Estimation and testing of higher-order spatial autoregressive panel data error component models

This paper develops an estimator for higher-order spatial autoregressive panel data error component models with spatial autoregressive disturbances, SARAR(R,S). We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define a generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their joint asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.     

First and second moments of non-linear least-squares estimators

The first two moments of non-linear and least-squares estimators are studied. Approximate expressions for the moments are derived and discussed. The results are compared with those ofJeudy [1988].     

The Exact Distribution of the Multilook Magnitude

Gierull provides a statistical analysis of multilook synthetic aperture radar interferograms. Various expressions for the probability density function, cumulative distribution function, and the moments of associated statistics are derived. It appears, however, that most of these expressions are based on some approximation. In this letter, the corresponding expressions are derived in their exact form, including some elementary representations for certain expressions given by Gierull. A numerical comparison of the exact and approximate expressions is provided     

附有条件的参数平差模型的有偏估计

讨论附有条件的参数平差模型参数的有偏估计问题。提出了约束岭估计和约束主成分估计,并证明了它们的优良性质,最后给出了一个算例,验证了所得结果。     

Estimation of the third and fourth order central moments of measurement errors from sums of powers of least squares adjustment residuals

Summary In the paper a method of determination of estimators of the central moments of the third and fourth order on the basis of the least squares adjustment is presented. These estimators concern the moments of the observation results as well as to readjustment (better) of observation sets with application of methods that take into consideration moments of higher order (not only the variance-covariance matrix).The obtained estimators are not biased, but their effectiveness was not studied. That is why the presented theory is not completed (in the sense of the estimators properties).     

Distributional theory for the DIA method

The DIA method for the detection, identification and adaptation of model misspecifications combines estimation with testing. The aim of the present contribution is to introduce a unifying framework for the rigorous capture of this combination. By using a canonical model formulation and a partitioning of misclosure space, we show that the whole estimation–testing scheme can be captured in one single DIA estimator. We study the characteristics of this estimator and discuss some of its distributional properties. With the distribution of the DIA estimator provided, one can then study all the characteristics of the combined estimation and testing scheme, as well as analyse how they propagate into final outcomes. Examples are given, as well as a discussion on how the distributional properties compare with their usage in practice.     

Empirical likelihood estimation of the spatial quantile regression

The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect.     

Gauss-Markov模型参数的部分根方估计

在分析根方估计，Stein均压缩估计，Sclove部分压缩估计各自特点的基础上，提出了一种新的有偏估计－部分根方估计，并讨论了它的优良性质。计算结果表明，在设计阵呈病态时，部分根方估计确能改善LS估计。     

On the probability density function of the GNSS ambiguity residuals

Integer GNSS ambiguity resolution involves estimation and validation of the unknown integer carrier phase ambiguities. A problem then is that the classical theory of linear estimation does not apply to the integer GPS model, and hence rigorous validation is not possible when use is made of the classical results. As with the classical theory, a first step for being able to validate the integer GPS model is to make use of the residuals and their probabilistic properties. The residuals quantify the inconsistency between data and model, while their probabilistic properties can be used to measure the significance of the inconsistency. Existing validation methods are often based on incorrect assumptions with respect to the probabilistic properties of the parameters involved. In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GPS carrier phase ambiguity residuals. The residuals and their properties depend on the integer estimation principle used. Since it is known that the integer least-squares estimator is the optimal choice from the class of admissible integer estimators, we will only focus on the PDF of the ambiguity residuals for this estimator. Unfortunately the PDF cannot be evaluated exactly. It will therefore be shown how to obtain a good approximation. The evaluation will be completed by some examples.     

An optimality property of the integer least-squares estimator

A probabilistic justification is given for using the integer least-squares (LS) estimator. The class of admissible integer estimators is introduced and classical adjustment theory is extended by proving that the integer LS estimator is best in the sense of maximizing the probability of correct integer estimation. For global positioning system ambiguity resolution, this implies that the success rate of any other integer estimator of the carrier phase ambiguities will be smaller than or at the most equal to the ambiguity success rate of the integer LS estimator. The success rates of any one of these estimators may therefore be used to provide lower bounds for the LS success rate. This is particularly useful in case of the bootstrapped estimator. Received: 11 January 1999 / Accepted: 9 July 1999     

m个相依回归方程系统回归参数的预检验岭估计

对于由 m个相依线性回归方程组成的线性回归系统 ,本文作者基于岭回归估计和预检验估计 ,提出了回归参数的一种新型估计 ,即预检验岭回归估计。并讨论了它的统计性质。     

Navigation message demodulation for GPS receiver on-board spinning rockets

We describe a demodulation scheme for the navigation message of GPS receivers on spin-stabilized rockets. Doppler frequencies due to fast and complex dynamics, in particular high-rate spin, cause errors in carrier frequency tracking. The effects of such errors on navigation message demodulation are described through theoretical analysis and numerical simulation. A demodulation scheme that includes a frequency estimator is proposed to account for frequency tracking errors. It is demonstrated that demodulation performance is degraded 5 dB due to frequency uncertainty. Simulation results showed that a demodulator which includes maximum likelihood (ML) frequency estimator achieves near-optimal symbol error rate under these conditions. Demodulation with ML estimator achieves a bit error rate below 10^?5 for a C/N ₀?=?35 dB–Hz, for spin rates below 2.7?Hz, and a rocket radius smaller than 1 m. For the cases in which computational capabilities of the on-board GPS receiver is insufficient to implement the demodulator with ML estimator, frequency estimation methods with low complexity were also tested through numerical simulation. The proposed Kay and Quinn-Fernandes combination achieves a bit error rate below 10^?5 for a C/N ₀?=?37 dB–Hz while requiring 1/10 of processing time.     

Integer aperture bootstrapping: a new GNSS ambiguity estimator with controllable fail-rate

In this contribution, we introduce a new bootstrap-based method for Global Navigation Satellite System (GNSS) carrier-phase ambiguity resolution. Integer bootstrapping is known to be one of the simplest methods for integer ambiguity estimation with close-to-optimal performance. Its outcome is easy to compute due to the absence of an integer search, and its performance is close to optimal if the decorrelating Z-transformation of the LAMBDA method is used. Moreover, the bootstrapped estimator is presently the only integer estimator for which an exact and easy-to-compute expression of its fail-rate can be given. A possible disadvantage is, however, that the user has only a limited control over the fail-rate. Once the underlying mathematical model is given, the user has no freedom left in changing the value of the fail-rate. Here, we present an ambiguity estimator for which the user is given additional freedom. For this purpose, use is made of the class of integer aperture estimators as introduced in Teunissen (2003). This class is larger than the class of integer estimators. Integer aperture estimators are of a hybrid nature and can have integer outcomes as well as non-integer outcomes. The new estimator is referred to as integer aperture bootstrapping. This new estimator has all the advantages known from integer bootstrapping with the additional advantage that its fail-rate can be controlled by the user. This is made possible by giving the user the freedom over the aperture of the pull-in region. We also give an exact and easy-to-compute expression for its controllable fail-rate.     

A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator

 A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates of vertical motion to the choice of estimator. Received: 9 September 1999 / Accepted: 15 March 2002     

一种基于四元数变换的彩色遥感影像检索方法

遥感影像常存在旋转和缩放等变化关系,这就要求检索时图像特征具有旋转和尺度不变等性质。目前,彩色遥感影像检索在提取这些特征时通常对色彩通道单独进行处理,导致3个通道之间的关系信息丢失,且没有充分利用数据本身所特有的几何特征,影响了检索精度。结合四元数与正交傅里叶-梅林矩的优点,提出了一种基于四元数变换的遥感影像检索方法。针对已有工作中存在的基于四元数傅里叶-梅林矩所提取的纹理特征只具有旋转不变性的问题,利用四元数正交傅里叶-梅林矩构造出具有旋转和尺度不变的纹理特征,并使用四其对图像进行边缘检测,得到边缘色彩图像并提取边缘色彩直方图,综合多种特征进行图像检索。实验结果表明,使用此方法进行遥感影像检索对于图像旋转和尺度变化具有良好的鲁棒性,检索性能明显提高。     

Short Static GPS Sessions: Robust Estimation Results

Least-squares estimation (LS) yields results of low accuracy in the presentce of GPS phase-corrupting environmental conditions. We present a robust estimator that clearly identifies outlying observations caused by obstacles like diagonal cables, branches, or leaves. It performs significantly better than standard LS and signal-to-noise ratio dependent weighting if unfavorable signal distortion occurs, and is equal to LS otherwise. The estimator is realized by an iterated LS algorithm using an equivalent weight matrix. It is a generalization of the Danish Method to heterogeneous and correlated observations. The excellent peformance of the estimator for processing short static sessions is demonstrated using data obtained from an investigation of GPS signal obstruction. ? 2002 Wiley Periodicals, Inc.     

粗差估值型抗差估计

在测量数据处理中,解差受到观测空间和设计空间的双重影响。本文导出了粗差估值与解差的关系,进而得出了以粗差估值表示的ＬＳ估计的影响函数。通过对粗差估值加以限制,根据等价权原理,实现ＬＳ估计对观测空间和设计空间的抗差性。算例表明,粗差估值型抗差估计对观测空间和设计空间均具有良好的抗差效果。     

The temporal variation of the spherical and Cartesian multipoles of the gravity field: the generalized MacCullagh representation

 The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation law allows a representation of the incremental mass density by the respective excitation function. A representation of an arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely: (1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of inertia. Received: 27 July 1999 / Accepted: 24 May 2000