Robust estimators for multipass SAR interferometry

Abstract

This paper introduces a framework for robust parameter estimation in multipass interferometric synthetic aperture radar (InSAR), such as persistent scatterer interferometry, SAR tomography, small baseline subset, and SqueeSAR. These techniques involve estimation of phase history parameters with or without covariance matrix estimation. Typically, their optimal estimators are derived on the assumption of stationary complex Gaussian-distributed observations. However, their statistical robustness has not been addressed with respect to observations with nonergodic and non-Gaussian multivariate distributions. The proposed robust InSAR optimization (RIO) framework answers two fundamental questions in multipass InSAR: 1) how to optimally treat images with a large phase error, e.g., due to unmolded motion phase, uncompensated atmospheric phase, etc.; and 2) how to estimate the covariance matrix of a non-Gaussian complex InSAR multivariate, particularly those with nonstationary phase signals. For the former question, RIO employs a robust M-estimator to effectively downweight these images; and for the latter, we propose a new method, i.e., the rank M-estimator, which is robust against non-Gaussian distribution. Furthermore, it can work without the assumption of sample stationarity, which is a topic that has not previously been addressed. We demonstrate the advantages of the proposed framework for data with large phase error and heavily tailed distribution, by comparing it with state-of-the-art estimators for persistent and distributed scatterers. Substantial improvement can be achieved in terms of the variance of estimates. The proposed framework can be easily extended to other multipass InSAR techniques, particularly to those where covariance matrix estimation is vital.