On the Method of Polarimetric SAR Calibration Using Distributed Targets

Abstract

In the companion paper (Zhang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2020), we identified two types of calibration models (CMs) that have been widely used in polarimetric calibration algorithms with distributed targets. An optimal method based on the covariance matching estimation technique (COMET), which we refer to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> method, was used therein but without proof of its optimality. This article supplies the details on parameter estimation using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> method and proves that it is optimal in the mean-squared sense: No other estimate has a smaller mean-squared error. For data affected by the Faraday rotation (FR), the feasibility of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> method is analyzed. Numerical experiments are presented to compare the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> method with existing methods and prove its optimality. The differences between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> method and another COMET-based calibration method are discussed. Moreover, we prove that estimating the distortion parameters while preserving the orientation angle is impossible, contrary to what is found by Ainsworth <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2006).