An Extended Closed-loop Subspace Identification Method for Error-in-variables Systems

A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.

加权整体最小二乘在激光跟踪仪转站中的应用

由于利用经典最小二乘原则对激光跟踪仪进行坐标转换时,系数矩阵中携带的随机测量误差会影响转站精度,故对激光跟踪仪的转站算法进行了研究。提出了基于线性EIV模型(Errors-in-Variables)和加权整体最小二乘法(WTLS)并利用间接平差形式迭代求解转站参数的方法;利用Matlab进行仿真分析并用API公司生产的激光跟踪仪进行实验。仿真结果显示WTLS法的单位权中误差的平均值和标准差分别为经典加权最小二乘法(WLS)的4/5和1/5;实验结果显示WTLS和WLS两种方法的单位权中误差分别为2.003 5mm和2.225 3mm;这些数据证明采用WTLS法的转站结果比WLS的精度更高且更稳定。该方法可为组建激光跟踪仪测量网络,优化网络布局奠定基础。

Strong Consistency of Estimators under Missing Responses

In this article, we focus on the semi-parametric error-in-variables model with missing responses: , where yi are the response variables missing at random, are design points, ζi are the potential variables observed with measurement errors μi, the unknown slope parameter ß?and nonparametric component g(·) need to be estimated. Here we choose two different approaches to estimate ß?and g(·). Under appropriate conditions, we study the strong consistency for the proposed estimators.

Modeling compatible single-tree aboveground biomass equations for masson pine(Pinus massoniana) in southern China

Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume equations. Based on the tree volume and aboveground biomass data of Masson pine （Pinus massoniana Lamb.） in southern China, we constructed one-, two- and three-variable aboveground biomass equations and biomass conversion functions compatible with tree volume equations by using error-in-variable simultaneous equations. The prediction precision of aboveground biomass estimates from one variable equa- tion exceeded 95%. The regressions of aboveground biomass equations were improved slightly when tree height and crown width were used together with diameter on breast height, although the contributions to regressions were statistically insignificant. For the biomass conversion function on one variable, the conversion factor decreased with increasing diameter, but for the conversion function on two variables, the conversion factor increased with increasing diameter but decreased with in- creasing tree height.

Developing individual tree-based models for estimating aboveground biomass of five key coniferous species in China

Estimating individual tree biomass is critical to forest carbon accounting and ecosystem service modeling.In this study,we developed one-（tree diameter only） and two-variable（tree diameter and height） biomass equations,biomass conversion factor（BCF） models,and an integrated simultaneous equation system（ISES） to estimate the aboveground biomass for five conifer species in China,i.e.,Cunninghamia lanceolata（Lamb.） Hook.,Pinus massoniana Lamb.,P.yunnanensis Faranch,P.tabulaeformis Carr.and P.elliottii Engelm.,based on the field measurement data of aboveground biomass and stem volumes from 1055 destructive sample trees across the country.We found that all three methods,including the one-and two-variable equations,could adequately estimate aboveground biomass with a mean prediction error less than 5%,except for Pinus yunnanensis which yielded an error of about 6%.The BCF method was slightly poorer than the biomass equation and the ISES methods.The average coefficients of determination（R^2） were 0.944,0.938 and 0.943 and the mean prediction errors were 4.26,4.49 and 4.29% for the biomass equation method,the BCF method and the ISES method,respectively.The ISES method was the best approach for estimating aboveground biomass,which not only had high accuracy but also could estimate stocking volumes simultaneously that was compatible with aboveground biomass.In addition,we found that it is possible to develop a species-invariant one-variable allometric model for estimating aboveground biomass of all the five coniferous species.The model had an exponent parameter of 7/3 and the intercept parameter a_0 could be estimated indirectly from stem basic density（a_0= 0.294 q）.

Construction of tree volume equations for Chinese fir plantations in Guizhou Province, southwestern China

Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chinese fir （Cunninghamia lanceolata） plantations in Guizhou Province in southwestern China, parallel one- and two-variable tree volume tables and tree height curves for central and other areas were constructed using an error-in-variable modeling method. The results show that, although the one-variable tree volume equations and height curves between the central and other areas were significantly different, the two-variable volume equations were sufficiently close, so that a generalized two-variable tree volume equation could be established for the entire province.

Corrected-loss estimation for Error-in-Variable partially linear model

We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.