﻿ SUT法偏差改正的Partial EIV模型方差分量估计及其精度评定
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 大地测量与地球动力学  2019, Vol. 39 Issue (7): 711-716, 770  DOI: 10.14075/j.jgg.2019.07.009

### 引用本文

WANG Leyang, DING Rui, WU Lulu. Partial EIV Model Variance Component Estimation and Accuracy Evaluation of SUT Method by Deviation Correction[J]. Journal of Geodesy and Geodynamics, 2019, 39(7): 711-716, 770.

### Foundation support

National Natural Science Foundation of China, No. 41874001, 41664001; Outstanding Young Talent Funding Program of Jiangxi Province, No. 20162BCB23050; National Key Research and Development Program of China, No. 2016YFB0501405; Science and Technology Project of the Education Department of Jiangxi Province, No. GJJ171368.

### 第一作者简介

WANG Leyang, PhD, associate professor, majors in geodetic inversion and geodetic data processing, E-mail:wleyang@163.com.

### 文章历史

SUT法偏差改正的Partial EIV模型方差分量估计及其精度评定

1. 东华理工大学测绘工程学院，南昌市广兰大道418号，330013;
2. 国家自然资源部流域生态与地理环境监测重点实验室，南昌市广兰大道418号，33001;
3. 江西省数字国土重点实验室，南昌市广兰大道418号，330013;
4. 江西水利职业学院建筑工程系，南昌市北山路99号，330013

1 Partial EIV模型解算

Partial EIV的数学模型[6]表示如下。函数模型为：

 $\left\{ \begin{array}{l} \mathit{\boldsymbol{y}} = \left( {{\mathit{\boldsymbol{\beta }}^{\rm{T}}} \otimes {\mathit{\boldsymbol{I}}_n}} \right)\left( {\mathit{\boldsymbol{h}} + \mathit{\boldsymbol{B\tilde a}}} \right) - {\mathit{\boldsymbol{e}}_y}\\ \mathit{\boldsymbol{a}} = \mathit{\boldsymbol{\tilde a}} - {\mathit{\boldsymbol{e}}_a}\\ {\rm{vec}}\left( {\mathit{\boldsymbol{\tilde a}}} \right) = \mathit{\boldsymbol{h}} + \mathit{\boldsymbol{B\tilde \alpha }} \end{array} \right.$ (1)

 $\mathit{\boldsymbol{e}} = \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{e}}_y}}\\ {{\mathit{\boldsymbol{e}}_a}} \end{array}} \right] \sim \left( {\left[ {\begin{array}{*{20}{l}} {\bf{0}}\\ {\bf{0}} \end{array}} \right],\sigma _0^2{\mathit{\boldsymbol{Q}}_e} = \sigma _0^2{\mathit{\boldsymbol{P}}^{ - 1}}} \right)$ (2)

 $\left[ {\begin{array}{*{20}{c}} \mathit{\boldsymbol{y}}\\ \mathit{\boldsymbol{a}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{e}}_y}}\\ {{\mathit{\boldsymbol{e}}_a}} \end{array}} \right] = f\left( x \right)$ (3)

 $\mathit{\boldsymbol{x}} = {\mathit{\boldsymbol{x}}_0} + \Delta \mathit{\boldsymbol{x}} = \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{\beta }}_0}}\\ {{\mathit{\boldsymbol{a}}_0}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} {\Delta \mathit{\boldsymbol{\beta }}}\\ {\Delta \mathit{\boldsymbol{a}}} \end{array}} \right]$ (4)
 $\left[ {\begin{array}{*{20}{c}} \mathit{\boldsymbol{y}}\\ \mathit{\boldsymbol{a}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{e}}_y}}\\ {{\mathit{\boldsymbol{e}}_a}} \end{array}} \right] = f\left( {{\mathit{\boldsymbol{x}}_0}} \right) + \mathit{\boldsymbol{\hat J}}\Delta \mathit{\boldsymbol{x}}$ (5)

 $\mathit{\boldsymbol{\hat L}} + \mathit{\boldsymbol{e}} = \mathit{\boldsymbol{\hat J}}\Delta \mathit{\boldsymbol{\hat x}}$ (6)

 $\Delta \mathit{\boldsymbol{\hat x}} = {\left( {{{\mathit{\boldsymbol{\hat J}}}^{\rm{T}}}\mathit{\boldsymbol{Q}}_e^{ - 1}\mathit{\boldsymbol{\hat J}}} \right)^{ - 1}}{\mathit{\boldsymbol{\hat J}}^{\rm{T}}}\mathit{\boldsymbol{Q}}_e^{ - 1}\mathit{\boldsymbol{\hat L}}$ (7)

 ${\mathit{\boldsymbol{\hat x}}^{i + 1}} = {\mathit{\boldsymbol{\hat x}}^i} + \Delta \mathit{\boldsymbol{\hat x}}$ (8)
 $\mathit{\boldsymbol{\hat e}} = \mathit{\boldsymbol{\hat J}}\Delta \mathit{\boldsymbol{x}} - \mathit{\boldsymbol{\hat L}}$ (9)
2 最小范数二次无偏估计法

 $\left\{ \begin{array}{l} \mathit{\boldsymbol{S}} = {\rm{tr}}\left( {\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_k}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_l}} \right) = \\ \;\;\;\;\;\;\left[ {\begin{array}{*{20}{c}} {{\rm{tr}}\left( {\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_1}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_1}} \right)}&{{\rm{tr}}\left( {\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_1}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_2}} \right)}\\ {{\rm{tr}}\left( {\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_2}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_1}} \right)}&{{\rm{tr}}\left( {\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_2}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_2}} \right)} \end{array}} \right]\\ \mathit{\boldsymbol{W}} = \left[ {\begin{array}{*{20}{c}} {{{\mathit{\boldsymbol{\hat e}}}^{\rm{T}}}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_1}\mathit{\boldsymbol{C\hat e}}}&{{{\mathit{\boldsymbol{\hat e}}}^{\rm{T}}}\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{Q}}_2}\mathit{\boldsymbol{C\hat e}}} \end{array}} \right] \end{array} \right.$ (10)

 $\mathit{\boldsymbol{\hat \theta }} = {\mathit{\boldsymbol{S}}^{ - 1}}\mathit{\boldsymbol{W}}$ (11)
3 SUT法

 $\mathit{\boldsymbol{\xi }} = \mathit{\Phi }\left( \mathit{\boldsymbol{X}} \right)$ (12)

SUT法的计算过程[14]如下：

1) 构造sigma点。根据随机量X的先验统计信息E(X)和D(X)构造2t+1个sigma点χi

 $\left\{ \begin{array}{l} {\mathit{\boldsymbol{\chi }}_0} = E\left( \mathit{\boldsymbol{X}} \right)\\ {\mathit{\boldsymbol{\chi }}_i} = E\left( \mathit{\boldsymbol{X}} \right) + {\left( {\sqrt {t + \lambda } \sqrt {D\left( \mathit{\boldsymbol{X}} \right)} } \right)_i}\\ \;\;\;\;\;\;i = 1,2, \cdots ,t\\ {\mathit{\boldsymbol{\chi }}_i} = E\left( \mathit{\boldsymbol{X}} \right) + {\left( {\sqrt {t + \lambda } \sqrt {D\left( \mathit{\boldsymbol{X}} \right)} } \right)_i}\\ \;\;\;\;\;\;i = t + 1,t + 2, \cdots ,2t \end{array} \right.$ (13)

2) 计算sigma点经过非线性变换后的样本点：

 ${\mathit{\boldsymbol{v}}_i} = \mathit{\Phi }\left( {{\mathit{\boldsymbol{\chi }}_i}} \right),i = 0,1, \cdots ,2t$ (14)

3) 确定样本点vi的权值：

 $\left\{ \begin{array}{l} W_0^m = \lambda /\left( {t + \lambda } \right)\\ W_0^c = \lambda /\left( {t + \lambda } \right) + 1 - {\alpha ^2} + \beta \\ W_i^m = W_i^c = 1/\left( {2\left( {t + \lambda } \right)} \right),i = 1,2, \cdots ,2t \end{array} \right.$ (15)

4) 计算非线性函数的均值以及协方差阵：

 $E(\mathit{\boldsymbol{\xi }}) = \sum\limits_{i = 0}^{2t} {W_i^m} {\mathit{\boldsymbol{v}}_i}$ (16)
 $D(\boldsymbol{\xi})=\sum\limits_{i=0}^{2 t} W_{i}^{c}\left(\boldsymbol{v}_{i}-E(\boldsymbol{\xi})\right)\left(\boldsymbol{v}_{i}-E(\boldsymbol{\xi})\right)^{\mathrm{T}}$ (17)
3.1 SUT法精度评定

 $g\left(\hat{\boldsymbol{x}}^{i+1}\right)=\hat{\boldsymbol{x}}^{i}+\left(\hat{\boldsymbol{J}}^{\mathrm{T}} \boldsymbol{Q}_{e}^{-1} \hat{\boldsymbol{J}}\right)^{-1} \boldsymbol{J}^{\mathrm{T}} \boldsymbol{Q}_{e}^{-1} \hat{\boldsymbol{L}}$ (18)

 $\hat{\boldsymbol{\beta}}^{0}=\varphi(\boldsymbol{l})$ (19)

 $\hat{\boldsymbol{\beta}}^{1}=g\left(\hat{\boldsymbol{\beta}}^{0}, \boldsymbol{l}\right)$ (20)

 $\mathit{\boldsymbol{\widehat \beta }} = {\mathit{\boldsymbol{\widehat \beta }}^{i + 1}} = \underbrace {g\left( {g\left( { \cdots g\left( {g\left( {} \right.} \right.} \right.} \right.}_{i + 1}\left. {\left. {\varphi \left( \mathit{\boldsymbol{l}} \right),\mathit{\boldsymbol{l}}} \right),\mathit{\boldsymbol{l}}} \right)\left. { \cdots \left. {,\mathit{\boldsymbol{l}}} \right),\mathit{\boldsymbol{l}}} \right)$ (21)

1) 通过Partial EIV模型方差分量估计法求得参数估值${\mathit{\boldsymbol{\hat \beta }}}$、改正数${\mathit{\boldsymbol{\hat V}}}$和方差分量$\hat{\boldsymbol{\theta}}_{0}^{2}=\left[\hat{\sigma}_{1}^{2}, \hat{\sigma}_{2}^{2}\right]^{\mathrm{T}}$

2) 根据输入量$l=[\boldsymbol{y}, \boldsymbol{a}]^{\mathrm{T}}、\hat{\boldsymbol{V}}、\boldsymbol{Q}_{{l}}$和方差分量估值$\hat{\boldsymbol{\theta}}_{0}^{2}$构建观测值向量l的均值和协方差阵$\hat{\boldsymbol{L}} $$= \mathit{\boldsymbol{l}} + \hat{\boldsymbol{V}}, {\mathit{\boldsymbol{D}}_l} = \left[ {\begin{array}{*{20}{c}} {\hat \sigma _1^2{\mathit{\boldsymbol{Q}}_y}}&{\bf{0}}\\ {\bf{0}}&{\hat \sigma _2^2{\mathit{\boldsymbol{Q}}_a}} \end{array}} \right] 3) 2t+1个sigma点列向量li由比例对称采样策略构建：  \left\{ \begin{array}{l} {\mathit{\boldsymbol{l}}_0} = \mathit{\boldsymbol{\hat l}}\\ {\mathit{\boldsymbol{l}}_i} = \mathit{\boldsymbol{\hat l}} + {\left( {\sqrt {t + \lambda } \sqrt {{\mathit{\boldsymbol{D}}_l}} } \right)_i}\\ \;\;\;\;\;i = 1,2, \cdots ,t\\ {\mathit{\boldsymbol{l}}_i} = \mathit{\boldsymbol{\hat l}} + {\left( {\sqrt {t + \lambda } \sqrt {{\mathit{\boldsymbol{D}}_l}} } \right)_i}\\ \;\;\;\;\;i = t + 1,t + 2, \cdots 2t \end{array} \right. (22) 式中，\sqrt{\boldsymbol{D}_{l}} Dl卡洛斯基分解得到的下三角矩阵， \left(\sqrt{t+\lambda} \sqrt{\boldsymbol{D}_{l}}\right)_{i}为矩阵 \left(\sqrt{t+\lambda} \sqrt{\boldsymbol{D}_{l}}\right)的第i列。\lambda=\alpha^{2}(t+k)-t 为比例参数，常数α的值为0.001；k为另一个比例常数，取0。 4) 计算sigma点列向量经过非线性变换方差分量估计后生成的样本：  \boldsymbol{v}_{i}^{\hat{\beta}}=g\left(\boldsymbol{l}_{i}\right), i=0,1,2, \cdots, 2 t (23) 5) 确定样本\boldsymbol{v}_{i}^{\hat{\beta}} 的权值：  \left\{\begin{array}{l}{W_{0}^{m}=\lambda /(t+\lambda)} \\ {W_{0}^{c}=\lambda /(t+\lambda)+1-\alpha^{2}+b} \\ {W_{i}^{m}=W_{i}^{c}=1 /(2(t+\lambda)), i=1,2, \cdots, 2 t}\end{array}\right. (24) 式中，b=2。 6) 加权计算参数估值的均值E(\mathit{\boldsymbol{\widehat \beta }}) 、参数估值近似协方差阵{\mathit{\boldsymbol{D}}_{\hat \beta \hat \beta }} 和标准差 \boldsymbol{\sigma}_{\hat{\beta}_{i}}  E(\mathit{\boldsymbol{\widehat \beta }}) = \sum\limits_{i = 0}^{2t} {W_i^m} \mathit{\boldsymbol{v}}_i^{\hat \beta } (25)  \hat{\boldsymbol{\beta}}=E(\hat{\boldsymbol{\beta}}) (26)  {\mathit{\boldsymbol{D}}_{\hat \beta \hat \beta }} = \sum\limits_{i = 0}^{2t} {W_i^c\left( {\mathit{\boldsymbol{v}}_i^{\hat \beta } - E\left( {\mathit{\boldsymbol{\hat \beta }}} \right)} \right){{\left( {\mathit{\boldsymbol{v}}_i^{\hat \beta } - E\left( {\mathit{\boldsymbol{\hat \beta }}} \right)} \right)}^{\rm{T}}}} (27)  {\mathit{\boldsymbol{\sigma }}_{\hat \beta }} = \sqrt {{\mathit{\boldsymbol{D}}_{\hat \beta \hat \beta }}} (28) 式中， E(\mathit{\boldsymbol{\widehat \beta }})即为SUT法求得的达到二阶精度的参数加权均值，{\mathit{\boldsymbol{\sigma }}_{\hat \beta }} 为其二阶精度信息。本文根据文献[14]方法，以观测值的平差值作为观测值的均值，以观测值的后验协方差阵作为观测值的协方差阵。 3.2 SUT法偏差改正 考虑到模型线性化时省略掉的高次项和复杂的非线性迭代导致的参数估值的有偏性影响，以及初值的变化对方差分量估值的影响较大，因此设计了算法2。在算法1的基础上，对参数估值和改正数进行偏差改正，将偏差改正后的变量进行SUT法采样计算协方差阵和标准差：  {\mathit{\boldsymbol{b}}_{\hat \beta }} = E(\mathit{\boldsymbol{\widehat \beta }}) - \mathit{\boldsymbol{\widehat \beta }} (29)  \mathit{\boldsymbol{\widetilde \beta }} = {\mathit{\boldsymbol{\widehat \beta }}_{{\rm{vee}}}} - {\mathit{\boldsymbol{b}}_{\hat \beta }} (30)  {\mathit{\boldsymbol{b}}_{{{\mathit{\boldsymbol{\hat e}}}_a}}} = E\left( {{{\mathit{\boldsymbol{\hat e}}}_a}} \right) (31)  {\mathit{\boldsymbol{\tilde e}}_a} = {\mathit{\boldsymbol{\hat e}}_a} - {\mathit{\boldsymbol{b}}_{{{\hat e}_a}}} (32) 进而可以得到偏差改正后的参数估值：  \mathit{\boldsymbol{\tilde x}} = \left[ {\begin{array}{*{20}{c}} {{{\mathit{\boldsymbol{\hat \beta }}}_{{\rm{vce}}}} - {\mathit{\boldsymbol{b}}_{{{\hat e}_a}}}}\\ {\mathit{\boldsymbol{a}} - {{\mathit{\boldsymbol{\tilde e}}}_a}} \end{array}} \right] (33) 并以此构造新的观测值向量均值 \mathit{\boldsymbol{\tilde l}} = \left[ {\begin{array}{*{20}{c}} \mathit{\boldsymbol{y}}\\ {\mathit{\boldsymbol{a}} - {{\mathit{\boldsymbol{\tilde e}}}_\mathit{\boldsymbol{a}}}} \end{array}} \right]，及其协方差阵 \boldsymbol{D}_{i}=\left[\begin{array}{cc}{\hat{\sigma}_{1}^{2} \boldsymbol{Q}_{y}} & {\bf{0}} \\ {\bf{0}} & {\hat{\sigma}_{2}^{2} \boldsymbol{Q}_{a}}\end{array}\right]。重复式(23)计算采样点的参数估值：  \mathit{\boldsymbol{v}}_i^{\hat \beta } = f\left( {{{\mathit{\boldsymbol{\tilde l}}}_i}} \right),i = 0,1,2, \cdots ,2t (34) 得到改正后参数估值的协方差阵和标准差：  {\mathit{\boldsymbol{D}}_{\hat \beta \hat \beta }} = \sum\limits_{i = 0}^{2t} {W_i^c\left( {\mathit{\boldsymbol{v}}_i^{\hat \beta } - \mathit{\boldsymbol{\tilde \beta }}} \right){{\left( {\mathit{\boldsymbol{v}}_i^{\hat \beta } - \mathit{\boldsymbol{\hat \beta }}} \right)}^{\rm{T}}}} (35)  {\mathit{\boldsymbol{\sigma }}_{\hat \beta }} = \sqrt {{\mathit{\boldsymbol{D}}_{\hat \beta \hat \beta }}} (36) 4 算例分析 4.1 算例1 为了验证本文思路及方法的有效性，算例1为直线拟合模型，设置参数真值β1β2分别为-1.5和3.2，在0.9~11区间等间距生成真值向量 {\mathit{\boldsymbol{\tilde x}}}，并求得{\mathit{\boldsymbol{\tilde y}}} ，分别给 {\mathit{\boldsymbol{\tilde x}}}$$ {\mathit{\boldsymbol{\tilde y}}}$加上由matlab函数mvnrnd生成的方差为0.02× Qx、0.02× Qy的随机误差，其中观测值yx和模拟的权值PyPx(Qx= Px－1, Qy= Py－1)见表 1，并用表 2算法进行实验。

 $\left[ {\begin{array}{*{20}{c}} {{y_1}}\\ {{y_2}}\\ \vdots \\ {{y_{10}}} \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} {{e_{{y_1}}}}\\ {{e_{{y_2}}}}\\ \vdots \\ {{e_{{y_{10}}}}} \end{array}} \right] = \left( {\left[ {\begin{array}{*{20}{c}} {{x_1}}&1\\ {{x_2}}&1\\ \vdots & \vdots \\ {{x_{10}}}&1 \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} {{e_{{x_1}}}}&0\\ {{e_{{x_2}}}}&0\\ \vdots & \vdots \\ {{e_{{x_{10}}}}}&0 \end{array}} \right]} \right)\left[ {\begin{array}{*{20}{c}} {{\beta _1}}\\ {{\beta _2}} \end{array}} \right]$ (37)

 $\mathit{\boldsymbol{h}} = {\left[ {\begin{array}{*{20}{c}} {\underbrace {0\;0 \cdots 0}_{10}}&{\underbrace {1\;1 \cdots 1}_{10}} \end{array}} \right]^{\rm{T}}}$ (38)
 $\mathit{\boldsymbol{B}} = \left[ {\begin{array}{*{20}{c}} 1\\ 0 \end{array}} \right] \otimes {\mathit{\boldsymbol{I}}_{10}}$ (39)

4.2 算例2

 $\begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{X_1}}\\ {{Y_1}}\\ \vdots \\ {{X_n}}\\ {{Y_n}} \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} {{e_{{X_1}}}}\\ {{e_{{Y_1}}}}\\ \vdots \\ {{e_{{X_n}}}}\\ {{e_{{Y_n}}}} \end{array}} \right] = \left( {\left[ {\begin{array}{*{20}{c}} {{x_1}}&{ - {y_1}}&1&0\\ {{y_1}}&{{x_1}}&0&1\\ \vdots & \vdots & \vdots & \vdots \\ {{x_n}}&{ - {y_n}}&1&0\\ {{y_n}}&{{x_n}}&0&1 \end{array}} \right] - } \right.}\\ {\left. {\left[ {\begin{array}{*{20}{c}} {{e_{{x_1}}}}&{ - {y_1}}&1&0\\ {{e_{{y_1}}}}&{{x_1}}&0&1\\ \vdots & \vdots & \vdots & \vdots \\ {{e_{{x_n}}}}&{ - {e_{{y_n}}}}&1&0\\ {{e_{{y_n}}}}&{{e_{{x_n}}}}&0&1 \end{array}} \right]} \right)\left[ {\begin{array}{*{20}{c}} {{\beta _1}}\\ {{\beta _2}}\\ {{\beta _3}}\\ {{\beta _4}} \end{array}} \right]} \end{array}$ (40)

 $\mathit{\boldsymbol{h}} = \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{h}}_1}}\\ {{\mathit{\boldsymbol{h}}_2}}\\ {{\mathit{\boldsymbol{h}}_3}} \end{array}} \right],\mathit{\boldsymbol{B}} = \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{B}}_1}}\\ {{\mathit{\boldsymbol{B}}_2}}\\ {{\mathit{\boldsymbol{B}}_3}}\\ {{\mathit{\boldsymbol{B}}_4}} \end{array}} \right]$

4.3 算例3

 图 1 4种方案100次模拟的参数估值偏差 Fig. 1 Parameter estimation deviation of the four algorithms when simulated 100 times

5 结语

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Partial EIV Model Variance Component Estimation and Accuracy Evaluation of SUT Method by Deviation Correction
WANG Leyang1,2,3     DING Rui1,2     WU Lulu4
1. Faculty of Geomatics, East China University of Technology, 418 Guanglan Road, Nanchang 330013, China;
2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, MNR, 418 Guanglan Road, Nanchang 330013, China;
3. Key Lab for Digital Land and Resources of Jiangxi Province, 418 Guanglan Road, Nanchang 330013, China;
4. Department of Architecture and Civil Engineering, Jiangxi Water Resources Institute, 99 Beishan Road, Nanchang 330013, China
Abstract: The partial errors-in-variables model of variance component estimation precision evaluation theory needs improvement, so we apply the SUT sampling method to the minimum norm quadratic unbiased estimation of Partial EIV model. Using the variance component estimation modified stochastic model, we then use it as a priori information to obtain the weighted mean and second-order precision information by the SUT sampling method. Considering the deviation of the nonlinear model, the deviation correction is carried out, and the second-order precision information is calculated by the SUT method. An experiment shows that combining SUT method and variance component estimation to deal with Partial EIV model can effectively avoid complicated derivation operation, and gets more accurate parameter values and reasonable second-order accuracy information. It also shows the necessity of deviation correction.
Key words: Partial EIV model; variance component estimation; parameter estimation; deviation correction; precision evaluation