This article analyses the effects of system distortions (crosstalk and channel imbalance), Faraday rotation and system noise on estimates of the cross-polarized backscattering coefficient, σhv0, by a spaceborne synthetic aperture radar. Modeling the unknown system errors and noise by a joint complex Gaussian distribution allows analytic first-order approximations to the mean and variance of the error in σhv0 to be derived that do not depend on the SAR operating frequency. Simulation shows these approximations to be very accurate, given the statistical model and the expected magnitudes of system errors and noise for the P-band instrument to be carried by the European Space Agency BIOMASS mission. Simulation further shows that the σhv0 errors are Gaussian distributed, so their exceedance probabilities can be calculated from just the analytic expressions for the mean and variance of the errors. Exceedance probabilities for above-ground biomass (AGB) can then be calculated under a power law relation between σhv0σhv and AGB that is consistent with P-band observations. This allows tradeoff curves between crosstalk and channel imbalance (shown to be segments of hyperbolas) to be calculated, along which the relative error in AGB is within a given percentage of its true value, from which limits on the permissible size of the errors can be determined if BIOMASS mission requirements are to be met.

中文翻译：

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系统畸变和噪声对高压后向散射的影响及其与星载 P 波段 SAR 数据地面生物量估计的相关性


本文分析了系统失真（串扰和通道不平衡）、法拉第旋转和系统噪声对星载合成孔径雷达交叉极化后向散射系数 σhv0 估计的影响。通过联合复数高斯分布对未知系统误差和噪声进行建模，可以导出 σhv0 中误差均值和方差的解析一阶近似值，该近似值不依赖于 SAR 工作频率。考虑到欧洲航天局 BIOMASS 任务所携带的 P 波段仪器的统计模型以及系统误差和噪声的预期大小，仿真表明这些近似值非常准确。仿真进一步表明，σhv0 误差是高斯分布的，因此可以仅根据误差均值和方差的解析表达式来计算其超出概率。然后可以根据 σhv0σhv 和 AGB 之间的幂律关系计算地上生物量 (AGB) 的超出概率，该关系与 P 波段观测结果一致。这样可以计算串扰和通道不平衡（显示为双曲线段）之间的权衡曲线，沿着该曲线，AGB 中的相对误差在其真实值的给定百分比内，由此可以得出误差允许大小的限制确定是否满足 BIOMASS 任务要求。