论文信息 - A further note on a general likelihood formula for random signals in Gaussian noise

A further note on a general likelihood formula for random signals in Gaussian noise

A general likelihood ratio formula of the author's for the detection of signals in independent white Gaussian noise is extended to allow a "one-sided" dependence in which only the future white noise is required to be independent of past signal and noise. The assumption of Gaussian additive noise is also somewhat relaxed. The proof is based on some recent martingale theorems and on the concept of the innovations process.

Thomas Kailath | T. Kailath

[1] J. Doob. Stochastic processes , 1953 .

[2] L. Shepp. Radon-Nikodym Derivatives of Gaussian Measures , 1966 .

[3] I. V. Girsanov. On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures , 1960 .

[4] H. Kunita,et al. On Square Integrable Martingales , 1967, Nagoya Mathematical Journal.

[5] M. Hitsuda. Representation of Gaussian processes equivalent to Wiener process , 1968 .

[6] P. Meyer. Probability and potentials , 1966 .

[7] Yu. V. Prokhorov. Convergence of Random Processes and Limit Theorems in Probability Theory , 1956 .

[8] Thomas Kailath,et al. A general likelihood-ratio formula for random signals in Gaussian noise , 1969, IEEE Trans. Inf. Theory.

[9] L. A. Shepp,et al. Conditions for absolute continuity between a certain pair of probability measures , 1970 .

[10] Thomas Kailath,et al. Likelihood ratios for Gaussian processes , 1970, IEEE Trans. Inf. Theory.