A Unified Approach to Detection, Estimation, and System Identification.
TEXAS UNIV AUSTIN ELECTRONICS RESEARCH CENTER
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A unified approach is presented for the problem of simultaneous detection of random signals in additive white Gaussian noise, estimation of the signals and identification of the systems that generate the signals. The approach is based on the state-variable representation for random processes and makes use of the Markovian nature of the state vectors. Optimal solutions are derived for the cases where both the dynamical system for the signal state and the observation data are continuous, and both the system and the observation data are discrete. Optimal solutions are presented in the form of optimal nonlinear filtering for the sufficient statistic for Bayes decision, the signal state-vector and the parameter vector that characterize the system. This problem is treated for both single shot and multishot observations of various signal sequences. In addition, the optimal state vector estimation for the linear systems where the initial state vector is non-Gaussian is presented. Author Modified Abstract
- Statistics and Probability