误差估计

The common method, that all strong-correlation terms of the model are eliminated, can bring the loss in the engineering application, so the new method is proposed that the identified model reserves some correlation. The augmented matrix A is constructed by the outputΔW and the matrix S. The"determinating order based on ratio of determinant"is brought out to screen the strong-correlation terms in the structure identification. The latent root estimation is improved in screening the eigenvalues and eigenvectors. Thus the estimation precision is improved greatly.The consistence check of guidance instrument error coefficients of flight test and ground test is the purpose of flight experiment. The causes of inconsistency of the two models are analyzed. The hypothesis test of linear regression model based on F statistics is proposed to check the consistence.Finally, the instability of error coefficients is probably caused by the change of the flight environments, therefore, the relation between the error coefficients and flight environment is analyzed. The approach is presented to identify SINS guidance instrument error models and compensate the error in the segmented sections corresponding to the change of vertical acceleration of aircraft.

在结构辨识中，常用的方法由于将模型中的强相关项全部剔除而给工程应用带来损失，因此，本文提出了新的有益思想，即在保留一定相关性的基础上进行辨识：将输出向量ΔW与环境函数矩阵S构成增广矩阵A，然后采用"比定阶行列式"来剔除相关向量的方法，这样既可以尽可能多地保留了对落点影响大的强相关参数，又可以对落点影响小的强相关参数给予剔除；在参数估计中，改进了特征根估计中特征根和特征向量的筛选方法，提出"近零"准则，从而大大提高了参数估计的精度；再者，鉴于天地模型"一致性"检验是飞行试验和SINS制导工具误差系数分离的主要目的，因此，本文又深入分析了造成天地模型不一致的原因，提出了采用基于F统计的线性回归模型假设检验方法来进行捷联制导工具误差模型的天地"一致性"检验；最后，鉴于飞行环境剧烈变化可能会对惯性仪表误差系数稳定性带来一定的影响，因此本文深入地分析了SINS制导工具误差系数与外界环境的关系，提出了基于过载变化大小的分段辨识和分段实时补偿的算法。

In this paper, we study characterizations of admissible in the general linear model Y, Xβ,ε|ε～(0,σ~2∑. We demonstrate that an admissible linear estimator is as the conditional generalized ridge-type estimation in the no constraint, equality constraint, inequality constraint general linear model. We study the superiority of this conditional generalized ridge-type estimation, and prove that it is superior to the restricted best linear unbiased estimator in terms of mean squares. We also give the choice of the matrix K.

本文主要研究了一般线性模型Y，Xβ，ε|ε～(0，σ~2∑中参数估计的可容许性特征，得到了一般线性模型在无约束，有等式约束及有不等式约束下，可容许线性估计均具有条件广义岭估计的形式的结论，并且讨论了这一条件广义岭估计的优良性，证明了其在均方误差和均方误差矩阵意义下都优于约束最小二乘估计，给出了参数矩阵K的选取方法。

And then some ellipses that AUGR estimator is better than the OLS estimator and AUGL estimator is better than the OLS estimator are given, respectively.Second, the definition of the almost unbiased unified biased estimator is proposed. This definition includes the familiar almost unbiased estimators in literatures, and it is the unified expression of the familiar almost unbiased estimators. Followed the biased and variance are compared of AUUB estimator and the unified biased estimator, respectively. AUUB estimator has smaller bias than UB estimator and the variance of AUUB estimator is between the variance of UB estimator and 4 times of the variance of UB estimator. Finally the properties of AUUB estimator are discussed. The conclusion is gained that there are parameters made AUUB estimator is better than OLS estimator in terms of their mean square error. The sufficient and necessary condition that AUUB estimator is admissible is given. The ellipse is given that AUUB estimator is

然后给出了几乎无偏统一有偏估计的定义，该定义包括了文献中常见的几乎无偏估计，实现了常见几乎无偏估计的统一表达式；接下来我们比较了几乎无偏统一有偏估计与统一有偏估计的偏度与方差，得出了几乎无偏统一有偏估计比统一有偏估计有较小的偏度，几乎无偏统一有偏估计的方差介于统一有偏估计的方差与统一有偏估计的方差的四倍之间的结论；最后我们对统一有偏估计的主要性质作了讨论，证明了存在参数K，S使得几乎无偏统一有偏估计在均方误差意义下优于最小二乘估计的结论，给出了几乎无偏统一有偏估计为可容许估计的充要条件，还给出了在均方误差阵意义下几乎无偏统一有偏估计优于最小二乘估计的椭球。

Secondly, based on the FO estimate, we formulate the timing error and channel estimation as a problem of composite hypothesis testing according to the first signal model, and then solve the problem by the composite hypothesis testing approaches.

该估计方法包括两步：第一步是根据第二个系统模型，推导了一种有效的最大似然频偏估计器；第二步是根据所获得的频偏估计值，利用第一个系统模型，将定时误差和信道估计表示成一个复合假设检验问题，然后再利用复合假设检验方法进行定时误差和信道估计。

On the basis of direct modelling method by using extended Kalman filter, a new method combining extended Kalman filter with adaptive extended Kalman filter is presented to model gyro drift directly from rotate angle of turntable. Extended Kalman filter has great estimation error, what is more, may be divergent if the model and noise statistic are not accurate or wrong. The new method solves the problem of general extended Kalman filter by using fictious noise with timevarying statistic to compensate the linearized model error of extended Kalman filter. The parameter estimators of single-axis and double-axis servo test are designed from it.

本文深入研究了根据伺服试验数据进行陀螺仪漂移误差模型建模的方法，在应用广义Kalman滤波器直接建模的方法基础上，针对广义Kalman滤波器对于不精确或错误的模型和噪声统计，估计误差较大，甚至滤波发散的缺陷，借助于用带时变噪声统计的虚拟噪声补偿广义Kalman滤波的线性化模型误差的新思想，提出了用广义Kalman滤波和自适应广义Kalman滤波算法相结合的方法由转台的转角数据直接建模陀螺仪漂移误差模型，并设计了陀螺仪单轴伺服和双轴伺服测试时参数估计的滤波器。

Second,a new estimator called generalized rootpower estimator of regression coefficients in growth curve model is obtained.For the newestimator,its superiority over the LS estimator and the root power estimator,and its admissibilityare proved.Two methods,two kinds of arithmetic of choosing the generalized root powerparameters are introduced.A demonstrative practical example is provided.

对增长曲线模型中的回归系数矩阵提出了一种新的估计——广义根方估计，并证明了通过广义根方偏参数的适当选取可使得该估计在均方误差和均方误差矩阵的意义下优于已有的最小二乘估计估计和根方估计；及证明了广义根方估计是可容许估计；还给出了选取广义根方偏参数的两种方法、算法和应用实例。

The measurement system error model analysis is introduced into power system real time network state analysis as an important part for the first time, which can improve on the state estimation quality and provide the capability to monitor the operation of the measurement system; 2. The theory and algorithm of the on-line estimation and update of measurement noise variance based on the relation between the residual variance and noise variance. The statistic properties of the sample variance are discussed and the relation between the estimation precision and sample size under given confidence level is derived; 3. The theory and algorithm of detection and identification of measurement bias are presented, which is based on the relation between residual mean and noise mean. The statistic properties of sample mean are discussed and the relation between estimation precision and sample size is derived; 4. The Givens orthogonal transformation algorithm is selected to be the essential algorithm of state estimation, the fast orthogonal transformation algorithm with damp factor and the algorithm which can handle the zero injection measurements efficiently are presented; 5. The quantity analysis theory of bad data detectivity and identifibility are presented, which describes the relation between the elements in matrix W〓 and bad data amplitude and can provide the theory base for measurement system design and valuation.

一、首次将量测系统误差模型分析做为一个环节引入电力系统实时网络状态分析中，为EMS系统增加了实时监视系统运行、修正量测系统误差模型的新功能，进一步发挥了实时网络状态分析应用软件的潜力；二、首次提出了应用样本方差在线估计与修正量测系统误差方差的基本理论，讨论了样本方差的统计性质和概率分布，推导出了样本容量、估计精度和置信度之间的关系，给出了在线估计与修正量测系统误差方差的算法；三、首次提出了应用样本均值在线检测与辨识量测偏差的基本理论，讨论了样本均值的统计性质，推导了样本容量、估计精度和置信度之间的基本关系，给出了在线检测与辨识量测偏差的算法；四、在状态估计算法设计中，以Givens变换算法做为基本算法，提出了快速正交变换阻尼因子法和可以有效地处理零注入量测的混合法，并对实时应用中的一些问题进行了讨论；五、提出了不良数据可检测性与可辨识性的定量分析理论，揭示了描述量测系统配置、网络结构与参数的残差灵敏度矩阵中的元素与不良数据的幅值在可检测、可辨识能力上的定量关系，为量测系统配置设计与评价提供了理论基础；六、综合国内外最新研究成果，采用自适应自回归预测技术和稀疏矢量技术，构造了较完善的不良数据检测与辨识算法。

Considering the limits of RDSS in active positioning mode,such as poor security,limited capacity,and inability to continuously provide position,velocity and attitude outputs,a technique of tightly coupled RDSS /SINS integrated navigation system is proposed for land vehicles by utilizing the time differenced carrier phase of 3 geostatic satellites.

针对北斗系统有源定位方式保密性差、用户数目有限，不能提供连续的位置、速度、姿态信息的问题，提出利用北斗系统3颗地球静止卫星的载波相位时间差分信息，与车载捷联惯导构成紧组合导航系统，通过扩展卡尔曼滤波器估计并修正惯导系统的速度误差；引入载体的侧向和天向速度约束，改善了速度估计精度；结合北斗系统的伪距信息，消除了长航时条件下位置误差的积累；推导了滤波器观测方程，对组合导航滤波器进行了设计；通过车载实验进行了验证，实验结果表明，速度误差和位置误差的积累受到了有效地抑制，精度满足陆地战车导航的要求。

Throughout comparing the above estimating methods, we have the following results: the estimators of the moments of the errors does not depend on the random effects, and that of the random effects does not depend on the errors, and then the corresponding asymptotic variances are very simple and optimal; when the random effects are multivariate, we can not construct different estimating equations for the random effects and errors respectively, which results that the asymptotic covariances of estimation are very complex and then the estimating efficiency is bad.

比较上述两种估计法，我们发现：当随机效应是一维的时侯，误差的各阶矩的估计不依赖不可观测的随机效应，随机效应的估计也不依赖误差，因此，估计的渐近方差结构特别简单也是最优的；而当随机效应是多维的，因为随机效应的协变量的影响，我们没有办法针对随机效应和误差的各阶矩分别建立估计方程，这导致所得的估计的渐近方差或者协方差矩阵特别复杂，从而估计的效果不是很好。

As reported, the celestial guidance of single-star scheme can correct initial localization, orientation errors and constant drifts of gyro in mobile launching ballistic missile, while we consider that the scheme can only compensate for partial constant gyro drift .

有参考文献认为，采用单星制导即可以估计和补偿初始定位误差、初始方位误差、陀螺常值漂移等误差源导致的弹载惯导系统定位误差，但我们认为，单星制导不能估计出全部的常值陀螺漂移。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。