Open Access
 Issue JNWPU Volume 39, Number 4, August 2021 919 - 929 https://doi.org/10.1051/jnwpu/20213940919 23 September 2021

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## 1 经度条带法对星座对地覆盖问题

### 1.1 覆盖问题的基本符号表示

1) 星座对地覆盖范围ΛC(t)或ΛC([tS, tE])的表示。

2) 星座对地覆盖范围与任意形状地面区域R相交范围的计算。

3) 任意球面不规则区域的面积度量。

### 1.2 经度条带的基本概念

1条经度条带可以看作经度与中央经线相差小于Δθ/2的点的集合

m[R]表示对任意一个球面区域R的面积度量。将地球半径归一化为1, 则通过球面面积公式可知, 纬度范围L[φL, φU](θ, Δθ)的球面面积为

### 1.4 球面圆盘与经度条带相交的纬度范围计算

Θ为一个中心(θ0, φ0)半径为α的球面圆盘, 其与经度条带L(θj, Δθ)相交的纬度范围Π

## 2 星座对地覆盖范围计算

### 2.1 累积性覆盖问题计算

 图1卫星对经线累积覆盖示意图

## 3 数值实验

### 3.1 累积覆盖问题数值仿真

 图2星座对目标的覆盖率上下界随条带精度的变化曲线
 图3经度条带法与传统网格点法求解累积覆盖问题计算时间随精度变化曲线

### 3.2 连续覆盖问题数值仿真

 图4不同时间间隔下星座对目标的连续性覆盖率上下界随条带精度的变化曲线
 图5经度条带法与传统网格点法求解连续性覆盖问题计算时间随精度变化曲线

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## All Figures

 图1卫星对经线累积覆盖示意图 In the text
 图2星座对目标的覆盖率上下界随条带精度的变化曲线 In the text
 图3经度条带法与传统网格点法求解累积覆盖问题计算时间随精度变化曲线 In the text
 图4不同时间间隔下星座对目标的连续性覆盖率上下界随条带精度的变化曲线 In the text
 图5经度条带法与传统网格点法求解连续性覆盖问题计算时间随精度变化曲线 In the text

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