Detection of Stochastic Processes

  title={Detection of Stochastic Processes},
  author={Thomas Kailath and H. Vincent Poor},
  journal={IEEE Trans. Inf. Theory},
This paper reviews two streams of development, from the 1940's to the present, in signal detection theory: the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance. This treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous-time stochastic processes… 


This paper contains first of all conditions for absolute continuity as well as a new likelihood ratio formula for detecting a random signal whose law is unknown, and which is obscured by noise that

System Uncertainty and Statistical Detection for Jump-diffusion Models

A likelihood ratio-based approach to statistical detection for a rich class of partially observed systems where the system state is modeled by some jump-diffusion process while the observation is of additive white noise.

Error Exponents for Neyman-Pearson Detection of a Continuous-Time Gaussian Markov Process From Regular or Irregular Samples

It is shown that the minimum Type II error probability decreases exponentially in the number of samples when the False Alarm probability is fixed, and it turns out that they are related to the asymptotic behavior of the Kalman Filter in random stationary environment.

Statistical model uncertainty for state-observation models driven by diffusion process

Abstract This paper is motivated by the fact that model uncertainty is common-seen in statistics and applied probability. As a response, a likelihood ratio-based approach is presented to statistical

Application of Stochastic Process in Signal Processing

In this paper introduction about birth and death Poisson process basic result of the markovian application in queuing theory used in signal processing, signal transfer from some to passion based on

On the error exponents for detecting randomly sampled noisy diffusion processes

This paper deals with the detection of a continuous random process described by an Ornstein-Uhlenbeck (O-U) stochastic differential equation, and it is shown that the Type II error probability decreases to zero exponentially in the number of samples.

Sequence Detection: Backward and Forward in Time

This chapter reviews the classical theory of signal detection, including the early contributions of Forney and others, and continuing with more recent work on multiuser detection and turbo decoding.

Constrained Signals: A General Theory of Information Content and Detection

It is demonstrated that the general theory of signals characterized by probabilistic constraints can readily classify signals governed by different constraint distributions as long as the mean value of the constraints for the two distributions is different.

Likelihood ratio detection of signals on reverberation noise

The likelihood ratio detection method is applicable to the active sonar which is a reverberation limited system and can be successfully applied in mobile communication for the channel dynamical allocation, as well as in radar applications.



Likelihood-Ratio Detection of Stochastic Signals.

Algorithms are given for the detection of a general stochastic signal imbedded in Gaussian or nonGaussian spherically-invariant noise and Adaptive and nonadaptive algorithms are described, along with specific procedures for their implementation.

Nonparametric detection

This paper considers some of the simpler nonparametric detection schemes and compares their asymptotic relative efficiencies to those of detectors which are optimal in the Neyman-Pearson sense. In

Signal Detection in Non-Gaussian Noise

This book contains a unified treatment of a class of problems of signal detection theory which is not required to have Gaussian probability functions in its statistical description, and which allow for formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification.

Likelihood ratios for Gaussian processes

  • T. Kailath
  • Computer Science, Mathematics
    IEEE Trans. Inf. Theory
  • 1970
It is shown that nonsingular detection problems of this form can always be interpreted as problems of the apparently more special "signal-in-noise" type, where the cross-covariance function of the signal and noise must be of a special "one-sided" form.

The modeling of randomly modulated jump processes

It turns out that this martingale model is very similar to the well-known signal-in-additive-white-Gaussian-noise model, so that it can be used conveniently in solving problems of detection of signals in jump processes and estimation of signals from jump processes.

Extraction and Detection Problems and Reproducing Kernel Hilbert Spaces

Problems involving the extraction, detection and prediction of signals in the presence of noise are among the central problems of statistical communication theory. Over the past few years I have

Signal detection in fractional Gaussian noise

Several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented to facilitate the study of signal detection in additive fractional Gaussian noise. This

An RKHS approach to detection and estimation problems-II: Gaussian signal detection

The theory of reproducing kernel Hilbert spaces is used to obtain a simple but formal expression for the likelihood ratio (LR) for discriminating between two Gaussian processes with unequal

A projection method for signal detection in colored Gaussian noise

  • T. Kailath
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1967
This work presents a method of reducing the detection problem to a finite-dimensional form where many of the difficulties with the infinite-series K-L expansion do not arise and the resulting simplicity provides more direct derivations of and more physical insights into several earlier results.

Exact and approximate filtering in signal detection: An example (Corresp.)

Simulation data is presented which shows that, at least for one example, using the appropriate linear filter instead results in a very small loss of detection power even though the variance of the linear filter is considerably greater than that of the nonlinear one.