# Hidden Markov Models: Estimation and Control

@inproceedings{Elliott1994HiddenMM, title={Hidden Markov Models: Estimation and Control}, author={Robert J R Elliott and Lakhdar Aggoun and John B. Moore}, year={1994} }

Hidden Markov Model Processing.- Discrete-Time HMM Estimation.- Discrete States and Discrete Observations.- Continuous-Range Observations.- Continuous-Range States and Observations.- A General Recursive Filter.- Practical Recursive Filters.- Continuous-Time HMM Estimation.- Discrete-Range States and Observations.- Markov Chains in Brownian Motion.- Two-Dimensional HMM Estimation.- Hidden Markov Random Fields.- HMM Optimal Control.- Discrete-Time HMM Control.- Risk-Sensitive Control of HMM…

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## 1,384 Citations

### Hidden Markov model state estimation with randomly delayed observations

- Computer ScienceIEEE Trans. Signal Process.
- 1999

This paper considers state estimation for a discrete-time hidden Markov model (HMM) when the observations are delayed by a random time. The delay process is itself modeled as a finite state Markov…

### An Expectation-Maximization Algorithm for Continuous-time Hidden Markov Models

- Computer Science, Mathematics
- 2021

We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time.…

### Some results on ergodic and adaptive control of hidden Markov models

- MathematicsProceedings of the 41st IEEE Conference on Decision and Control, 2002.
- 2002

The dynamics of a discrete time, state process are assumed to depend on the current value of the state of a possibly unobserved hidden Markov model. Both the state and the hidden process are…

### Parameter estimation of Gaussian hidden Markov models when missing observations occur

- Mathematics
- 2002

The basic Gaussian Hidden Markov model is introduced and some joint probability density functions of the process are presented, some of which are shown below.

### Subspace estimation and prediction methods for hidden Markov models

- Computer Science, Mathematics
- 2009

This paper examines subspace estimation methods for HMMs whose output lies a finite set, and shows that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation, and that the m-step linear predictor computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear m- step predictor.

### Causal Recursive Parameter Estimation for Discrete-Time Hidden Bivariate Markov Chains

- MathematicsIEEE Transactions on Signal Processing
- 2015

An algorithm for causal recursive parameter estimation of a discrete-time hidden bivariate Markov chain is developed and the performance of the algorithm is demonstrated in estimating the model's parameter and its sojourn time distribution in a numerical example.

### Recursive estimation of multivariate hidden Markov model parameters

- Computer ScienceComput. Stat.
- 2019

The properties of the proposed recursive expectation–maximization (EM) algorithm were explored by a computer simulation solving test examples and demonstrate that this algorithm can be efficiently applied to solve online tasks related to HMM parameter estimation.

### Optimal Control of Hidden Markov Models With Binary Observations

- MathematicsIEEE Transactions on Automatic Control
- 2014

A nonlinear state-space representation for the estimator, analytical expressions for the control law are developed, and numerical methods for efficient computation of the optimal control are presented.

### Filtering and change point estimation for hidden Markov-modulated Poisson processes

- MathematicsAppl. Math. Lett.
- 2014

### Exact and approximate hidden Markov chain filters based on discrete observations

- Mathematics, Computer ScienceArXiv
- 2014

This paper derives exact formulas for the necessary densities in the case the state space of the HMM consists of two elements only, by relating the underlying integrated continuous-time Markov chain to the so-called asymmetric telegraph process and by using recent results on this process.