Robust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm

For deriving the robust estimation by the EM (expectation maximization) algorithm for a model, which is more general than the linear model, the nonlinear Gauss Helmert (GH) model is chosen. It contains the errors-in-variables model as a special case. The nonlinear GH model is difficult to handle because of the linearization and the Gauss Newton iterations. Approximate values for the observations have to be introduced for the linearization. Robust estimates by the EM algorithm based on the variance-inflation model and the mean-shift model have been derived for the linear model in case of homoscedasticity. To derive these two EM algorithms for the GH model, different variances are introduced for the observations and the expectations of the measurements defined by the linear model are replaced by the ones of the GH model. The two robust methods are applied to fit by the GH model a polynomial surface of second degree to the measured three-dimensional coordinates of a laser scanner. This results in detecting more outliers than by the linear model.     

Robust bayesian estimation

Classical least squares Bayesian estimation consists of minimizing the sum of the squared residuals of observations and the corrections to prior estimates of parameters.Many authors have produced more robust versions of this estimation by replacing the square by something else, such as the absolute value. In this article, three robust (M-LS, LS-M and M-M) estimators for three corresponding error models are described based on the principle of maximum likelihood type estimates (M-estimates). The influence functions of the three robust Bayesian estimators are given. The algorithm implementation problems are discussed and the expressions for the posterior variance-covariance are derived.     

SAR图像河流提取的主动轮廓模型的稳健估计算法

针对现有主动轮廓模型无法精确提取SAR图像中河流的难题,提出了一种结合L₁范数和拉普拉斯能量的主动轮廓模型。首先,将Chan-Vese(CV)模型中L₂范数形式的外部能量约束项替换为L₁范数形式的外部能量约束项,得到新的能量泛函;其次,提出了一种基于拉普拉斯核函数的外部能量约束项,并将其添加到上述能量泛函中,同时赋予两种外部能量约束项不同的调节系数;最后,引入曲线内外区域像素灰度绝对中位差的均值替代模型中的常数曲线内外能量权值,以得到完整的提出模型。针对实际SAR图像进行河流提取,结果表明:与现有主动轮廓模型相比,本文提出的模型在河流提取准确性和提取效率两方面具有明显优势。     

基于EIV模型的稳健估计

EIV（error-in-variables）模型同时考虑观测向量和系数矩阵的误差,自提出以来便得到广泛应用。目前针对EIV模型的整体最小二乘解法（TLS）假设观测值仅含有偶然误差,当观测值存在粗差时其解并不是最优的。文中通过选定合适的权函数,结合加权整体最小二乘迭代算法,导出基于EIV模型的稳健整体最小二乘迭代解法（RTLS）。线性拟合实验表明,文中方法能对粗差进行定位,且估计量受粗差影响较小,具有稳健性。     

Robust estimation of geodetic datum transformation

The robust estimation of geodetic datum transformation is discussed. The basic principle of robust estimation is introduced. The error influence functions of the robust estimators, together with those of least-squares estimators, are given. Particular attention is given to the robust initial estimates of the transformation parameters, which should have a high breakdown point in order to provide reliable residuals for the following estimation. The median method is applied to solve for robust initial estimates of transformation parameters since it has the highest breakdown point. A smooth weight function is then used to improve the efficiency of the parameter estimates in successive iterative computations. A numerical example is given on a datum transformation between a global positioning system network and the corresponding geodetic network in China. The results show that when the coordinates are contaminated by outliers, the proposed method can still give reasonable results. Received: 25 September 1997 / Accepted: 1 March 1999     

Robust estimation based on energy minimization principles

 It is argued that the tendency of nature to minimize energy may be used as a unifying basis for all robust estimators. Robustness is defined and discussed based on mechanical rather than empirical and abstract tools. This mechanical view of robustness is then extended to design new and useful robust data editors that suppress the outlying content of the contaminated observations. These editors are applied to edit samples of sea-surface heights, gravity observations and reduced global positioning system baselines. Received: 12 July 1997 / Accepted: 8 June 1999     

Robust biased estimation and its applications in geodetic adjustments

In this paper, a number of robust biased estimators (e.g. ordinary robust ridge estimator, robust principal components estimator, robust combined principal components estimator, robust single-parametric principal components estimator, robust root-root estimator) are established by means of a unified expression of biased estimators and based on the principle of equivalent weight. The most attractive advantage of these new estimators is that they can not only overcome the ill-conditioning of the normal equation but also have the ability to resist outliers. A numerical example is used to illustrate that these new estimators are much better than the least-squares estimator and various biased estimators even when both ill-conditioning and outliers exist. Received: 14 November 1995/Accepted: 11 February 1998     

GPS向量网的抗差方差分量估计

GPS向量网的整体平差中，基线向量间的精度往往存在评定标准不一的问题，如各同步区采用不同的基线解算软件，各同步区观测环境不同等。这类问题可能会造成权比的失调，并因此影响最后的平差结果。另外，由于GPS观测量的粗差出现率也较常规大地控制网的粗差出现率高，若不采用有效措施，也会影响最后的平差结果，本文针对上述情况，讨论了抗差方差分量估计，并给出了算例。     

Robust estimation of systematic errors of satellite laser range

Methods for analyzing laser-ranging residuals to estimate station-dependent systematic errors and to eliminate outliers in satellite laser ranges are discussed. A robust estimator based on an M-estimation principle is introduced. A practical calculation procedure which provides a robust criterion with high breakdown point and produces robust initial residuals for following iterative robust estimation is presented. Comparison of the results from the least-squares method with those of the robust method shows that the results of the station systematic errors from the robust estimator are more reliable. Received: 18 March 1997 / Accepted: 17 March 1999     

GLONASS inter-frequency phase bias rate estimation by single-epoch or Kalman filter algorithm

GPS Solutions - GLONASS double-differenced (DD) ambiguity resolution is hindered by the inter-frequency bias (IFB) in GLONASS observation. We propose a new algorithm for IFB rate estimation to...     

自适应阈值的基础矩阵估计算法

针对RANSAC算法在估计基础矩阵过程中需要人为设定阈值的问题,该文提出一种自适应阈值的基础矩阵估计算法。该算法首先引入ORSA算法,计算内点集以及基础矩阵,随后将得到的内点集与基础矩阵作为最小中值算法的初始值做进一步加权优化,在保证基础矩阵估计精度的前提下得到更好的内点集。其中,利用ORSA算法估计时通过计算误匹配警报数(NFA)值评判估计精度,舍去了RANSAC算法中人为设定阈值的步骤;利用最小中值算法加权优化的过程中采用最小化误差中值的方式,避免人为设定阈值。实验结果显示,该算法在保证基础矩阵估计精度的同时,能够获得最佳的内点集,且具有一定的抗噪声能力。     

尺度比稳健估计及参考椭球参数确定

短程精密测距精度一般优于GNSS测量精度,工程中常用GNSS测量与精密测距方法联合建立高精度工程测量控制网,对两者所存在的尺度差异,常采用尺度比进行统一,其关键是尺度比的合理选择。文中参照精密测距边长确定的实测尺度比相对于理论尺度比的残差,建立空间分布与尺度残差线性关系,对尺度差异进行估计并确定合理的尺度比,再在投影层面将尺度比等价转换成参考椭球参数进行数据归算,从而实现GNSS与精密测距成果的高度融合,得到高精度工程测量控制网的可靠成果。     

附加运动学约束的BDS抗差UKF导航算法

针对城市复杂环境中单一BDS导航受多路径（multipath,MP）和非视距（non-line-of-sight,NLOS）信号干扰导致精度下降的问题,提出一种附加运动学约束的抗差无迹卡尔曼滤波（unscented Kalman filter,UKF）算法。该算法基于新息向量构造等价权函数,克服了位置及接收机钟差初值不准确引起的抗差性能下降问题。同时,利用载体的近似运动方向和高程约束,进一步增强滤波解。实测车载试验结果表明,本文方法可有效抑制MP和NLOS信号的干扰,提高城市环境中的BDS导航精度。     

Robust estimation of deformation from observation differences for free control networks

Deformation measurements have a repeatable nature. This means that deformation measurements are performed often with the same equipment, methods, geometric conditions and in a similar environment in epochs 1 and 2 (e.g., a fully automated, continuous control measurements). It is, therefore, reasonable to assume that the results of deformation measurements can be distorted by both random errors and by some non-random errors, which are constant in both epochs. In other words, there is a high probability that the difference in the accuracy and precision of measurement of the same geometric element of the network in both epochs has a constant value and sign. The constant errors are understood, but the manifestation of these errors is difficult to determine in practice. For free control networks (the group of potential reference points in absolute control networks or the group of potential stable points in relative networks), the results of deformation measurements are most often processed using robust methods. Classical robust methods do not completely eliminate the effect of constant errors. This paper proposes a new robust alternative method called REDOD. The performed tests showed that if the results of deformation measurements were additionally distorted by constant errors, the REDOD method completely eliminated their effect from deformation analysis results. If the results of deformation measurements are only distorted by random errors, the REDOD method yields very similar deformation analysis results as the classical IWST method. The numerical tests were preceded by a theoretical part. The theoretical part describes the algorithm of classical robust methods. Particular attention was paid to the IWST method. In relation to classical robust methods, the optimization problem of the new REDOD method was formulated and the algorithm for its solution was derived.     

Robust estimation for correlated observations: two local sensitivity-based downweighting strategies

An iterative robust estimation procedure for correlated observations is proposed, in which the a-prior correlation coefficient matrix is not updated to alleviate the computational burden. Selection of the downweighting strategy plays a key role in the proposed method. Two local sensitivity-based strategies, one is based on the uniformly most powerful test statistics, the other is based on the standardized least squares residuals, are developed and analyzed. Monte Carlo simulations in the GPS network adjustment scenario demonstrate that, the two strategies can provide a certain resistance against the deteriorating effect of outlying observations on the parameter estimates; the former downweighting strategy is superior to the latter one, both in terms of robustness and computational efficiency.     

面向低成本车载IMU的安装姿态估计

车载IMU相对于车体的安装姿态信息是应用车辆非完整约束的必需条件,而车辆非完整约束可以有效解决GNSS信号长时间中断的情形下低成本INS+GNSS组合导航系统精度降低的问题。本文针对车载场景下的低成本消费级IMU,基于卡尔曼滤波和粒子滤波提出了一种估计IMU安装姿态的算法。该算法无需限制IMU相对于车体的姿态为小角度;随后,基于仿真平台对低成本消费级IMU进行建模,利用生成的若干组不同安装姿态的IMU数据对算法进行验证;最后进行车载测试。仿真结果和车载测试结果都表明,该算法可以准确地估计IMU相对于车体的安装姿态,对于低成本INS+GNSS组合导航系统精度的提高具有实际意义。     

病态不确定性平差模型的岭估计算法

测量数据在获取的过程中,常存在不确定性,它们会影响参数估计结果,不确定性平差模型的解算方法可以有效提高参数估计的有效性和可靠性。当观测方程的系数矩阵存在接近零的奇异值,采用岭估计可有效抑制观测方程病态性对参数估值结果的影响。当不确定性平差模型出现病态,其受系数矩阵误差和观测值误差的影响更为严重,本文将岭估计法应用于病态不确定性平差模型,推导了迭代算法,以提高解的稳定性,并用算例验证,结果表明了新方法的有效性和可行性。     

抗差岭型组合主成分估计及误差影响

本文从有偏估计类中的岭型组合主成分估计出发 ,结合抗差估计理论 ,利用抗差M估计模型 ,提出了一种新的抗差有偏估计法———抗差岭型组合主成分估计。推导了平差参数的抗差岭型组合主成分估计解 ,以及平差参数的验后精度和误差影响函数。计算结果表明 ,抗差岭型组合主成分估计不但能克服法方程系数阵病态性的影响 ,而且能有效地抵制观测值中精差的异常干扰 ,使参数的解更为准确可靠     

我国IGS基准站高程时间序列抗差功率谱估计

为更清晰地了解基准站高程序列的周期运动特性,本文采用抗差最小二乘迭代与功率谱估计相结合的方法,分析了我国6个IGS基准站近11年观测得到的高程时间序列数据。在功率谱分析获取准确的高程运动第一主周期项的基础上,继续抗差迭代,并分离出高程方向运动的其他主周期项和振幅,得到了主要周期项对高程方向运动能量的贡献大小,基准站高程方向具有接近一年的年周期运动和多于一年的第二主周期项运动,半周年项运动所占的比重很小。