By Topic

RKHS approach to detection and estimation problems--I: Deterministic signals in Gaussian noise

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Kailath, T. ; Stanford University, Stanford, CA, USA

First it is shown how the Karhunen-Loève approach to the detection of a deterministic signal can be given a coordinate-free and geometric interpretation in a particular Hilbert space of functions that is uniquely determined by the covariance function of the additive Gaussian noise. This Hilbert space, which is called a reproducing-kernel Hilbert space (RKHS), has many special properties that appear to make it a natural space of functions to associate with a second-order random process. A mapping between the RKHS and the linear Hilbert space of random variables generated by the random process is studied in some detail. This mapping enables one to give a geometric treatment of the detection problem. The relations to the usual integral-equation approach to this problem are also discussed. Some of the special properties of the RKHS are developed and then used to study the singularity and stability of the detection problem and also to suggest simple means of approximating the detectability of the signal. The RKHS for several multidimensional and multivariable processes is presented; by going to the RKHS of functionals rather than functions it is also shown how generalized random processes, including white noise and stationary processes whose spectra grow at infinity, are treated.

Published in:

Information Theory, IEEE Transactions on  (Volume:17 ,  Issue: 5 )