Quadrature-based credible set estimation for radar feature extraction

Efficient and accurate extraction of physically-relevant features from measured radar data is desirable for automatic target recognition (ATR). In this paper, we present an estimation technique to find credible sets of parameters for any given feature model. The proposed approach provides parameter estimates along with confidence values. Maximum a posteriori (MAP) estimates provide a single (vector) parameter value, typically found via sampling methods. However, computational inefficiency and inaccuracy issues commonly arise when sampling multi-modal or multi-dimensional posteriors. As an alternative, we use Gaussian quadrature to compute probability mass functions, covering the entire probability space. An efficient zoom-in approach is used to iteratively locate regions of high probability. The (possibly disjoint) regions of high probability correspond to sets of feasible parameter values, call credible sets. Thus, our quadrature-based credible set estimator (QBCSE) includes values very near the true parameter and confuser values that may lie far from the true parameter but map with high probability to the same observed data. The credible set and associated probabilities are computed and should both be passed to an ATR algorithm for informed decision-making. Applicable to any feature model, we demonstrate the proposed QBCSE scheme using canonical shape feature models in synthetic aperture radar phase history.