﻿ 惯导系统传递对准误差评估方法
 舰船科学技术  2020, Vol. 42 Issue (10): 157-161    DOI: 10.3404/j.issn.1672-7649.2020.10.030 PDF

1. 海军研究院，北京 100073;
2. 中国舰船研究院，北京 100192;
3. 哈尔滨工业大学电气工程及自动化学院，黑龙江 哈尔滨 150001

Research on inertial navigation system transfer alignment error evaluation method
DU Hong-song1, YIN Hong-liang2, HAO Qiang3
1. The Research Institute of Navy Academy, Beijing 100073, China;
2. China Ship Research and Development Academy, Beijing 100192, China;
3. School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China
Abstract: As based on the Speed + Attitude matching transfer alignment evaluation attitude error method is of high degree of theory, the application of the low degree of problems, from the perspective of engineering application, this study put forward a kind of engineering transfer alignment error evaluation method, and designs the relevant transfer alignment scheme, on the basis of the practical application has carried out considering/does not consider the lever arm and flexural deformation simulation analysis, the test results show that the proposed method can effectively realize the error evaluation, lay the foundation for the subsequent application.
Key words: transfer alignment     error evaluation     the lever arm error     bending deformation
0 引　言

1 传递对准误差评估方案设计

2 传递对准误差评估算法设计 2.1 姿态量测方程构造

 ${{C}}_{{b_m}}^{{b_s}} = \left[ {{{I}} - \left( {{{\lambda}} \times } \right)} \right]\text{，}$ (1)
 ${\hat{ C}}_{{b_m}}^n = \left[ {{{I}} - \left( {{{{\varphi}} _m} \times } \right)} \right]{{C}}_{bm}^n\text{，}$ (2)
 ${\hat{ C}}_n^{{b_s}} = {{C}}_n^{{b_s}}\left[ {{{I}} + \left( {{{\varphi}} \times } \right)} \right]\text{。}$ (3)

 $\begin{split} {{\bf{Z}}_{DCM}} &= {\hat{\bf C}}_{{b_m}}^n{\hat{ C}}_n^{{b_s}} = \\& \left[ {{{I}} - \left( {{{{\varphi}} _m} \times } \right)} \right]{{C}}_{{b_m}}^n{{C}}_n^{{b_s}}\left[ {{{I}} + \left( {{{\varphi}} \times } \right)} \right] = \\& \left[ {{{I}} - \left( {{{{\varphi}} _m} \times } \right)} \right]{{C}}_{{b_m}}^n\left[ {{{I}} - \left( {{{\lambda}} \times } \right)} \right]{{C}}_n^{{b_m}}\left[ {{{I}} + \left( {{{\varphi }} \times } \right)} \right] = \\& {{I}} - \left( {{{{\varphi}} _m} \times } \right) - \left[ {\left( {{{C}}_{{b_m}}^n{{\lambda }}} \right) \times } \right] + \left( {{{\varphi}} \times } \right) \text{。} \end{split}$ (4)

 $\left\{ \begin{array}{l} {Z_x} = \left( {{{{Z}}_{DCM}}\left( {3,2} \right) - {{{Z}}_{DCM}}\left( {2,3} \right)} \right)/2\text{，} \\ {Z_y} = \left( {{{{Z}}_{DCM}}\left( {1,3} \right) - {{{Z}}_{DCM}}\left( {3,1} \right)} \right)/2 \text{，}\\ {Z_z} = \left( {{{{Z}}_{DCM}}\left( {2,1} \right) - {{{Z}}_{DCM}}\left( {1,2} \right)} \right)/2 \text{，} \end{array} \right.$ (5)

 ${{{Z}}_\theta } = {{\varphi }} - {{C}}_{{b_m}}^n{{\lambda}} + {{V}}\text{。}$ (6)

2.2 状态方程构造

 \left\{ {\begin{aligned} & {{\dot{\bf \varphi }} = - {\bf{\omega }}_{in}^n \times {\bf{\varphi }} - {{C}}_{{b_s}}^n{\bf{\varepsilon }}_b^{{b_s}} - {{C}}_{{b_s}}^n{\bf{\varepsilon }}_w^{{b_s}}} \\ & \delta {\dot{ V}}_e^n = \left( {{{C}}_{{b_s}}^n{{f}}_s^{{b_s}}} \right) \times {\bf{\varphi }} - \left( {2{\bf{\omega }}_{ie}^n + {\bf{\omega }}_{en}^n} \right) \times \\& \qquad \quad \delta {{V}}_e^n + {\bf{C}}_{{b_s}}^n\nabla _b^{{b_s}} + {\bf{C}}_{{b_s}}^n\nabla _w^{{b_s}} \\& \dot \lambda = 0 \\ & {{\dot{\bf \varepsilon }}_b^{{b_s}} = {{0}}} \\ & {\dot \nabla _b^{bs} = {{0}}} \end{aligned}} \right. (7)

 ${\dot{ X}} = {{FX}} + {{GW}}\text{，}$ (8)

${{F}} \!=\! \left[\!\!\!\! {\begin{array}{*{20}{c}} { - {\bf{\omega }}_{in}^n \times }&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{ - {{C}}_{{b_s}}^n}&{{0_{3 \times 3}}} \\ {\left( {{{C}}_{{b_s}}^n{{f}}_s^{{b_s}}} \right) \times }&{ - \left( {2{\bf{\omega }}_{ie}^n + {\bf{\omega }}_{en}^n} \right) \times }&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{{C}}_{{b_s}}^n} \\ {{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}} \end{array}} \!\!\!\right]$ ${{G}} = \left[ {\begin{array}{*{20}{c}} { - {{C}}_{{b_s}}^n}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{{C}}_{{b_s}}^n} \\ {{0_{3 \times 3}}}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{0_{3 \times 3}}} \end{array}}\!\!\! \right]$ ${{W}} = \left[ {\begin{array}{*{20}{c}} {{\bf{\varepsilon }}_w^{{b_s}}} \\ {\nabla _w^{{b_s}}} \end{array}} \right]$

 $\begin{split} Z & =\left[ {\begin{array}{*{20}{c}} {{{{Z}}_\theta }} \\ {{{{Z}}_V}} \end{array}} \right]= \\ & \left[ {\begin{array}{*{20}{c}} {{I_{3 \times 3}}}&{{0_{3 \times 3}}}&{ - {\bf{C}}_{{b_m}}^n}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{I_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}}&{{0_{3 \times 3}}} \end{array}} \right]{{X}} + {{V}} \text{，} \end{split}$ (9)

 图 1 传递对准误差评估方案流程图 Fig. 1 Flow chart of transfer alignment error evaluation scheme
3 设计方案研究验证 3.1 仿真条件

 图 2 挠曲变形角 Fig. 2 Deflection angle

 图 3 挠曲变形角速度 Fig. 3 Angular velocity of deflection
3.2 不考虑杆臂与挠曲变形仿真

1）仿真1

 图 4 传递对准误差 Fig. 4 Transfer alignment error

2）仿真2

 图 5 传递对准误差 Fig. 5 Transfer alignment error

3）仿真3

 图 6 传递对准误差 Fig. 6 Transfer alignment error

4）仿真4

 图 7 传递对准误差 Fig. 7 Transfer alignment error

3.3 考虑杆臂与挠曲变形仿真

1）仿真5

 图 8 传递对准误差 Fig. 8 Transfer alignment error

2）仿真6

 图 9 传递对准误差 Fig. 9 Transfer alignment error

3）仿真7

 图 10 传递对准误差 Fig. 10 Transfer alignment error

4）仿真8

 图 11 传递对准误差 Fig. 11 Transfer alignment error

4 结　语

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