PATTERN RECOGNITION OF STOCHASTIC PROCESSES (REVISED).
Abstract
Representations for the likelihood functions of separable stochastic processes in terms of a denumerable set of functionals of the processes are developed. The objective in utilizing these representations is as an aid in signal detection, classification (waveform recognition), parameter extraction, etc. The approach to these operations is from the point of view of maximum likelihood (Bayes risk). Knowledge of the distributional properties of the functionals is sufficient to derive those of the process. It is shown that when the process has orthogonal bounded increments, the functionals are multivariate normal; the means and covariance matrix being readily calculable. Additionally, if the process has stationary (wide-sense) increments, the functionals are statistically independent. It is further shown that (a) the orthogonal-increment process can be described by a normal distribution and (b) if its increments are stationary (wide-sense), the process is distributed and behaves as a Wiener process. Examples of the application of these results to stochastic-process signal detection and waveform pattern recognition are given. Explicit expressions for the coefficients of the Wiener canonical expansion for the likelihood function of such a process are derived. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 23, 1967
- Accession Number
- AD0654199
Entities
People
- Donald B. Brick
- Joel Owen