L1-范估计的无偏性

根据一元Laplace分布的概率密度函数及分布函数公式,推导了当观测值个数n为偶数时,中位数的概率密度函数;在此基础上证明了L1-范估计的无偏性.     

基于Copula的降水量不确定性建模

传统的地统计学方法需要区域降水量满足多元正态假设才能给出无观测站位置降水量的概率密度函数,经典的统计学方法则用唯一的概率密度函数对区域内任一无观测站位置的降水量进行统计描述。尝试用基于Copula的地统计学方法对无观测站位置月降水量的不确定性进行建模,并与上述两种方法进行对比分析。案例研究表明,基于Copula的地统计学方法可以得到任一无观测站位置的概率密度函数,且不同位置的概率密度函数与其周围观测站的分布及其观测值有关率优于普通克里格和基于Box-cox变换的普通克里格。     

一元Laplace分布的L1—范估计的无偏性

根据Laplace分布的概率密度函数公式，推导了了中位数的概率密度，在此基础上证明了L1－范估计的无偏性。     

P-范分布熵的近似估计

P-范分布复杂的概率密度函数表达式不利于熵的计算和实际应用,提出利用简单分布的熵组合近似估计P-范分布的熵,可简化计算过程。数值演算对比表明,P-范分布熵的近似估计误差均不超过0.09,尤其当1≤p≤2时,最大误差仅为0.008 8,可实证近似计算的有效性。     

一元P-范分布参数估计的改进方法

当观测误差服从P范分布时,本文从P范分布的概率密度函数和统计性质出发,利用绝对矩得到了参数p和方差的合理选择公式,给出了一种P范分布的参数的估计方法,可以使误差分布更加接近真实分布.将得到的参数估值作为应用极大似然估计法进行迭代时的初值,从而减少了运算时间,提高了运算效率.同时,将模型展开为泰勒级数,取至二次项,从而使...     

一元p范分布的参数快速估计方法

首先得到了一元p范分布在不同情况下的估计效率公式,给出了选择不同尺度参数时Lp估计的效率,说明了选择合适尺度参数的重要性;然后根据误差分布的实际情况,从一元p范分布的概率密度函数和统计性质出发,利用绝对矩得到了尺度参数和方差的合理选择公式。通过曲线拟合的公式,给出了一种一元p范分布的参数p的估计方法,并用两个模拟算例对本文方法进行了验证。     

Matlab和C#混合编程在SAR图像船只检测中的应用

目前,SAR图像船只检测只能在当前编程软件中实现,无法被其他软件调用,很难在后续开发的软件系统中得到广泛的应用。为此,本文基于C#和Matlab混合编程,开发出了一种可以被调用的SAR图像船只检测界面性应用窗体。该窗体运行后,生成K分布、G^0分布和直方图统计模型的概率密度函数曲线和相应的检测结果图像,通过比较,可判别出K分布更适合应用于SAR图像的船只检测中。     

一种新的稳健估计方法的权函数选取

介绍了利用误差分布律的概率密度函数定义权函数的一种稳健估计方法。首先从理论上阐述了此种稳健方法的计算步骤,并通过实例同最小二乘法和几种稳健估计方法（Huber估计法、Hampel估计法、丹麦估计法）作了比较;证明了此种方法的优越性。     

一种新的稳健估计方法的权函数选取

介绍了利用误差分布律的概率密度函数定义权函数的一种稳健估计方法。首先从理论上阐述了此种稳健方法的计算步骤,并通过实例同最小二乘法和几种稳健估计方法(Huber估计法、Hampel估计法、丹麦估计法)作了比较;证明了此种方法的优越性。     

基于信息扩散的极大似然估计

提出了扩散极大似然估计方法，利用实际观测值的概率密度函数的信息扩散估计，代替了对观测值分布的主观假设，从而具有很强的自适应性。最后设计了两个算例，说明了扩散极大似然估计的过程，并考察了扩散极大似然估计的特性。     

Generalized maximum-likelihood estimation of variance–covariance components with non-informative prior

 A new estimator of variance–covariance components is presented. The proposed estimator is derived by applying the principle of maximum-likelihood estimation to the posterior probability density function for the case when no prior information is available. Received: 9 August 1999 / Accepted: 10 November 2000     

The probability distribution of the ambiguity bootstrapped GNSS baseline

 The purpose of carrier phase ambiguity resolution is to improve upon the quality of the estimated global navigation satellite system baseline by means of the integer ambiguity constraints. However, in order to evaluate the quality of the ambiguity resolved baseline rigorously, its probability distribution is required. This baseline distribution depends on the random characteristics of the estimated integer ambiguities, which in turn depend on the chosen integer estimator. In this contribution is presented an exact and closed-form expression for the baseline distribution in the case that use is made of integer bootstrapping. Also presented are the bootstrapped probability mass function and easy-to-compute measures for the bootstrapped baseline's probability of concentration. Received: 28 September 2000 / Accepted: 11 January 2001     

On the Distribution of the Estimated Coherence

The recent paper by Abdelfattah and Nicolas proposed a novel coherence magnitude estimator and studied its properties. Here, we derive simpler and more explicit expressions for four of the properties that were studied: 1) the probability density function; 2) moments; 3) Mellin transform; and 4) second-kind moments. We establish numerical efficiency of these expressions and provide simple Maple programs for inversion. We expect that the results presented here could enhance applicability of the new estimator.     

观测误差的P分布与估计准则

本文导出了观测误差服从一族指数分布－Ｐ分布的密度函数，讨论了Ｐ分布的离差，数学特征和估计准则等问题，描述了误差分布与估计方法的关系，有利于进一步讨论估计方法的抗差性。     

DEM 地形描述误差的概率分布特征研究

以黄土丘陵1:1万DEM为基础数据,通过稀疏抽点法获取不同格网点布设位置下的DEM,进而分析不同分辨率DEM中单个地面点和区域地形单元的Et概率分布特征。实验结果表明:对于任意格网分辨率DEM,无论是不同布设方案下的单个地面点,还是区域地形单元,其Et的概率密度均呈现正态分布特征。对于单个地面点,如果以其为中心的3×3DEM格网单元区域以凸地形为主,其Et概率密度呈现出右偏正态分布特征;如果以凹地形为主,则呈现左偏正态分布特征,其他区域则呈现标准正态分布特征。     

Position-domain integrity risk-based ambiguity validation for the integer bootstrap estimator

Integrity monitoring for ambiguity resolution is of significance for utilizing the high-precision carrier phase differential positioning for safety–critical navigational applications. The integer bootstrap estimator can provide an analytical probability density function, which enables the precise evaluation of the integrity risk for ambiguity validation. In order to monitor the effect of unknown ambiguity bias on the integer bootstrap estimator, the position-domain integrity risk of the integer bootstrapped baseline is evaluated under the complete failure modes by using the worst-case protection principle. Furthermore, a partial ambiguity resolution method is developed in order to satisfy the predefined integrity risk requirement. Static and kinematic experiments are carried out to test the proposed method by comparing with the traditional ratio test method and the protection level-based method. The static experimental result has shown that the proposed method can achieve a significant global availability improvement by 51% at most. The kinematic result reveals that the proposed method obtains the best balance between the positioning accuracy and the continuity performance.     

The success rate and precision of GPS ambiguities

 An application of a theorem on the optimality of integer least-squares (LS) is described. This theorem states that the integer LS estimator maximizes the ambiguity success rate within the class of admissible integer estimators. This theorem is used to show how the probability of correct integer estimation depends on changes in the second moment of the ambiguity `float' solution. The distribution of the `float' solution is considered to be a member of the broad family of elliptically contoured distributions. Eigenvalue-based bounds for the ambiguity success rate are obtained. Received: 11 January 1999 / Accepted: 2 November 1999     

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.     

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