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A Baseline Design Method for Interferometric SAR Ocean Current Measurements Using a Dual-satellite Distributed System
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摘要: 传统星载SAR单基线顺轨干涉体制因基线固定难以满足复杂海况下海面流场测量需求。针对分布式SAR卫星系统多基线协同测流基线设计的问题，该文在干涉相干性与测流敏感性双重约束下，提出一种面向海流测量的多基线优化设计方法，并推导了多基线加权最小二乘融合反演海面流场的理论精度上界。结果表明，该方法可显著降低径向流速误差；当基线数量增加到一定程度后，精度逼近理论上限。不同海况下，融合误差均满足0.1 m/s的测速精度要求，且X频段和C频段需求的短基线较Ku频段更长。该方法可以有效支撑分布式干涉SAR海流测量卫星系统设计。Abstract: Due to their fixed baselines, traditional single-baseline spaceborne along-track interferometric Synthetic Aperture Radar (SAR) systems struggle to meet the measurement requirements for ocean surface current, particularly under complex sea conditions. To overcome this limitation and optimize multi-baseline designs for distributed SAR satellite systems, this study introduces a multi-baseline optimization method for ocean current measurements. The method operates under the dual constraints of interferometric coherence and current measurement sensitivity. The study also derives the theoretical upper bound of accuracy for multi-baseline weighted least squares fusion inversion of ocean surface current. Results show that this method significantly reduces radial current velocity error, with accuracy approaching the theoretical upper limit as the number of baselines increases. Under various sea conditions, the fusion error meets the required velocity measurement accuracy of 0.1 m/s. Notably, the X and C-band require longer baselines than the Ku-band. This method effectively supports the design of distributed interferometric SAR satellite systems for ocean current measurements.
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图 1 一发M 收星座在轨测流示意图
Figure 1. Schematic diagram of on-orbit current measurement of the M receiving constellation
图 2 混合基线斜视卫星几何示意图
Figure 2. Schematic diagram of the geometry of a hybrid baseline strabismus satellite
图 3 不同多视数，流场测量误差随相干系数变化
Figure 3. OSC measurement error variation with coherence coefficient under different multi-look numbers
图 4 一个轨道周期交轨钟摆双星相对位置和基线示意图
Figure 4. Schematic diagram of relative position and baseline of pendulum
图 5 一种典型分布式SAR卫星系统几何构型示意图
Figure 5. Schematic illustration of a representative geometric configuration for a distributed SAR system
图 6 单基线流速测量RMSE随有效基线长度变化示意图
Figure 6. Single-baseline velocity measurement RMSE variation with effective baseline length
图 8 不同海况下多基线加权融合精度随基线数量变化曲线示意图
Figure 8. Schematic of the variation curve of multi-baseline weighted fusion accuracy with baseline number under different sea states
图 7 多基线加权融合精度随基线数量的收敛特性示意图
Figure 7. Convergence characteristics of multi-baseline weighted fusion accuracy with the number of baselines
表 1 交轨钟摆双星编队轨道六根数
Table 1. The orbital elements of the pendulum
卫星 半长轴(km) 离心率 轨道倾角(°) 近地点辐角(°) 升交点赤经(°) 平近点角(°) 主星 7133.137 0.0001 97.4 0 0 0 辅星 7133.137 0.0001 97.4 0 0.0024 0.0031 
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表 2 系统仿真参数
Table 2. System simulation parameters
参数 数值 波长$ \lambda $ 0.022 m 卫星飞行速度$ {V}_{\text{s}} $ 7400 m/s斜视角$ \psi $ 45° 入射角$ {\theta }_{{i}} $ 30° 轨道高度$ {H} $ 755 km 风速$ {U}_{10} $ 3～12 m/s 径向流速$ {v}_{{\mathrm{r}}} $ 0.05～2.0 m/s 海面散射系数$ {\sigma }^{0} $ −12.5～−6.2 dB 噪声等效后向散射系数NESZ −20 dB 等效多视数$ {N}_{\text{L}} $ 1600 处理去相干$ {\gamma }_{\text{proc}} $ 0.98 垂直基线去相干$ {\gamma }_{\text{B}} $ 0.97
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表 3 6条基线时间去相干系数汇总表
Table 3. Summary of time decorrelation coefficients for six rear-vew baselines
基线 天线对 物理基线长度 有效顺轨基线长度 时间基线(ms) $ {\gamma }_{\text{temp}} $ 适用场景 $ {\text{B}}_{1} $ A1-A2 3.5 m 159 $ \lambda $ 0.473 0.992 全海况，高相干 $ {\text{B}}_{2} $ A2-B1 338 m 1727 $ \lambda $5.135 0.377 中-低海况 $ {\text{B}}_{3} $ B1-B2 3.5 m 159 $ \lambda $ 0.473 0.992 全海况，高相干 $ {\text{B}}_{4} $ A1-B1 341.5 m 1886 $ \lambda $ 5.608 0.313 中-低海况 $ {\text{B}}_{5} $ A2-B2 341.5 m 1886 $ \lambda $ 5.608 0.313 中-低海况 $ {\text{B}}_{6} $ A1-B2 345 m 2045 $ \lambda $ 6.081 0.255 中-低海况，高测流敏感性
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表 4 各干涉通道总相干性对比表
Table 4. Verification of total coherence for each interferometric channel
通道 海况$ {U}_{10} $ $ {\gamma }_{\text{SNR}} $ $ {\gamma }_{\text{temp}} $ $ {\gamma }_{\text{total}} $ 是否满足 $ \geq 0.3 $ 短基线(B1) 3 m/s 0.85 1.00 0.81 √ 7 m/s 0.93 0.99 0.88 √ 12 m/s 0.96 0.98 0.89 √ 长基线(B6) 3 m/s 0.85 0.78 0.63 √ 7 m/s 0.93 0.25 0.23 × 12 m/s 0.96 0.02 0.02 ×
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表 5 各通道干涉相位模糊约束对比表
Table 5. Verification of interferometric phase ambiguity constraints for each channel
通道 $ {\phi }_{\text{max}} $(rad) $ {\phi }_{\text{max}} \lt \text{π} $ 备注 短(B1) 0.27 √ 高相干，无模糊 中(B2) 2.93 √ 接近$ \text{π} $，利用B1解缠 长(B6) 3.47 × 超出$ \text{π} $，利用B1/B2逐级解缠
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表 6 各通道径向流速测量精度对比表
Table 6. Verification of phase ambiguity constraints for each channel
通道 $ {\gamma }_{\text{total}} $ $ {\sigma }_{\phi } $(rad) $ {\sigma }_{{{v}_{r}}} $(m/s) 备注 短基线(B1) 0.88 0.013 0.096 高相干，低测流敏感性 长基线(B6) 0.23 0.102 0.059 低相干，高测流敏感性 融合(等效) — — 0.027 六基线加权融合后精度
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