Electrical and Electronic Engineering - Theses

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Author: Logothetis, Andrew × Type: PhD thesis ×

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    EM algorithms for state and parameter estimation of stochastic dynamical systems
    Logothetis, Andrew ( 1997)
    This thesis studies the use of the Expectation Maximization (EM) algorithm for state and parameter estimation of stochastic dynamical systems. Optimal maximum likelihood parameter estimates via the EM are computed for: i) Gaussian state space models, where explicit rules are given for optimally partitioning the parameter space to update some parameters using the Newton-Raphson method and the EM method (on the remaining parameters). The partitioning is optimized to ensure minimum processing time for computing the estimates, ii) Errors-in-variables models driven by additive Gaussian and finite-state Markovian disturbances, and iii) 1-bit quantized Markov modulated autoregressive process, generalizing the binary time series algorithm of [Kedem 1980] for linear time series to Markov modulated time series. While the EM is widely used as an iterative numerical method for maximum likelihood parameter estimation of partially observed stochastic models, a significant contribution here is to use the EM for optimal state estimation. In particular, the EM is used to compute maximum a posterior state sequence estimates of jump Markov linear systems. An off-line optimal state estimator is derived, which iteratively combines a Hidden Markov Model Smoother and a Kalman Smoother. Two applications are extensively studied: i) Maximum a posterior state estimates of a maneuvering target in clutter. and ii) Narrowband interference suppression in spread spectrum code division multiple access systems. This thesis also studies open-loop control strategies using information theoretic criteria. Optimal observer paths are derived for the bearings-only tracking problem. Optimal optimization techniques, such as forward and backward dynamic programming and enumeration with optimal pruning are derived. Furthermore, a number of computationally tractable suboptimal optimization techniques, such as approximate reduced complexity forward dynamic programming and one-step ahead (suboptimal) control strategies are presented.