Analysis of the Page Test With Nuisance Parameter Estimation for Various SignalTypes

摘要

The Page test with nuisance parameter estimation is applied to the detection ofthe following signal types: (a) complex Gaussian distributed data with a shift in mean signal and unknown variance, (b) exponentially distributed data with an unknown noise power, and (c) multivariate complex Gaussian distributed data with a deterministic array signal and an unknown interference covariance matrix. For each signal type, a detector nonlinearity is developed and the Siegmund based approximations to the average sample number derived. Comparison to simulation indicates that the Siegmund based approximations are more accurate than the Wald based approximations and that there is a sensitivity to corruption of the auxiliary data by signal presence when the buffer size is inadequate at low signal to noise ratios. Operating characteristic curves for each of the signal types are generated describing the performance of the detectors as a function of threshold and SNR. The probability of detecting a finite duration signal is approximated by the Brownian motion and moment matching approximation of (Han et al.) and estimated by the Poisson mixture method of (Abraham) where it was observed that the Poisson mixture method provided the least total estimation error. Nonparametric signal onset detection is discussed within the framework of the Page test with nuisance parameter estimation.