Robust Detection of Fading Narrow-band Signals in Non-gaussian Noise

Continued With uncertainty taken directly on the noise samples, we develop an estimation-detection theoretic approach: the detection statistic preserves the structure of the quadrature matched filter, but in place of the linear sample mean, a minimax robust estimator of the random amplitude is substituted. This test is shown to be asymptotically maximin optimal (in the sense of Huber) for a wide family of decision rules and for several common target signal models. In addition, the maximin bound on the desired detection probability is sufficiently large to be in the range of practical interest. This test is then extended to handle the important case of unknown power level. When noise reference samples are available, the extended test utilizes an adaptive threshold, which serves as an estimator of the variance of the amplitude estimator under the noise-only situation. This version is shown to be maximin robust in the class of "Sliding-window" tests. Its implementation in the nominally Gaussian case is relatively simple, as it requires only o-trimmed estimators. When detection is to be performed with the signal-plus-noise observations only, scale invariance is achieved by coupling the "location" estimators with a robust scale estimator. Here, only qualitative robustness is achieved. However, within various parametrized mixture families, the false-alarm (detection) probability can be bounded from above (below). Finally, Monte Carlo simulation results show that the asymptotic analysis accurately predicts the small sample performance, down to n = 16 samples. Moreover, the proposed tests substantially outperform the corresponding robust tests derived from the traditional weak signal assumption. Robust Detection of Fading Narrow-Band Signals in Non-Gaussian Noise M. Weiss and S.C. Schwartz Department of Electrical Engineering and Computer Science Princeton University Princeton, NJ 08544 A B S T R A C T In this report, we study procedures for robust detection of slowly fading narrowband signals in nearly Gaussian noise, a common model for radar/sonar systems. For the classical quadrature matched filter test, we introduce an uncertainty about the envelope statistic and develop a robust test for this one-sample situation. It is demonstrated that this test is capable of protecting only against relatively weak contaminations. With uncertainty taken directly on the noise samples, we develop an estimationdetection theoretic approach: the detection statistic preserves the structure of the quadrature matched filter, but in place of the linear sample mean, a minimax robust estimator of the random amplitude is substituted. This test is shown to be asymptotically maximin optimal (in the sense of Huber) for a wide family of decision rules and for several common target signal models. In addition, the maximin bound on the desired detection probability is sufficiently large to be in the range of practical interest. This test is then extended to handle the important case of unknown power level. When noise reference samples are available, the extended test utilizes an adaptive threshold, which serves as an estimator of the variance of the amplitude estimator under the noise-only situation. This version is shown to be maximin robust in the class of "Sliding-window" tests. Its implementation in the nominally Gaussian case is relatively simple, as it requires only a-trimmed estimators. When detection is to be performed with the signal-plusnoise observations only, scale invariance is achieved by coupling the