一种新的K分布形状参数估计器

该文提出了一种将已有的U估计器和X估计器结合起来估计K分布形状参数的新估计器。仿真结果表明,与以前提出的方法相比,新估计器在我们所关心的小v值范围能够提供更加准确的形状参数估计,几乎相当于通过数值方法计算的最大似然估计器的性能。     

基于多维矩特征联合的K分布杂波参数估计

K分布杂波参数估计在海洋雷达自适应目标检测中起着关键作用。传统的矩估计器通过联立两个矩求解参数,其估计性能受限于有限矩的信息。因此,本文提出一种基于多维矩特征联合的参数估计方法,旨在拓展矩信息的维度。首先,从观测数据中,提取多个精心设计的线性矩和对数矩,构建一个特征向量。其次,将传统基于统计分布的参数估计问题转换为非线性优化问题。然后,通过引入梯度提升决策树（Gradient Boosting Decision Tree, GBDT）算法,建立特征向量和形状参数之间的函数关系,实现形状参数的估计。此外,推导证明特征向量与尺度参数的独立性以及二阶矩只依赖于尺度参数,从而解决两个参数估计的相关性问题。最后,仿真和实测数据结果表明,所提估计器能利用多个矩的丰富信息,进一步提高参数估计性能。特别是在小形状参数时,其估计性能显著优于现有矩估计法和zrlog(z)期望法。     

基于高斯曲面特征矩阵的扩展目标形状估计

针对传统方法难以准确估计扩展目标形状的问题,提出一种新的基于高斯曲面拟合的量测模型和基于高斯曲面特征矩阵的形状估计算法。首先,建立能反映目标真实形状的结构点,并产生多个高斯曲面,通过曲面叠加形成任意形状的量测空间分布模型;然后,根据高斯曲面拟合原理,用矩阵表示该拟合曲面主要区域的分布特征,并通过映射方程建立矩阵坐标与笛卡尔坐标的映射关系;最后,通过贝叶斯滤波体系更新拟合矩阵。与现有算法相比,本文算法不需要准确预设目标形状,在量测噪声较大的环境下,可以自适应的拟合目标真实形状。并且,在不需要预设目标形状方程的情况下,可以估计包括空心形状在内的任意不规则目标形状。实验结果表明,在目标初始形状参数不准确的情况下,本文算法正确估计了飞机形状、空心形状和集群目标形状,并且具有较好的扩展目标形状估计性能和较强的鲁棒性。     

基于HRRP序列的空间进动目标参数估计方法

空间目标的微动特征可以用来识别空间目标并估计目标参数。在空间进动锥体目标参数估计过程中,针对缺少目标结构参数等先验信息以及部分参数存在耦合问题,本文提出一种基于高分辨距离测量以实现进动参数和形状参数估计的新方法。该方法首先利用弹头目标的径向长度序列的极值信息估计出进动参数和形状参数的耦合结果,然后再根据径向长度序列构造一个辅助函数来实现进动参数和形状参数解耦。最后利用电磁仿真数据实验验证了该方法的有效性和适应性。     

利用三维点云的圆锥状弹头目标参数估计

以激光雷达三维点云对弹头目标形状、姿态、位置估计与目标识别为应用背景。针对导弹弹头的形状特点,将其近似建模为一个圆锥,并可通过6个参数来表征。提出了基于激光成像雷达得到的三维点云与Levenberg-Marquardt(L-M)算法的圆锥状目标参数估计方法,并指出这种方法也可用于对圆锥状目标的识别。通过仿真实验,给出了弹头参数估计误差与三维点云的距离分辨率、点云规模的关系。仿真和实测数据的实验结果表明:该方法在一定的观测距离分辨率下可以较精确地估计出圆锥状弹头目标的参数,并可以根据得到的参数以及对目标函数的优化结果,对目标进行识别。     

SAR图像目标超分辨的变范数正则化算法

 基于正则化变分的框架,提出了SAR图像目标超分辨的变范数算法.考虑目标在成像区域中的稀疏特性,利用广义高斯分布对目标区域的幅度进行建模,在Bayes估计的框架下,推导了l_p范数约束的正则化变分模型和广义高斯分布形状参数的关系.采用迭代的方法在逐次估计真实图像的过程中,将p的取值与逐次估计结果相关联,逐步估计目标区域分布的形状参数,并修正l_p范数的具体形式,由此得到变范数的正则化模型.该方法克服了通过经验选取p值的局限,以及由观测数据估计p值的误差.仿真和实测SAR图像的处理结果表明了该方法的有效性.     

逆高斯纹理复合高斯杂波对异常样本稳健的三分位点估计方法

逆高斯纹理的复合高斯分布(IG-CG分布)是描述高分辨率海杂波常用的模型,其参数估计在高分辨海用雷达自适应目标检测中起着关键作用。由于参数估计中数据不可避免地存在来自海面目标、岛礁的异常样本,对异常样本稳健的双分位点估计是近年来提出的有效方法之一。该文提出一种对异常点稳健的IG-CG分布三分位点参数估计(Tri-per)方法,其是对双分位点估计的改进。改进来自两个方面,通过双分位点位置优化提高逆形状参数的估计精度;通过第3个分位点的引入和位置优化提高尺度参数的估计精度。最后,用仿真和实测数据检验了提出估计方法的有效性和稳健性。     

定数截尾Weibull分布下恒定应力加速寿命试验统计分析

设产品寿命服从Weibull分布，尺度参数为η＞0，形状参数为m＞0，在加速应力水平Si下，加速方程为Inηi=a＋bφ（Si）（i=1，2，…，k）本文绘出了定数截尾Weibull分布各应力下形状参数mi的极大似然估计的一种改进迭代算法，利用[1]类似的方法对各应力下所得估计进行修正，后对各应力下mi的估计值进行加权平均得m的近似无偏估计；利用定数截尾Weibull分布尺度参数ηi的极大似然估计，通过Weibull分布与指数分布之间不关系以及指数分布的性质，求得各应力下尺度参数的自然对数Inηi的近似无偏估计，利用Inηi的估计值与加速方程，建立线性模型，利用Gauss－Markov定理得加速方程系数a和b的近似最佳线性无偏估计值．通过模型由此可求出正常应力S0下各种可靠性特征量的估计．模拟结果表明本方法是具有较高的精度，且本方法计算比较简单，在工程上比较适用．     

定数截尾Weibull分布的形状参数的最短化置信区间

通过数值计算的方法,对于给定的置信度,在样本容量从3～20的范围内,求得了定数截尾Weibull分布的形状参数的最短置信区间,并对通常方法求得的置信区间的长度与最短置信区间的长度进行了对比分析。结果表明：在小样本≤11的情形下,用最短置信区间来作未知参数的区间估计,将会使估计精度得到显著的提高。     

适用于高速移动场景的信道估计方法

目前存在的各种信道估计方法,通常假设信道参数在一个正交频分复用（OFDM）符号内是恒定不变的。但是在高速场景中,信道在一个OFDM符号内呈现出较为明显的变化,这时子载波间干扰（ICI）就会影响传统的信道估计方法,使估计性能明显下降。本文提出通过幂级数基的形式来建模无线信道变化的方法,将时变的信道估计转变成有限参数变量在幂级数基上的投影,这大大减少了估计信道参数的个数。理论分析及仿真结果表明,该方法能有效地跟踪和估计时变的信道参数,具有良好性能。     

Bayes Interval Estimation for the Shape Parameter of the Power Distribution

The power distribution is considered as failure model and uses a square-error loss function. Bayes credibility interval estimators for the shape parameter have been obtained assuming 1) the following priors for the shape parameter: Jeffrey's invariant prior, gamma, and inverted gamma; 2) the following priors for reliability: beta and log gamma function. It is straightforward to obtain estimators for reliability when the estimators for the shape parameter are known.     

On Bayes Estimation of Reliability for the Birnbaum-Saunders Fatigue Life Model

Estimation of reliability for the Birnbaum-Saunders fatigue life distribution is considered. The scale parameter is also the median lifetime, and assuming that the scale parameter is known, Bayes estimators of the reliability function are obtained for a family of proper conjugate priors as well as for Jeffreys' vague prior for the shape parameter. When both parameters are unknown, a modified Bayes estimator of reliability is proposed using a moment estimator of the scale parameter. In addition to being computationally simpler than the MLE of reliability, Monte Carlo simulations for small samples show that the modified Bayes estimator is better than the MME for all values of the shape parameter and as good as the MLE for small values of the shape parameter in the sense of root mean squared errors.     

An Evaluation of Exponential and Weibull Test Plans

MIL-STD-781B gives sampling plans (sequential and fixed length) for reliability tests under the assumption of a constant failure rate. Using Monte Carlo techniques, the authors compare s-expected time to a decision and producer and consumer risks for some of these plans. It is shown that plans which assume an exponential distribution are not robust to departures from that assumption. A simple modification of these plans for use when life has a Weibull distribution with known shape parameter not equal to one, and an adaptive test procedure for use when life has a Weibull distribution with unknown shape parameter are proposed. The modified plans for a Weibull distribution with known shape parameter have the same designated producer and consumer risks, but different s-expected time to a decision than the corresponding exponential plans. Using Monte Carlo techniques, the authors determine s-expected time to a decision and producer and consumer risks for various forms of the adaptive procedure.     

A Monte Carlo Technique for Obtaining System Reliability Confidence Limits from Component Test Data

A digital computer technique is developed, using a Monte Carlo simulation based on common probability models, with which component test data may be translated into approximate system reliability limits at any confidence level. The probability distributions from which the component failures are assumed to come are the exponential, Weibull (shape parameter K known), gamma (shape parameter ? known), normal, and lognormal. The components can be arranged in any system configuration, series, parallel, or both. Since reliability prediction is meaningful only when expressed with an associated confidence leve, this method provides a valuable and economical tool for the reliability analyst.     

Approximate Tolerance Limits and Confidence Limits on Reliability for the Gamma Distribution

No exact method is known for determining tolerance limits or s-confidence limits for reliability for the gamma distribution when both parameters are unknown. Perhaps the simplest approximate method is to determine a tolerance limit assuming the shape parameter known and then replace the shape parameter with its ML estimate to obtain approximate limits. Simulated values of the true probability levels, achieved by this method, indicate that this method is not suitable, contrary to what has been anticipated. A second approach is to consider the corresponding tolerance limits assuming the distribution mean known and the shape parameter unknown, and then replace the distribution mean by the sample mean. This approach gives useful results for many practical cases. Simulated values of the true probability levels achieved are presented for some typical cases and limiting values are provided. This method appears satisfactory for all values of the shape parameter, for the common s-confidence levels, and moderate sample sizes.     

Reliability tests for Weibull distribution with varyingshape-parameter, based on complete data

The Weibull distribution indexed by scale and shape parameters is generally used as a distribution of lifetime. In determining whether or not a production lot is accepted, one wants the most effective sample size and the acceptance criterion for the specified producer and consumer risks. (μ₀ ≡ acceptable MTTF; μ₁ ≡ rejectable MTTF). Decide on the most effective reliability test satisfying both constraints: Pr{reject a lot | MTTF = μ₀} ⩽ α, Pr{accept a lot | MTTF = μ₁ } ⩽ β. α, β are the specified producer, consumer risks. Most reliability tests for assuring MTTF in the Weibull distribution assume that the shape parameter is a known constant. Thus such a reliability test for assuring MTTF in Weibull distribution is concerned only with the scale parameter. However, this paper assumes that there can be a difference between the shape parameter in the acceptable distribution and in the rejectable distribution, and that both the shape parameters are respectively specified as interval estimates. This paper proposes a procedure for designing the most effective reliability test, considering the specified producer and consumer risks for assuring MTTF when the shape parameters do not necessarily coincide with the acceptable distribution and the rejectable distribution, and are specified with the range. This paper assumes that α < 0.5 and β < 0.5. This paper confirms that the procedure for designing the reliability test proposed here applies is practical     

A new model for step-stress testing

The mathematical intractability of the Weibull cumulative exposure model (CE-M) has impeded the development of statistical procedures for step-stress accelerated life tests. Our new model (KH-M) is based on a time transformation of the exponential CE-M. The time-transformation enables the reliability engineer to use known results for multiple-step, multiple-stress models that have been developed for the exponential step-stress model. KH-M has a realistically appealing proportional-hazard property. It is as flexible as the Weibull CE-M for fitting data, but its mathematical form makes it easier to obtain parameter estimates and standard deviations. Maximum likelihood estimates are given for test plans with unknown shape parameter. The mathematical similarity to the constant-stress Weibull model is shown. Chi-square goodness of fit tests are performed on simulated data to compare the fit of the models     

Bayesian Analysis of the Weibull Process With Unknown Scale and Shape Parameters

Previously, the Weibull process with an unknown scale parameter was examined as a model for Bayesian decision making. The analysis is extended by treating both the shape and scale parameters as unknown. It is not possible to find a family of continuous joint prior distributions on the two parameters that is closed under sampling, so a family of prior distributions is used that places continuous distributions on the scale parameter and discrete distributions on the shape parameter. Prior and posterior analyses are examined and seen to be no more difficult than for the case in which only the scale parameter is treated as unknown, but preposterior analysis and determination of optimal sampling plans are considerably more complicated in this case. To illustrate the use of the present model, an example is presented in which it is necessary to make probability statements about the mean life and reliability of a long-life component both before and after life testing.     

A Bayesian estimate of reliability in the Weibull distribution

A two parameter Weibull distribution is assumed to be the appropriate model of an engineering device. A Bayesian estimate of reliability is developed by assuming that a value β₀ of the shape parameter is known. Then we transform the Weibull distribution to the equivalent Exponential distribution by the transformation t′ = t^β0, so that techniques of analysis for the case of an exponential model can be applied to the transformed Weibull distribution. Then we can get the Bayesian estimate of reliability for this exponential distribution using a suitable loss function.     

Empirical Bayes Estimation in the Weibull Distribution

In part I empirical Bayes estimation procedures are introduced and employed to obtain an estimator for the unknown random scale parameter of a two-parameter Weibull distribution with known shape parameter. In part II, procedures are developed for estimating both the random scale and shape parameters. These estimators use a sequence of maximum likelihood estimates from related reliability experiments to form an empirical estimate of the appropriate unknown prior probability density function. Monte Carlo simulation is used to compare the performance of these estimators with the appropriate maximum likelihood estimator. Algorithms are presented for sequentially obtaining the reduced sample sizes required by the estimators while still providing mean squared error accuracy compatible with the use of the maximum likelihood estimators. In some cases whenever the prior pdf is a member of the Pearson family of distributions, as much as a 60% reduction in total test units is obtained. A numerical example is presented to illustrate the procedures.