Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
An introduction to signal detection and estimation (2nd ed.)
An introduction to signal detection and estimation (2nd ed.)
Distributed Detection and Data Fusion
Distributed Detection and Data Fusion
Cfar: The Principles of Automatic Radar Detection in Clutter
Cfar: The Principles of Automatic Radar Detection in Clutter
Detection of stochastic processes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Editorial: Some Recent Trends in Applied Stochastic Modeling and Multidimensional Data Analysis
Computational Statistics & Data Analysis
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In many applications, observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. When the observations are independent and the probabilities of presence of the signals are upper-bounded by some value in [0,1), a theoretical result is established for the noise standard deviation. The latter is the only positive real number satisfying a specific convergence criterion when the number of observations and the minimum amplitude of the signals tend to infinity. This convergence involves neither the probability distributions nor the probabilities of presence of the signals. An estimate of the noise standard deviation is derived from this theoretical result. A binary hypothesis test based upon this estimate is also proposed. This test performs the detection of signals whose norms are lower-bounded by some known real value and whose probabilities of presence are less than or equal to one half. Neither the estimate nor the test requires prior knowledge of the probability distributions of the signals. Experimental results are given for the case of practical importance where the signals are independent two-dimensional random vectors modelling modulated sinusoidal carriers. These experimental results suggest that the asymptotic conditions of the limit theorem are not so constraining and can certainly be significantly relaxed in practice. Typical applications concern radar, sonar, speech processing but also proximity sensing and Electronic (Warfare) Support Measures.