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 哈尔滨工程大学学报  2019, Vol. 40 Issue (4): 839-843  DOI: 10.11990/jheu.201710014 0

### 引用本文

WANG Yanbao, HAO Xiaoning, DONG Guanming, et al. Analysis on error of 1-dimension active phase scanning series-feed array radar angle measurement[J]. Journal of Harbin Engineering University, 2019, 40(4), 839-843. DOI: 10.11990/jheu.201710014.

### 文章历史

1. 西安电子工程研究所 目标指示雷达总体部, 陕西 西安 710100;
2. 哈尔滨工程大学 科学技术研究院, 黑龙江 哈尔滨 150001

Analysis on error of 1-dimension active phase scanning series-feed array radar angle measurement
WANG Yanbao 1, HAO Xiaoning 1, DONG Guanming 2, ZHOU Yongwei 1
1. General System Department on Target Designation Radar, Xi'an Electronic Engineering Research Institute, Xi'an 710100, China;
2. Research Institute of Science and Technology, Harbin Engineering University, Harbin 150001, China
Abstract: To solve the problem of radar azimuth and pitching angle errors caused by a wide range of pitching angles, we propose a large dispersion angle and radar tilt angle for a 1D active-phase scanning radar.According to the relationship between the angles, the relational formula between azimuth, pitching angle and dispersion angle, and radar tilt angle of the 1-D active phase scanning can be derived.Compared with conventional correction methods, the proposed method does not need complex coordinate conversion, and the amount of calculation is small, which is convenient for engineering applications.Through analysis of radar flight detection data, the correctness and effectiveness of the correction algorithm are verified, and the angular measurement accuracy of similar radar products can be improved further.
Keywords: 1-dimension active-phase array radar    frequency sweep    string feed    dispersion angle    tilt angle    angle measurement accuracy    angle measurement error    angle correction

1 坐标系定义

 Download: 图 1 直角坐标系定义示意 Fig. 1 Rectangular coordinate definition diagram
 Download: 图 2 球坐标系定义示意 Fig. 2 Spherical coordinate definition diagram

2 测角误差源分析与研究 2.1 色散角导致的方位、俯仰测角误差

 Download: 图 3 色散角导致的测角误差几何关系 Fig. 3 Geometric relationship of the angle error due to dispersion angle

 $\alpha ^\prime = {\rm{arcsin}}\left( {\frac{{{\rm{sin}}\alpha }}{{{\rm{cos}}\beta }}} \right)$ (1)

2.2 天线倾斜导致的方位、俯仰测角误差

 $\left\{ \begin{array}{l} {\rm{sin}}\theta = \frac{{AB}}{{AO^\prime }} = \frac{{{\rm{sin}}\beta }}{{{\rm{cos}}\alpha }}\\ \theta = {\rm{arcsin}}\left( {\frac{{{\rm{sin}}\beta }}{{{\rm{cos}}\alpha }}} \right) \end{array} \right.$ (2)
 $\left\{ \begin{array}{l} {\rm{tan}}\alpha ^\prime = \frac{{OO^\prime }}{{O^\prime D}} = \frac{{{\rm{sin}}\alpha }}{{{\rm{cos}}\alpha {\rm{cos}}\left( {\theta + \varphi } \right)}}\\ \alpha ^\prime = {\rm{arctan}}\left( {\frac{{{\rm{sin}}\alpha }}{{{\rm{cos}}\alpha {\rm{cos}}\left( {\theta + \varphi } \right)}}} \right) \end{array} \right.$ (3)
 $\left\{ \begin{array}{l} {\rm{sin}}\beta ^\prime = \frac{{AD}}{{AO}} = {\rm{cos}}\alpha {\rm{sin}}\left( {\theta + \varphi } \right)\\ \beta ^\prime = {\rm{arcsin}}\left( {{\rm{cos}}\alpha {\rm{sin}}\left( {\theta + \varphi } \right)} \right) \end{array} \right.$ (4)
 Download: 图 4 倾斜角导致的测角误差几何关系 Fig. 4 Geometric relationship of the angle error due to radar tilt angle

2.3 天线测试方法导致的方位、俯仰测角误差研究

 $\left\{ \begin{array}{l} {\rm{sin}}\beta = {\rm{sin}}\theta {\rm{cos}}\alpha \\ \beta = {\rm{arcsin}}\left( {{\rm{sin}}\theta {\rm{cos}}\alpha } \right) \end{array} \right.$ (5)
 Download: 图 5 雷达测试方法导致的测角误差几何关系 Fig. 5 Geometric relationship of the angle error due to radar test method

 $\alpha ^\prime = {\rm{arctan}}\left( {\frac{{{\rm{sin}}\alpha }}{{{\rm{cos}}\alpha {\rm{cos}}\left( {\beta + \varphi } \right)}}} \right)$ (6)
 $\beta ^\prime = {\rm{arcsin}}\left( {{\rm{cos}}\alpha {\rm{sin}}\left( {\beta + \varphi } \right)} \right)$ (7)

2.4 检测结果及分析

 Download: 图 6 修正前后参数变化 Fig. 6 Change of parameters before and after correction

3 结论

1) 方位测角误差和色散角、目标俯仰角有关，在色散角不为零的情况下，目标在天线阵面球坐标系下的方位测角误差会随着俯仰角的增大而变大，随着色散角与俯仰角的同时增大，方位测角误差将迅速增加。

2) 雷达球坐标系下测角误差和雷达倾斜角度有关，色散角、倾斜角度越大，方位、俯仰测角误差将随目标俯仰角度的增加而增大。