Strictly positive definite correlation functions

John Dolloff; Brian Lofy; Alan Sussman; Charles Taylor

doi:10.1117/12.663967

17 May 2006 Strictly positive definite correlation functions

John Dolloff, Brian Lofy, Alan Sussman, Charles Taylor

Proceedings Volume 6235, Signal Processing, Sensor Fusion, and Target Recognition XV; 62351A (2006) https://doi.org/10.1117/12.663967
Event: Defense and Security Symposium, 2006, Orlando (Kissimmee), Florida, United States

Abstract

Sufficient conditions for strictly positive definite correlation functions are developed. These functions are associated with wide-sense stationary stochastic processes and provide practical models for various errors affecting tracking, fusion, and general estimation problems. In particular, the expected magnitude and temporal correlation of a stochastic error process are modeled such that the covariance matrix corresponding to a set of errors sampled (measured) at different times is positive definite (invertible) - a necessary condition for many applications. The covariance matrix is generated using the strictly positive definite correlation function and the sample times. As a related benefit, a large covariance matrix can be naturally compressed for storage and dissemination by a few parameters that define the specific correlation function and the sample times. Results are extended to wide-sense homogeneous multi-variate (vector-valued) random fields. Corresponding strictly positive definite correlation functions can statistically model fiducial (control point) errors including their inter-fiducial spatial correlations. If an estimator does not model correlations, its estimates are not optimal, its corresponding accuracy estimates (a posteriori error covariance) are unreliable, and it may diverge. Finally, results are extended to approximate error covariance matrices corresponding to non-homogeneous, multi-variate random fields (a generalization of non-stationary stochastic processes). Examples of strictly positive definite correlation functions and corresponding error covariance matrices are provided throughout the paper.

Citation Download Citation

John Dolloff, Brian Lofy, Alan Sussman, and Charles Taylor "Strictly positive definite correlation functions", Proc. SPIE 6235, Signal Processing, Sensor Fusion, and Target Recognition XV, 62351A (17 May 2006); https://doi.org/10.1117/12.663967

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available