Reliable InSAR Phase History Uncertainty Estimates

Abstract

Deformation estimation from radar interferometric stacks has to confront speckle over decorrelating distributed targets. Inferring the speckle-induced uncertainty in the estimated phase history is challenging. Previously published estimates based on Fisher information (FI) can underestimate the errors by an order of magnitude. Here, we introduce three improvements to mitigate the bias. We: 1) account for uncertainty in the magnitudes of the interferometric covariance matrix elements; 2) penalize the likelihood to reduce the impact of coherence biases on the phase history uncertainty estimates; and 3) constrain the covariance magnitudes to stabilize the estimation. In simulations, these improvements substantially reduced the bias in the uncertainty estimates. Bias reduction was due to an increase in the predicted uncertainty (improvements 1–3) and a decrease in the actual error (improvements 2 and 3). Temporal correlations–crucial for model fitting and testing–were also estimated more accurately. In observations, the underestimation relative to the observed spatial variability was largely eliminated. In contrast to the alternative estimates based on spatial variability, the improved FI uncertainty estimates are applicable to small-scale phenomena such as sinkholes. They can serve as foundation for reliable uncertainty estimates of the deformation derived in subsequent interferometric processing steps, thus bolstering model testing and data fusion.