Nonparametric Likelihood-Ratio Detection of Noise-Like Signals

摘要

The detection problem is solved in an almost optimum manner for signal and noise processes observed over a finite period of time. Signal and noise must show 'local' statistical stability and have finite second and fourth order moments. The observed variable is sampled at intervals that make the samples approximately chain-dependent, thus reducing the dimensionality of the probability-density functions (PDE) used. The detector operates as an adaptive likelihood-ratio detector, where the zero hypothesis PDF is an average PDF. This average is taken over a number of direction sectors in a direction-sensitive system, which reduces the possibility of adaptation under false hypothesis. The adaptive property consists of a repeated updating of the likelihood functions directly from the samples. The price of updating is decision delay. Tests with recorded noise and signals in the frequency band 100-300 Hz have been made on a computer. Detector performance is shown as receiver-operating characteristics and as detector output as a function of time. This is done for various values of the signal-to-noise ratio, the number of samples per decision, the number of direction sectors, etc. The likelihood-ratio detector is also compared with a sampled square-law detector. The former is superior at low false-alarm probabilities, P sub fa