Abstract Optimal estimation (OE) is a core method in quantitative Earth observation. The optimality of OE depends on the errors in the prior, measurements and forward model being zero mean and having well-known error covariance. Often these assumptions are not met. We show how to use matches of satellite observations to in situ reference measurements to estimate parameters for use in OE that bring the retrieval framework closer to the theoretical optimality. This is done by retrieving bias correction and error covariance parameters. Bias correction parameters for some components of the retrieved state and for the satellite radiances are anchored by the in situ reference measurements, and are obtained by a modification of Kalman filtering. Error covariance matrices for the prior state and for the observation-simulation difference are iteratively obtained by applying equations for diagnosing internal retrieval consistency. The theory is applied to the case of OE of sea surface temperature from a sensor on a geostationary platform. Relative to an initial OE implementation, all measures of retrieval performance are improved when the optimised OE is tested on independent data: mean difference from validation data is reduced from −0.08 K to −0.01 K, and the standard deviation from 0.47 to 0.45 K; retrieval sensitivity to sea surface temperature increases from 71% to 76%; and a 20% underestimation of retrieval uncertainty is corrected. Perhaps more significant than the quantitative improvements are the coherent new insights into the forward model simulations and prior assumptions that are also obtained. These include estimates of prior bias in the absence of in situ information, an important consideration when in situ information is not globally distributed. Biases and lack of information about error covariances arise in remote sensing very often. While illustrated here for a particular case, the principles and methods we present for constraining that lack of knowledge systematically using ground truth will be widely applicable in remote sensing.

中文翻译：

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通过利用匹配的原位参考进行最佳估计的偏差校正和协方差参数

摘要 最优估计（OE）是地球定量观测的核心方法。OE 的最优性取决于先验、测量和前向模型中的误差为零均值并具有众所周知的误差协方差。通常这些假设没有得到满足。我们展示了如何使用卫星观测与原位参考测量的匹配来估计 OE 中使用的参数，从而使检索框架更接近理论最优。这是通过检索偏差校正和误差协方差参数来完成的。检索状态的某些分量和卫星辐射的偏差校正参数由原位参考测量锚定，并通过卡尔曼滤波的修改获得。通过应用用于诊断内部检索一致性的方程，迭代地获得先验状态和观察模拟差异的误差协方差矩阵。该理论应用于地球静止平台上的传感器对海面温度进行 OE 的情况。相对于最初的 OE 实施，当优化的 OE 在独立数据上进行测试时，所有检索性能的度量都得到了改进：与验证数据的平均差异从 -0.08 K 减少到 -0.01 K，标准偏差从 0.47 减少到 0.45 K；检索对海面温度的敏感度从 71% 增加到 76%；并且纠正了对检索不确定性的 20% 低估。也许比定量改进更重要的是对正向模型模拟和先前假设的连贯新见解。这些包括在没有原位信息的情况下对先验偏差的估计，当原位信息不是全球分布时，这是一个重要的考虑因素。遥感中经常出现偏差和缺乏关于误差协方差的信息。虽然此处针对特定案例进行了说明，但我们提出的用于系统地使用地面实况来限制知识缺乏的原则和方法将广泛适用于遥感。遥感中经常出现偏差和缺乏关于误差协方差的信息。虽然此处针对特定案例进行了说明，但我们提出的用于系统地使用地面实况来限制知识缺乏的原则和方法将广泛适用于遥感。遥感中经常出现偏差和缺乏关于误差协方差的信息。虽然此处针对特定案例进行了说明，但我们提出的用于系统地使用地面实况来限制知识缺乏的原则和方法将广泛适用于遥感。