De-correlated unbiased sequential filtering based on best unbiased linear estimation for target tracking in Doppler radar

In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the measurement and the target state increases with the introduction of the Doppler measurement.Therefore,target tracking in the Doppler radar is a nonlinear filtering problem.In order to handle this problem,the Kalman filter form of best linear unbiased estimation(BLUE)with position measurements is proposed,which is combined with the sequential filtering algorithm to handle the Doppler measurement further,where the statistic characteristic of the converted measurement error is calculated based on the predicted information in the sequential filter.Moreover,the algorithm is extended to the maneuvering target tracking case,where the interacting multiple model(IMM)algorithm is used as the basic framework and the model probabilities are updated according to the BLUE position filter and the sequential filter,and the final estimation is a weighted sum of the outputs from the sequential filters and the model probabilities.Simulation results show that compared with existing approaches,the proposed algorithm can realize target tracking with preferable tracking precision and the extended method can achieve effective maneuvering target tracking.

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

基于短期观测记录的重现期风速预测

在偏僻地区或山区建设重要建筑物、构筑物或桥梁时,通常在附近安装风速观测仪器,获得至少1年的短期风速记录。提出了根据短期风速记录预测指定重现期风速极值及风压方法,为结构抗风设计提供了科学依据。提出独立风暴法提取短期风速记录的最大值,建立极值I型概率分布模型,采用最好线性无偏估计方法确定概率分布参数。依据短期风速最大值概率与年风速最大值概率的变换关系,建立年发生最大值的概率分布及重现期风速、风压的表达式。算例结果表明,重现期风速预测值的离散性与风速阈值有关,在预测值离散系数较小的情况下可确定重现期风速及其置信区间。

威布尔极值分布及其参数估计方法在储罐底板RBI计算中的应用

在常压储罐底板定量风险评估(RBI)过程中,底板腐蚀速率的选取会影响储罐整体风险等级的确定。基于威布尔极值分布理论,针对储罐边缘板,采用最佳线性无偏估计(BLUE)的方法计算了威布尔分布参数;针对储罐中幅板,采用简单线性无偏估计(GLUE)的方法计算了威布尔分布参数,随后通过线性回归理论分别计算了边缘板和中幅板的腐蚀速率,并将其赋予为腐蚀速率专家值对储罐底板进行了RBI计算。结果表明,威布尔极值分布理论计算可以科学合理地预估储罐底板腐蚀速率,边缘板的腐蚀速率为0.133 mm/a,中幅板的腐蚀速率为0.095 mm/a,与理论算法腐蚀速率的误差为3.6%,储罐底板风险等级为中高风险,在一定程度上解决了储罐RBI计算过程中腐蚀速率选取的难题,可为今后检验检测机构RBI的评估工作提供一定的技术支撑。

Best Linear Unbiased Estimators of Location and Scale Ranked Set Parameters under Moving Extremes Sampling Design

In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Record Values from the Inverse Weibull Lifetime Model: Different Methods of Estimation

In this paper, we use the lower record values from the inverse Weibull distribution (IWD) to develop and discuss different methods of estimation in two different cases, 1) when the shape parameter is known and 2) when both of the shape and scale parameters are unknown. First, we derive the best linear unbiased estimate (BLUE) of the scale parameter of the IWD. To compare the different methods of estimation, we present the results of Sultan (2007) for calculating the best linear unbiased estimates (BLUEs) of the location and scale parameters of IWD. Second, we derive the maximum likelihood estimates (MLEs) of the location and scale parameters. Further, we discuss some properties of the MLEs of the location and scale parameters. To compare the different estimates we calculate the relative efficiency between the obtained estimates. Finally, we propose some numerical illustrations by using Monte Carlo simulations and apply the findings of the paper to some simulated data.

Fisher information for generalized Rayleigh distribution in ranked set sampling design with application to parameter estimation

In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.

基于频谱特征分析的多谐波时间调制阵列测向方法

针对基于谐波特征分析的时间调制阵列(time-modulated array,TMA)测向技术中信息利用率低的问题,提出了一种基于信号频谱特征分析的多谐波TMA测向方法.通过分析接收信号的频谱特征,构建了基于信号频谱特征多谐波测向模型,推导了基于频谱特征的来波方向最优线性无偏估计(best linear unbiased estimation,BLUE)表达式,从而提高了测向精度及稳定性.以BPSK信号为例,通过仿真实验验证了所提算法的有效性,同时搭建了工作于S频段的二单元TMA测向系统证实了所提方法的可行性.

On Bayes linear unbiased estimation of estimable functions for the singular linear model

The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under mean square error matrix (MSEM)criterion.

基于BLUE的雷达/红外异步融合算法研究

多传感器融合是提高态势感知能力的重要手段。为提高探测能力,将雷达和红外传感器组网,各传感器独立工作,在统一调度下,完成探测、跟踪、识别任务。研究该系统的雷达/红外数据融合算法,针对传感器异步探测特点,采用观测驱动的融合跟踪方法:雷达探测到目标时,采用基于状态预测的改进BLUE(Best Lin-ear Unbiased Estimation)滤波,通过方位预测的辅助,减小测角误差非线性效应,提高跟踪性能;红外探测到目标时,基于方位预测和斜距观测,构造新的转换量测模型,实现基于不完备观测的修正BLUE滤波器。理论分析和仿真证明:所述雷达/红外数据融合方法,在不同传感器布局下都具备更优的综合性能,其设计思想可解决其他类似的多传感器融合问题,有较好的应用推广潜力。

可处理多普勒量测的最佳线性无偏估计算法

基于目标位置量测的一些量测转换方法已被广泛使用在目标跟踪应用中,使得卡尔曼滤波器得以在直角坐标系中应用。但是,这些量测转换方法有一些会导致估计性能恶化的根本缺陷。事实上,除了位置量测外,理论计算和实践已经证明,包含目标速度信息的多普勒量测具有有效提高目标状态估计精度的潜力。该文在直角坐标系下提出一种可使用转换多普勒量测(即距离量测与多普勒量测的乘积)的滤波器。从理论上讲,它是在最佳线性无偏估计准则下的最优线性无偏滤波器,并且避免了量测转换方法的根本缺陷。通过将近似处理后的新型最优线性滤波器与目前4种流行的方法进行仿真比较,验证了所提出的滤波器的优越性。

最佳无偏整体估计方法

提出一种最佳无偏整体估计方法 ,给出整体参数的估计量及其协方差公式 ,建立正态分布、Weibull分布和极值分布等位置—尺度分布族的点估计与区间估计。传统的回归分析只适用于正态分布和完全数据 ,最佳无偏整体估计方法则将回归分析推广到工程中常见的位置—尺度分布族和截尾数据的情况。该方法可以将不同条件 (状态 )下的试验数据作为一个整体进行统计推断 ,能够全面开发利用不同条件下试验数据之间的横向信息 ,使其可利用的信息量远远大于只能分别在各自条件下对试验数据进行处理的传统最佳线性无偏估计方法。最佳无偏整体估计方法对一种条件下只有一个失效数据的情况也能进行分析 ,传统最佳线性无偏估计方法则要求在一种条件下有较多的失效数据 ,因此前者具有小样本性质 ;并且前者的参数估计量是所有条件下顺序统计量的线性函数 ,后者的参数估计量只是一种条件下顺序统计量的线性函数 ,所以前者的参数估计量具有更好的正态分布特性。大量MonteCarlo模拟和工程应用表明 ,在试样数相同的情况下 ,文中方法比传统方法具有更高的精度 ,而在精度相同的情况下 。

BLUP法在公猪产仔数遗传评估上的应用

根据分布于6个场的206头女儿春、秋两季分娩的第一胎纯繁窝产仔数资料,用BLUP法估计了11头湖北白猪Ⅳ系公猪的育种值。混合模型中考虑了随机的公猪效应以及固定的场-季效应与公猪组效应,公猪间平均分子亲缘相关系数为0.0707。为比较不同遗传评估法的准确性,还用未校正的Robertson法(R-UD)、校正的Robertson法(R-AD)和最小二乘分析法(LS)与之对比。结果指出,BLUP评估值与R-UA、R-AD、LS评估值之间的秩相关系数分别为0.69、0.64、0.65(均为P<0.05),R-UA与R-AD、LS分别为0.92、0.93(均为P<0.001),R-AD与LS为0.98(P<0.001)。BLUP、R-UA、R-AD评估值和LS评估值的平均预测误差方差分别为0.14、0.38、0.22和0.42。现有资料表明,用BLUP法对公猪排队比其他方法准确。

基于分布式BLUE的多雷达数据融合方法

针对线性系统与非线性观测的混合跟踪融合问题,推导目标匀加速运动时的三维最佳线性无偏估计(BLUE)滤波器,给出基于分布式BLUE滤波的多雷达数据融合方法。由各单元雷达对直角坐标系下的目标状态进行BLUE估计,对多部雷达的目标状态在融合中心进行融合估计,采用位置、速度均方根误差和平均归一化估计误差平方作为融合性能评价标准。仿真结果表明,与基于NC的去偏转换状态融合方法和基于MMC的无偏转换状态融合方法相比,该方法对于过程噪声和测量噪声的变化不敏感,比基于NC和MMC的方法具有更小的位置和速度均方根误差,即使在大误差的情况下,仍然具有较高的融合精度和可靠性。

极坐标系下可处理多普勒量测的BLUE跟踪算法

事实已表明包含目标速度信息的多普勒量测具有有效提高目标状态估计精度的潜力.该文在直角坐标系下提出两种可使用转换多普勒量测(即距离量测与多普勒量测的乘积)的滤波器,一种借助了构造的多普勒伪状态,另一种没有借助多普勒伪状态.从理论上讲,它们都是在最佳线性无偏估计准则下的最优线性无偏滤波器,并且避免了量测转换方法的根本缺陷.通过将近似处理后的两种新型最优线性滤波器与目前几种流行的方法进行仿真比较,验证了所提出的滤波器的优越性.

非齐次等式约束线性回归模型回归系数的条件岭型估计

对非齐次等式约束线性回归模型提出一种有偏估计,即条件岭型估计,证明了在一定的条件下,在均方误差及均方误差矩阵意义下都优于回归系数的约束最小二乘估计,并给出了两次随机数据模拟的结果,模拟数据结果表明在一定的条件下,条件岭型估计优于最小二乘估计.

基于高程补偿的BLUE算法在塔康中的应用研究

基于塔康系统的斜距、方位和高程可对目标定位,但较大的量测误差影响定位精度。为提高估计精度,研究塔康中最佳线性无偏估计(best linear unbiased estimation,BLUE)滤波器的实现。建立地面站对目标的量测模型,并分析量测转换误差特性,推导出对应的BLUE滤波模型;针对目标从地面站上空过顶时出现无效量测的问题,通过对高程量测补偿的方法予以克服,解决传统算法在强非线性量测下误差较大的弊病。与经典方法的性能对比表明,改进算法有效地抑制了强非线性量测下的滤波发散,有很强的鲁棒性和实时性。

混合模型及其导出模型下估计量间的关系

考虑混合模型A ={ y,Xβ,Uζ,σ2 eV}和它的三个导出模型 ,其中X ,U =(U1:… :Uk)为已知设计阵 ,β为固定效应向量 ,ζ′=(ζ′1:… :ζ′k)为随机效应向量 ,且V≥ 0 ,R(X :U) R(V) .给出了可估函数Cβ在模型A和其导出模型下的最佳线性无偏估计 (BLUE)相等的充要条件 ,σ2 e 在不同模型下的最小范数二次无偏估计 (MINQUE)相等的充要条件 .