Optimal detectors for multi-target environments

The matched filter is known to be the optimal detector for a single target with known impulse response in white noise. However, many radar systems operate in multi-target environments, for which the matched filter is suboptimal due to modeling mismatch of the background signal. In this paper, we study the hypothesis testing problem of detecting a target at a given range cell while modeling all targets at other range cells as a correlated background process. We consider both deterministic-unknown and random amplitude target models, and derive the corresponding optimal detectors. For the deterministic-unknown signal model, we show that special cases of the optimal detector reduce to ridge regression (a classical solution for inverse problems), sidelobe suppression (a heuristic solution for target detection in multi-target environments), or adaptive pulse compression. The detector resulting from the random amplitude signal model reduces to that of the deterministic signal model for targets modeled as occupying a single range cell. Range-Doppler extension are given. We illustrate the performance of the detector using simulated data and the civilian vehicle data dome set.