An end-to-end error model for classification methods based on a SAR intensity ratio

This paper aims at defining the expression of the probability of error of classification methods using a Synthetic Aperture Radar (SAR) intensity ratio as a classifier. The two SAR intensities involved in this ratio can be measurements from different dates, polarizations or possibly also frequency bands. Previous works provided a baseline expression of the probability of error addressing the two-class problem with equal a priori class probabilities and no calibration error. This study brings up a novel expression of the error, providing the possibility to assess the effect of class probabilities and calibration errors. The effect of calibration errors such as channel gain imbalance and radiometric stability is assessed in the general case. Results indicate that channel gain imbalance is generally not a decisive parameter, but that radiometric stability is more critical in methods based on the temporal change. This error model can be used to test the impact of other SAR system parameters (time-lapse between repeat-pass orbits, ambiguity ratio, number of looks) and constitutes a tool for the design of future SAR missions and for the development of robust classification methods using existing SAR instruments.