implementing details of the proposed method are tabulated. A real BeiDou Navigation Satellite System data set is used to check the performance of the proposed method. Most cycle slips, no matter trivial or nontrivial, can be estimated in float values with satisfactorily high accuracy and their integer values can hence be correctly obtained by simple rounding. To be more specific, all manually introduced nontrivial cycle slips are correctly repaired.     

DEM支持下的单倾斜影像三维量测方法

提出了基于DEM的单张倾斜航片快速量测方法.该方法根据影像与建筑物之间的位置、姿态等特征,推导出单张影像量测数学模型及计算公式,并选择试验区域对本文算法的精度进行验证.试验结果表明,研究区内平面点位误差小于0.13 m,建构筑物每层的垂直误差约为0.11 m,能够满足城市规划与管理的应用需求,可为城市三维数据获取提供经验和借鉴.     

植被调节下的干旱区不透水面覆盖率遥感估算方法

基于DMSP/OLS夜间灯光数据的居住区指数模型（HSI）广泛应用于区域尺度城市不透水面扩张监测。但是,在干旱区由于受到裸岩、沙漠、戈壁等低植被覆盖区干扰,HSI算法的精度和适应性受到了一定的影响。为解决这一问题,本文利用植被覆盖度作为调节系数,对灯光数据与植被指数进行动态调整,构建了适用于干旱区的城市植被调节不透水指数（VAISI）;然后采用SVR模型,通过机器学习的方法构建了城市不透率参考数据与VAISI之间的非线性关系模型,实现对干旱区区域尺度不透水面覆盖率估算;最后,对模型估算结果进行了精度验证和比较分析。试验结果表明：在干旱区,VAISI解决了由于灯光溢出问题及城市周边裸土等低植被覆盖等因素导致的城市周边裸土像元不透率估算过高问题,一定程度上提高了城市内部不透水面空间分布信息的表达能力,有效克服了非灯光区估算结果高于背景值的现象。平均相关系数R由0.69提升到0.79,RMSE由0.17降至0.14。     

利用预测残差和选权滤波构造的分类因子在GPS/INS组合导航中的应用

针对组合导航观测个数少、采用单因子自适应滤波会损失间接可测参数精度的问题,利用预测残差和选权滤波思想构造了分类自适应因子。实测算例计算结果表明,该算法不仅能够很好地控制状态扰动异常影响,而且还能避免损失间接可测参数的精度,进一步提高了导航精度。     

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.     

Stratified aboveground forest biomass estimation by remote sensing data

Remote sensing-assisted estimates of aboveground forest biomass are essential for modeling carbon budgets. It has been suggested that estimates can be improved by building species- or strata-specific biomass models. However, few studies have attempted a systematic analysis of the benefits of such stratification, especially in combination with other factors such as sensor type, statistical prediction method and sampling design of the reference inventory data. We addressed this topic by analyzing the impact of stratifying forest data into three classes (broadleaved, coniferous and mixed forest). We compare predictive accuracy (a) between the strata (b) to a case without stratification for a set of pre-selected predictors from airborne LiDAR and hyperspectral data obtained in a managed mixed forest site in southwestern Germany. We used 5 commonly applied algorithms for biomass predictions on bootstrapped subsamples of the data to obtain cross validated RMSE and r² diagnostics. Those values were analyzed in a factorial design by an analysis of variance (ANOVA) to rank the relative importance of each factor. Selected models were used for wall-to-wall mapping of biomass estimates and their associated uncertainty. The results revealed marginal advantages for the strata-specific prediction models over the unstratified ones, which were more obvious on the wall-to-wall mapped area-based predictions. Yet further tests are necessary to establish the generality of these results. Input data type and statistical prediction method are concluded to remain the two most crucial factors for the quality of remote sensing-assisted biomass models.     

Estimation and modelling of the local empirical covariance function using gravity and satellite altimeter data

The estimation of a local empirical covariance function from a set of observations was done in the Faeroe Islands region. Gravity and adjusted Seasat altimeter data relative to theGPM2 spherical harmonic approximation were selected holding one value in celles of1/8°×1/4° covering the area. In order to center the observations they were transformed into a locally best fitting reference system having a semimajor axis1.8 m smaller than the one ofGRS80. The variance of the data then was273 mgal ² and0.12 m ² respectively. In the calculations both the space domain method and the frequency domain method were used. Using the space domain method the auto-covariances for gravity anomalies and geoid heights and the cross-covariances between the quantities were estimated. Furthermore an empirical error estimate was derived. Using the frequency domain method the auto-covariances of gridded gravity anomalies was estimated. The gridding procedure was found to have a considerable smoothing effect, but a deconvolution made the results of the two methods to agree. The local covariance function model was represented by a Tscherning/Rapp degree-variance model,A/((i−1)(i−2)(i+24))(R _B /R _E )²ⁱ⁺², and the error degree-variances related to the potential coefficient setGPM2. This covariance function was adjusted to fit the empirical values using an iterative least squares inversion procedure adjusting the factor A, the depth to the Bjerhammar sphere(R _E −R _B ), and a scale factor associated with the error degree-variances. Three different combinations of the empirical covariance values were used. The scale factor was not well determined from the gravity anomaly covariance values, and the depth to the Bjerhammar sphere was not well determined from geoid height covariance values only. A combination of the two types of auto-covariance values resulted in a well determined model.