Parameter Estimation for Superimposed Weighted Exponentials
Abstract
The approach of modeling measured signals as superimposed exponentials in white Gaussian noise is popular and effective. However, estimating the parameters of the assumed model is challenging, especially when the data record length is short, the signal strength is low, or the parameters are closely spaced. In this dissertation, we first review the most effective parameter estimation scheme for the superimposed exponential model: maximum likelihood. We then provide a historical review of the linear prediction approach to parameter estimation for the same model. After identifying the improvements made to linear prediction and demonstrating their weaknesses, we introduce a completely tractable and statistically sound modification to linear prediction that we call iterative generalized least squares. It is shown, that our algorithm works to minimize the exact maximum likelihood cost function for the superimposed exponential problem and is therefore, equivalent to the previously developed maximum likelihood approach. However, our algorithm is indeed linear prediction, and thus revives a methodology previously categorized as inferior to maximum likelihood. With our modification, the insight provided by linear prediction can be carried to actual applications. We demonstrate this by developing an effective algorithm for deep level transient spectroscopy analysis. The signal of deep level transient spectroscopy is not a straight forward superposition of exponentials. However, with our methodology, an estimator, based on the exact maximum likelihood cost function for the actual signal, is quickly derived. At the end of the dissertation, we verify that our estimator extends the current capabilities of deep level transient spectroscopy analysis.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1996
- Accession Number
- ADA310879
Entities
People
- Edwards A. Ingham
Organizations
- Air Force Institute of Technology