Automatic target recognition (ATR) performance models are needed for online adaptation and for effective use (e.g., in fusion) of ATR products. We present empirical models focused on synthetic aperture radar (SAR) ATR algorithms. These models are not ATR algorithms in themselves; rather they are models of ATRs developed with the intention of capturing the behavior, at least on a statistical basis, of a reference ATR algorithm. The model covariates (or inputs) might include the ATR operating conditions (sensor, target, and environment), ATR training parameters, etc. The model might produce performance metrics (Pid, Pd, Pfa, etc.) or individual ATR decisions. "Scores" are an intermediate product of many ATRs, which then go through a relatively simple decision rule. Our model has a parallel structure, first modeling the score production and then mapping scores to model outputs. From a regression perspective, it is impossible to predict individual ATR outcomes for all possible values of this covariate space since samples are only available for small subsets of the total space. Given this limitation, and absent a purely theoretical model meaningfully matched to the true complexity of this problem, our approach is to examine the empirical behavior of scores across various operating conditions, and identify trends and characteristics of the scores that are apparently predictable. Many of the scores available for training are in so-called standard operating conditions (SOC), and a far smaller number are in so-called extended operating conditions (EOCs). The influence of the EOCs on scores and ATR decisions are examined in detail.

We consider the joint inverse problems of sensor data registration and automatic target recognition. Singleplatform, multi-sensor registration is posed as a model-based, data fusion problem using Bayesian and maximum likelihood frameworks. The sensor model parameters typically consist of platform pose parameters, sensor pointing angles, and internal calibration factors, and these are used to define a transformation that maps raw data recorded in the sensor frame to a ground-referenced, world coordinate system. The fusion estimation problem is one joint inversion since the sensor model parameters common to multiple sensors are simultaneously estimated (along with sensor-specific model parameters). For the ATR problem we pose the joint optimization problem over these sensor model parameters (constrained by the global scene) and target model parameters (e.g., for selected target chips). In addition, we pose a cooperative inversion approach that captures uncertainty from the system model estimation process for use in a refined ATR inversion. The latter consists of a search over target model parameters and a constrained system model parameter space with realization samples consistent with the estimated system model covariance. Estimation robustness is achieved through use of a hybrid global/local search method (to avoid final convergence to local minima), robust kernels that down-weight data residual outliers (generated from test and reference image feature correspondences), and the use of multi-sensor data to increase the number and diversity of data constraints. In summary, we have developed a model-based fusion approach which draws on well-developed methods in photogrammetry, computer vision and automatic target recognition for enhanced registration and recognition performance.