﻿ 利用夹角几何关系的超短基线定位方法
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (8): 1474-1479  DOI: 10.11990/jheu.201808081 0

### 引用本文

LIANG Guolong, ZHANG Yifeng, FU Jin. Angle-based underwater source localization for USBL[J]. Journal of Harbin Engineering University, 2019, 40(8), 1474-1479. DOI: 10.11990/jheu.201808081.

### 文章历史

1. 哈尔滨工程大学 水声技术重点实验室, 黑龙江 哈尔滨 150001;
2. 哈尔滨工程大学 水声工程学院, 黑龙江 哈尔滨 150001

Angle-based underwater source localization for USBL
LIANG Guolong 1,2, ZHANG Yifeng 1,2, FU Jin 1,2
1. Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China;
2. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: We propose an angle-based underwater source localization method for ultrashort baselines (USBLs) to overcome deficiencies in localization accuracy in traditional USBLs. The model for USBL source localization and error analysis is constructed through the proposed method to study the influence of depth information on the localization accuracy of USBL. This investigation is performed in accordance with the angle-based geometrical relation in USBL. The proposed method increases localization accuracy by utilizing effective depth information to decrease the effect of the main error source on localization accuracy. Theoretical and simulative studies show that this method can considerably increase the localization accuracy of USBL, especially when estimating the error in phase differences. Moreover, the method can improve localization accuracy in most areas.
Keywords: ultrashort baseline    source localization    error analysis    depth information    angle-based geometrical relation    high accuracy

1 传统超短基线定位原理及误差分析 1.1 定位原理

 $\cos {\beta _0} = {\phi _{13}}/kd$ (1)
 $\cos \alpha_{0}=\phi_{24} / k d$ (2)

 $y=R \cos \beta_{0}=R \phi_{13} / k d$ (3)
 $x=R \cos \alpha_{0}=R \phi_{24} / k d$ (4)

1.2 定位误差分析

 $\sqrt{\overline{\Delta y^{2}} / R^{2}}=\sqrt{\left(\overline{\Delta R^{2}} / R^{2}\right) \cos ^{2} \beta_{0}+\sin ^{2} \beta_{0} \overline{\Delta \beta_{0}^{2}}}$ (5)
 $\sqrt{\overline{\Delta x^{2}} / R^{2}}=\sqrt{\left(\overline{\Delta R^{2}} / R^{2}\right) \cos ^{2} \alpha_{0}+\sin ^{2} \alpha_{0} \overline{\Delta \alpha_{0}^{2}}}$ (6)

 $\sqrt{\overline{\Delta y^{2}} / R^{2}}=\sqrt{\left(\overline{\Delta R^{2}} / R^{2}\right) \cos ^{2} \beta_{0}+\overline{\Delta \phi_{13}^{2}} /(k d)^{2}}$ (7)
 $\sqrt{\overline{\Delta x^{2}} / R^{2}}=\sqrt{\left(\overline{\Delta R^{2}} / R^{2}\right) \cos ^{2} \alpha_{0}+\overline{\Delta \phi_{24}^{2} /(k d)^{2}}}$ (8)

2 基于夹角几何关系的高精度定位算法及误差分析 2.1 定位原理

 $\cos \beta=\cos \gamma \cos \theta$ (9)
 $\cos \alpha=\cos \gamma \sin \theta$ (10)

 $y=R \cos \beta$ (11)
 $x=R \cos \alpha$ (12)

 $\sqrt{\overline{\Delta y^{2}} / R^{2}}=\sqrt{\left(\overline{\Delta R^{2}} / R^{2}\right) \cos ^{2} \beta+\sin ^{2} \beta \cdot \overline{\Delta \beta^{2}}}$ (13)
 $\sqrt{\overline{\Delta x^{2}} / R^{2}}=\sqrt{\left(\overline{\Delta R^{2}} / R^{2}\right) \cos ^{2} \alpha+\sin ^{2} \alpha \cdot \overline{\Delta \alpha^{2}}}$ (14)

 $\cos ^{2} \alpha+\cos ^{2} \beta=\cos ^{2} \gamma$ (15)

 $\Delta \alpha \cos \alpha \sin \alpha+\Delta \beta \cos \beta \sin \beta=\Delta \gamma \cos \gamma \sin \gamma$ (16)

 $\sin \gamma=h / R$ (17)

 $\cos \gamma \cdot \Delta \gamma=(\Delta h \cdot R-h \cdot \Delta R) / R^{2}$ (18)

 $\sin ^{2} \alpha \cdot \overline{\Delta \alpha^{2}}=r_{\beta}+p_{y}+q_{y}$ (19)

 $\frac{h^{2} \overline{\Delta h^{2}}}{R^{4}}+\frac{h^{4} \overline{\Delta R^{2}}}{R^{6}}<\left(\cos ^{2} \alpha_{0}-\cos ^{2} \beta_{0}\right) \overline{\Delta \phi^{2}} /(k d)^{2}$ (20)

 $\left\{ {\begin{array}{*{20}{l}} {{{\cos }^2}\alpha = {{\cos }^2}\gamma - {{\cos }^2}\beta }\\ {{\rm{ s}}{\rm{.t}}{\rm{. }}\min \left\| {\mathit{\boldsymbol{\alpha }} - {\mathit{\boldsymbol{\alpha }}_0}} \right\|} \end{array}} \right.$ (21)

 $\sin ^{2} \beta \cdot \overline{\Delta \beta^{2}}=r_{\alpha}+p_{x}+q_{x}$ (22)

 $\frac{h^{2} \overline{\Delta h^{2}}}{R^{4}}+\frac{h^{2} \overline{\Delta R^{2}}}{R^{6}}<\left(\cos ^{2} \beta_{0}-\cos ^{2} \alpha_{0}\right) \overline{\Delta \phi^{2}} /(k d)^{2}$ (23)

 $\left\{ {\begin{array}{*{20}{l}} {{{\cos }^2}\beta = {{\cos }^2}\gamma - {{\cos }^2}\alpha }\\ {{\mathop{\rm s}\nolimits} .{\rm{t.min}}\left\| {\mathit{\boldsymbol{\beta }} - {\mathit{\boldsymbol{\beta }}_0}} \right\|} \end{array}} \right.$ (24)

2.2 定位误差分析

 $\begin{array}{*{20}{c}} {\sqrt {\frac{{\overline {\Delta {x^2}} }}{{{R^2}}}} = \sqrt {{u_\beta } + \frac{{\overline {\Delta {\phi ^2}} }}{{{{(kd)}^2}}}} }\\ {\sqrt {\frac{{\overline {\Delta {y^2}} }}{{{R^2}}}} = \sqrt {{u_\alpha } + \frac{{{{\cos }^2}\beta }}{{{{\cos }^2}\alpha }}\frac{{\overline {\Delta {\phi ^2}} }}{{{{(kd)}^2}}} + {p_y} + {q_y}} } \end{array}$ (25)

 $\sqrt{\frac{\overline{\Delta x^{2}}+\overline{\Delta y^{2}}}{R^{2}}}=\sqrt{\frac{\cos ^{2} \gamma}{\cos ^{2} \alpha} \frac{\overline{\Delta \phi^{2}}}{(k d)^{2}}+p_{y}+u_{\gamma}+q_{y}}$ (26)

 $\left\{\begin{array}{l}{\sqrt{\frac{\overline{\Delta x^{2}}}{R^{2}}}=\sqrt{u_{\beta}+\frac{\cos ^{2} \alpha}{\cos ^{2} \beta} \frac{\overline{\Delta \phi^{2}}}{(k d)^{2}}+p_{x}+q_{x}}} \\ {\sqrt{\frac{\overline{\Delta y^{2}}}{R^{2}}}=\sqrt{u_{\alpha}+\frac{\overline{\Delta \phi^{2}}}{(k d)^{2}}}}\end{array}\right.$ (27)

 $\sqrt{\frac{\overline{\Delta x^{2}}+\overline{\Delta y^{2}}}{R^{2}}}=\sqrt{\frac{\cos ^{2} \gamma}{\cos ^{2} \beta} \frac{\overline{\Delta \phi^{2}}}{(k d)^{2}}+u_{\gamma}+p_{x}+q_{x}}$ (28)
3 仿真实验与分析

 Download: 图 3 超短基线系统定位均方根误差水平空间分布 Fig. 3 RMSE horizontal spatial distribution using USBL

 Download: 图 4 超短基线系统定位均方根误差垂直空间分布 Fig. 4 RMSE vertical spatial distribution using USBL

 Download: 图 5 定位相对误差与相位差误差的关系 Fig. 5 The relationship between the relative error of positioning and the error of phase difference
4 结论

1) 相比于传统算法，基于夹角的高精度定位算法在和方向均能提高定位精度，定位精度最高可提高约0.25%。

2) 除坐标轴及其附近区域外，目标越靠近坐标轴，则基于夹角的高精度定位算法在该轴方向上的定位精度提高得就越明显。

3) 从总的定位误差的角度看，相比于传统算法，基于夹角的高精度定位算法的定位精度在绝大多数区域均有显著提高。

4) 当目标与两条基线近似垂直时，三者的几何关系难以满足基于夹角的高精度定位算法的适用条件，因此，该方法在这一条件下无法应用。

5) 在纵切面上看，当目标位于稍大开角的情况，采用基于夹角的高精度定位算法能够提高定位精度，且提高精度与开角变化关系不明显。

6) 对于以相位差为主要误差源的的超短基线定位问题，基于夹角的高精度定位算法提高的定位精度更为显著。

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