﻿ 基于航向传感器数据的阵形估计方法
 舰船科学技术  2020, Vol. 42 Issue (1): 172-174 PDF

Method for array shape-estimation based on heading sensor data
LAI Zhou
Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
Abstract: The array shape need to be estimated when towed array is not a straight line, the estimate method of using heading sensor data for a high order fitting curve facing difficulties of the divergence and the requirement of the accuracy of heading sensor, this paper proposed an second order polynomial to fit the shape . The result of the simulation indicated this method tracking the shape well, and has tolerance to the accuracy of heading sensor.
Key words: towed array     array shape estimation     heading sensor
0 引　言

1 平面内阵形畸变估计方法

 图 1 平面阵形 Fig. 1 Plane array shape

 $y = f(x) = {a_2}{x^2} + {a_1}x{\text{。}}$ (1)

 ${l_{ij}} = \int_{{x_i}}^{{x_j}} {\sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}}{\rm d}x}{\text{，}}$ (2)

 \begin{aligned} & {k_i} = \tan ({\theta _i}) = 2{a_2}{x_i} + {a_1} {\text{，}}\\ & {k_j} = \tan ({\theta _j}) = 2{a_2}{x_j} + {a_1}{\text{，}} \end{aligned} (3)

 ${l_{ij}} = \frac{1}{{4{a_2}}}\left( {{k_j}\sqrt {1 + k_j^2} - {k_i}\sqrt {1 + k_i^2} + \ln \left(\frac{{{k_j} + \sqrt {1 + k_j^2} }}{{{k_i} + \sqrt {1 + k_i^2} }}\right)} \right){\text{。}}$ (4)

 \begin{align} &{a_2} = \frac{1}{{C_M^2}}\sum\limits_{i = 1,j \ne i}^M \frac{1}{{4{l_{ij}}}}\\ &\left( {{k_j}\sqrt {1 + k_j^2} - {k_i}\sqrt {1 + k_i^2} + \ln \left(\frac{{{k_j} + \sqrt {1 + k_j^2} }}{{{k_i} + \sqrt {1 + k_i^2} }}\right)} \right) {\text{。}} \end{align} (5)

 图 2 流程图 Fig. 2 Flow chart
2 仿真结果与分析 2.1 仿真1

 图 3 阵形畸变 Fig. 3 Shape distortion

 图 4 航向角 Fig. 4 Heading angle

 图 5 阵形估计 Fig. 5 The estimated shape

2.2 仿真2

 $e = \frac{1}{M}\sum\limits_{i = 1}^M {\sqrt {{{\left( {{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{x} }_i} - {x_i}} \right)}^2} + {{\left( {{{\hat y}_i} - {y_i}} \right)}^2}} }{\text{。}}$

 图 6 误差曲线 Fig. 6 The error curve

3 结　语

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