基于最小模估计及Tikhonov正则方法的脑磁源重建

脑磁图 (magnetoencephalogram,MEG)研究中的磁源分布图象重建 ,属于不适定问题 ,需要引入合适的先验约束 ,把它转化为适定问题。采用非参数的分布源模型 ,磁源成象问题即为求解一病态的欠定的线性方程组。这里采用的方法是建立在最小模估计和Tikhonov正则的基础上 ,从数学算法本身及相关的解剖学和神经生理学的信息 ,对解空间加以限制 ,提出了区域加权算子 ,再结合深度加权 ,以期得到合理的神经电流分布。通过仿真实验表明能得出理想的重建结果 。

扩展增长曲线模型中协差阵的最小模估计问题

考虑扩展增长曲线模型Ｙ＝∑ｍｉ＝１ＸｉＢｉＺ′ｉ＋Ｕε其中Ｘｉ、Ｚｉ、Ｕ（≠０）均为已知矩阵，Ｒ（Ｚ１）…Ｒ（Ｚｍ），Ｂｉ是回归系数矩阵，Ｙ＝（ｙ（１），…，ｙ（ｎ）′和ε＝（ε（１），…，ε（ｓ）′分别是ｎ×ｐ观测资料矩阵和ｓ×ｐ随机误差矩阵，ｐ＞１．ε（１），…，ε（ｓ）～ｉｄＥＣｐ（０，Σ，φ），其中Σ≥０未知，φ已知，且φ∈Φｐ＝｛φ（）∶φ（ｔ２１＋…＋ｔ２ｐ）是一个特征函数｝，随机变量Ｒ（≥０）非退化，Ｒφ，对给定的矩阵Ｃ＝Ｃ′≠０，本文给出了ｔｒ（ＣΣ）可估时的ＭＩＮＱＥ（Ｕ，Ｉ）。

一个推广生长曲线模型协差阵的最小模估计

给出了一个推广生长曲线模型中 tr CΣ中的无偏不变最小模二次估计 (MINQE(U,I ) ) ,并得到了 MINQE(U,I)成为一致最小方差不变二次无偏估计 (UMVIQ UE)的充要条件 .关键词 :推广生长曲线模型 (EGCM) ;无偏不变最小模二次估计 (MINQ E(U,I) ) ;一致最小方差不变二次无偏估计 (U MVIQUE)

有协变量的推广增长曲线模型中协差阵的最小模估计

对于有协变量的推广增长曲线模型:Y=X1B1W′1+X2B2W′2+B3W′3+R,其中,μ(W2) μ(W1),而对W3没有任何限制,本文利用最小模原理和一般射影定理得到了可估参数函数tr(C∑)的无偏不变最小模二次估计(MINQE(U,I)).

一种约束最小模方估计的图像迭代重建算法

较少投影重建问题一直是成像领域研究的重点,传统的卷积反投影(CBP)不能产生满意的重建图像――伪影严重、误差大,而迭代算法却具有一些较好的特性。本文以CT成像为基础,以最小模方为目标函数提出了一种约束迭代重建算法,本算法与无约束迭代算法相比,在花费相同时间的情况下,可以重建出误差更小,拟合度更高的图像。以扇束扫描投影数据重建的结果验证了本文的结论。

最小L_1-模估计与有界线性规划问题

对任意有限制的有界解集的线性规划问题与从最小L_1-模估计导出的线性规划问题的对隅形式等价性的定理证明做了改进,并从这一定理出发,利用求解线性规划的有效集法得到了求解有界线性规划问题的一阶段方法。

扩展增长曲线模型中协差阵与回归系数阵的同时估计及其优良性

在棉球等高分布情形下给出了扩展增长曲线模型中协差阵与回归系数阵的最小模估计，并得到了最小模估计成为一致最小方差不变二次加线性无偏估计的充要条件．

椭球等高分布情形下扩展增长曲线模型中协差阵的最优估计

在椭球等高分布情形下给出了扩展增长曲线模型中协差阵的最小模估计 ,并得到了最小模估计成为一致最小方差不变二次无偏估计以及一致最小方差不变二次无偏估计存在的充要条件。

基于最小模方法的相干源方位估计

采用最小模算法对于空间非相干信号有很好的分辨效果.本文详细地介绍了最小模方法的原理,并通过仿真指出了最小模算法对空间相干信号难以区分的缺点.为此本文提出了一种有效的解决方案,采用空间平滑处理来去除信号的空间相干效应,通过仿真证明了算法的有效性.

增长曲线模型中协差阵的最优估计

在椭球等高分布情形下给出了增长曲线模型中协差阵的最小模估计 。

增长曲线模型中协差阵与回归系数阵的最优估计

在椭球等高分布情形下给出了增长曲线模型中协差阵与回归系数阵的最小模不变二次加线性无偏估计 。

A New Class of Biased Linear Estimators in Deficient-rank Linear Models

In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.

GCM中方差分量的MINQE(U,I)及其优良性

给出了生长曲线模型中方差分量的无偏不变最小模二次估计,并且讨论了它成为一致最小方差不变二次无偏估计的充要条件.

Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

Min-norm spatial spectrum based on acoustic vector-sensor linear array

The high resolution of DOA（direction of arrival） estimation could be obtained by using the min-norm algorithm. In this paper, the expression of the min-norm spatial spectrum based on acoustic vector-sensor（AVS） linear arrays was presented and simulation study was carried out. Results of simulations indicated that left/right ambiguity could be removed and better performance for DOA estimation was obtainable when dealing with sources close to endfire than using pressure hydrophone linear arrays, and the interelement spacing was allowed to exceed the half-wavelength upper limit. A three-element vector hydrophone linear array with two meters interspace was designed. The AVS experiment was carried out at Songhua Lake in Jinlin Province. Experimental results show a high resolution tracking of targets can be obtained using the rain-norm algorithm.

Comparative Study of Response Surface Designs with Errors-in-Variables Model

This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables.Three performance criteria are proposed.The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors.The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors.The last performance measure is the mean squared scaled prediction variance change with and without errors.In the simulations,1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design.The independent variables are coded variables in these designs.Comparative results show that for the low level errors in variables,central composite face-centered design is optimal;otherwise,Box-Behnken design has a relatively better performance.

Fuzzy steering control to serpentine tracked robots in unknown environment

To solve the problem of multi-turning attitudes,unknown ground parameters and complex skidsteering control for serpentine tracked robots(STR),a fuzzy control method based on the estimation of track curvature and side slip angles is proposed.Based on the track-ground interaction,mathematical models are established for stable turning in the way of recursive homogeneous transformation.The navigation parameters such as rack curvature and side slip angles have approximately linear relationship with the yaw angles of articulate joints.Then attitude models in turning control are studied and summarized.Transforming strategies of attitude models are optimized.Based on the strategies,an adjustable fuzzy controller is designed.In the controller,an estimator is set to solve the problem of unknown and variable universe.The estimator predicts the track curvature by metabolic linear least squares estimate.Experiments have verified the feasibility and validity of the controller.

RANDOM WEIGHTING METHOD FOR CENSORED REGRESSION MODEL

Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “Tobit” model).

BERRY-ESSEEN BOUNDS OF ERROR VARIANCE ESTIMATION IN PARTLY LINEAR MODELS

Consider the regression model Y i=x τ iβ+g(t i)+ε i for i=1,…, n. Here (x i, t i) are known and nonrandom design points and ε i are i.i.d. random errors.The family of nonparametric estimates n(·) of g(·) including some known estimates is proposed. Based on the model Y i=x τ i+ n(t i)+ε i, the Berry-Esseen bounds of the distribution of the least-squares estimator of β are investigated.

A NOTE ON THE CONSISTENCY OF LS ESTIMATES IN LINEAR MODELS

It is well known that when the random errors are iid. with finite variance, the week and the strong consiStency of LS estimate of multiple regression coefficients are equivalent. This note, by constructing a counter-example, shows that this equivalence no longer holds true in case that the random errors possess only the r-th moment with 1≤5 T ＜ 2.