Detection and estimation of transient signals in coloured Gaussian noise

The authors present an adaptive method to detect transient signals of unknown waveform in colored Gaussian noise. The signal is modeled as the impulse response of a rational transfer function. After a prewhitening of the observed signal, the order of the rational transfer function is estimated by a method based on the covariance matrix perturbation and the coefficients by a maximum-likelihood estimator with constraint. The detection of the signal is performed by means of the generalized likelihood ratio test. The method is compared to an adaptive detection scheme using an autoregressive (AR) model of the signal and to the conventional energy detector. Theoretical detection probabilities are compared to the experimental ones obtained by Monte Carlo simulations