Robust SAR ATR by hedging against uncertainty

For the past two years in this conference, we have described techniques for robust identification of motionless ground targets using single-frame Synthetic Aperture Radar (SAR) data. By "robust identification," we mean the problem of determining target ID despite the existence of confounding statistically uncharacterizable signature variations. Such variations can be caused by effects such as mud, dents, attachment of nonstandard equipment, nonstandard attachment of standard equipment, turret articulations, etc. When faced with such variations, optimal approaches can often behave badly-e.g., by mis-identifying a target type with high confidence. A basic element of our approach has been to hedge against unknowable uncertainties in the sensor likelihood function by specifying a "random error bar" (random interval) for each value of the likelihood function corresponding to any given value of the input data. In this paper, we will summarize our recent results. This will include a description of the "fuzzy maximum a posteriori (MAP)" estimator. The fuzzy MAP estimate is essentially the set of conventional MAP estimates that are plausible, given the assumed uncertainty in the problem. Despite its name, the fuzzy MAP is derived rigorously from first probabilistic principles based on random interval theory.