?CIF: Small: Recursive Estimation of Randomly Modulated Processes?
Many phenomena observed in science and engineering exhibit random variations over time. Internet traffic, speech signals, and biological signals, are a few such examples. Choosing a random process to model such phenomena involves a tradeoff between accuracy versus complexity. This project investigates fast computational methods for modeling random phenomena using a class of versatile random processes called randomly modulated processes. A randomly modulated process consists of two simpler random processes, one which is observable and another which modulates the observable process. By exploiting the structural properties of randomly modulated processes, the investigators are devising efficient and accurate methods to model a wide class of random phenomena. Specifically, the project develops recursive estimators to characterize Internet traffic accurately in real-time. Other important applications of the estimators can be found in speech processing, nuclear medicine, biology, genetics, and finance.
The project focuses on the intertwined problems of signal and parameter estimation of randomly modulated processes. Using a transformation of measure approach, the investigators are developing recursive estimators for such processes and investigating feasible approaches for solving the associated stochastic differential equations. The research involves in-depth investigation and comparison of the transformation of measure approach with respect to traditional likelihood-based approaches that lead invariably to batch algorithms that can only be executed offline. The project also involves the derivation of asymptotic properties of maximum likelihood estimators for randomly modulated processes. Implementations of the recursive estimators are being applied to Internet traffic traces, with the objective of leveraging the estimators for network admission control and anomaly detection.
