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A Low-Memory Approach For Best-State Estimation Of Hidden Markov Models With Model Error

Mihai Anitescu(anitescu***at***mcs.anl.gov)
Xiaoyan Zeng(zeng***at***mcs.anl.gov)
Emil Constantinescu(emconsta***at***mcs.anl.gov)

Abstract: We present a low-memory approach for the best-state estimate (data assimilation) of hidden Markov models where model error is considered. In particular, our findings apply for the 4D- Var framework. The novelty of our approach resides in the fact that the storage needed by our estimation framework, while including model error, is dramatically reduced from O(number of time steps) to O(1). The main insight is that we can restate the objective function of the state estimation (the likelihood function) from a function of all states to a function of the initial state only. We do so by restricting the other states by recursively enforcing the optimality conditions. This results in a regular nonlinear equation or an optimization problem for which a descent direction can be computed using only a forward sweep. In turn, the best estimate can be obtained by limited-memory quasi-Newton algorithms that need only O(1) storage with respect to the time steps. Our findings are demonstrated by numerical experiments on Burgers' equations.

Keywords: Data Assimilation, Weakly Constrained 4DVar, Hidden Markov Models, Limited Memory Methods, Quasi-Newton Methods

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Applications -- Science and Engineering (Civil and Environmental Engineering )

Category 3: Applications -- Science and Engineering (Statistics )

Citation: Preprint ANL/MCS-P1919-0711, Argonne National Laboratory, Mathematics and Computer Science Division

Download: [PDF]

Entry Submitted: 03/17/2012
Entry Accepted: 03/17/2012
Entry Last Modified: 03/17/2012

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