Adaptive CFAR Performance Prediction in an Uncertain Environment

The well-known sonar equation (SE) is the classical method of predicting passive sonar performance. The SE is derived assuming both the signal wavefront and noise field directionality are known exactly. As a consequence, the SE depends only on post-detection signal-to-noise ratio (SNR). Detection performance calculations in uncertain environments with known noise field directionality has been previously addressed using Gaussian signal wavefront models and are also being developed by Nolte using Bayesian priors on environmental variables. In our work, we evaluate detection performance when both the signal wavefront and noise field are unknown. This is the so-called adaptive detection problem where, in addition to SNR, detection performance is limited by both signal wavefront uncertainty and the amount of training data available to estimate the noise covariance matrix. We use the adaptive subspace detection framework developed in (Kraut, et.al. [1]) for an M sensor array with a p dimensional signal subspace which increases with environmental uncertainty. The value of p is found from the signal wavefront covariance matrix computed over an ensemble of environmental realizations. Adaptive detection, in this framework, assumes that a set of K “signal-free” training data vectors are available to estimate the noise covariance matrix. Strictly speaking, this is not true in the passive sonar problem where the signal may be in the training data. However, the performance of optimal adaptive detectors considered here can reasonably be expected to bound the performance of the more realistic, but thus far theoretically intractable, situation.