An Approach to Time Series Smoothing and Forecasting Using the Em Algorithm

Shumway, Robert H.; Stoffer, David S.

doi:10.1111/j.1467-9892.1982.tb00349.x

Cited by 1,251 publications

(972 citation statements)

References 15 publications

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“…As x t is unobservable in our case, it is replaced by the "complete-data" likelihood Ψ = E [log L(θ|y t , x t )] which entire expression can be found in [31,11].…”

Section: The Likelihood Functionmentioning

confidence: 99%

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stebler¹,

Guerrier²,

Skaloud³

et al. 2011

Meas. Sci. Technol.

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Abstract. Stochastic modeling is a challenging task for low-cost sensors which errors can have complex spectral structures. This makes the tuning process of the INS/GNSS Kalman filter often sensitive and difficult. For example, first-order Gauss-Markov processes are very often used in inertial sensor models. But the estimation of their parameters is a non-trivial task if the error structure is mixed with other types of noises. Such estimation is often attempted by computing and analyzing Allan variance plots. This contribution demonstrates solving situations when the estimation of error parameters by graphical interpretation is rather difficult. The novel strategy performs direct estimation of these parameters by means of the Expectation-Maximization (EM) algorithm. The algorithm results are first analyzed with a critical and practical point of view using simulations with typically encountered error signals. These simulations show that the EM algorithm seems to perform better than the Allan variance and offers a procedure to estimate first-order Gauss-Markov processes mixed with other types of noises. At the same time, the conducted tests revealed limits of this approach that are related to the convergence and stability issues. Suggestions are given to circumvent or mitigate these problems when complexity of error structure is "reasonable". This work also highlights the fact that the suggested approach via EM algorithm and the Allan variance may not be able to estimate reasonably well parameters of complex error models, and shows the need for new estimation procedures to be developed in this context. Finally, an empirical scenario is presented to support the former findings. There, the positive effect of using the more sophisticated EM-based error modeling on a filtered trajectory is highlighted.

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“…As x t is unobservable in our case, it is replaced by the "complete-data" likelihood Ψ = E [log L(θ|y t , x t )] which entire expression can be found in [31,11].…”

Section: The Likelihood Functionmentioning

confidence: 99%

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stebler¹,

Guerrier²,

Skaloud³

et al. 2011

Meas. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…It is a convenient idea to examine several different sets of starting values, since the EM algorithm may reach different kinds of stationary values corresponding to local rather than global maxima. For more details of the EM techniques, see [18], [19].…”

Section: System Parameter Identificationmentioning

confidence: 99%

A Robust Anomaly Detection Technique Using Combined Statistical Methods

Ndong

Salamatian

2011

2011 Ninth Annual Communication Networks and Services Research Conference

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“…We used the EM algorithm (Dempster et al 1997;Smith and Brown 2003;Smith et al 2004Smith et al , 2005Shumway and Stoffer 1982), to estimate simultaneously all of the model parameters, including the initial condition x 0 . We computed the reaction time and the learning curves, and their associated 95% confidence intervals from (A.12) and (A.13), respectively, in the appendix.…”

Section: Mixed Filter Analysis Of An Actual Learning Experimentsmentioning

confidence: 99%

A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

et al. 2008

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Continuous (reaction times) and binary (correct/incorrect responses) measures of performance are routinely recorded to track the dynamics of a subject's cognitive state during a learning experiment. Current analyses of experimental data from learning studies do not consider the two performance measures together and do not use the concept of the cognitive state formally to design statistical methods. We develop a mixed filter algorithm to estimate the cognitive state modeled as a linear stochastic dynamical system from simultaneously recorded continuous and binary measures of performance. The mixed filter algorithm has the Kalman filter and the more recently developed recursive filtering algorithm for binary processes as special cases. In the analysis of a simulated learning experiment the mixed filter algorithm provided a more accurate and precise estimate of the cognitive state process than either the Kalman or binary filter alone. In the analysis of an actual learning experiment in which a monkey's performance was tracked by its series of reaction times, and correct and incorrect responses, the mixed filter gave a more complete description of the learning NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript process than either the Kalman or binary filter. These results establish the feasibility of estimating cognitive state from simultaneously recorded continuous and binary performance measures and suggest a way to make practical use of concepts from learning theory in the design of statistical methods for the analysis of data from learning experiments.

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An Approach to Time Series Smoothing and Forecasting Using the Em Algorithm

Cited by 1,251 publications

References 15 publications

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

A Robust Anomaly Detection Technique Using Combined Statistical Methods

A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

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