SVD Square-root Iterated Extended Kalman Filter for Modeling of Epileptic Seizure Count Time Series with External Inputs

Moontaha, Sidratul; Galka, Andreas; Siniatchkin, Michael; Scharlach, Sascha; Spiczak, Sarah von; Stephani, Ulrich; May, Theodor W.; Meurer, Thomas

doi:10.1109/embc.2019.8857159

Cited by 5 publications

(8 citation statements)

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“…The disadvantage of this choice for the observation function is the fact that it diverges exponentially for large positive arguments. In previous work, we have occasionally encountered numerical breakdown of Kalman filtering algorithms due to the resulting extremely large values [25,26]; details will be provided below in Section 3.1. For this reason, we propose a different nonlinear observation function, to be called the "affinely distorted hyperbolic" function, as given in Equation (6); while for negative arguments it behaves like the exponential function, for positive arguments it converges to the linear function, rising with a slope of C, see Figure 1.…”

Section: Independent Components Linear State Space (Ic-lss) Modelsmentioning

confidence: 99%

“…Square-root variants of the Kalman filter that employ SVD were proposed in 1992 by Wang et al [13], and in 2017 by Kulikova and Tsyganova [32]. In an earlier paper, we proposed a square-root variant of the IEKF that employs SVD [26], based on the algorithm of Kulikova and Tsyganova.…”

Section: Singular Value Decomposition Iterated Extended Kalman Filter...mentioning

confidence: 99%

“…Therefore, the primary objective of this contribution is to explore and develop state space modeling algorithms tailored explicitly for event count time series, with a particular focus on the modeling of seizure count time series, as an illustrative example. To the best of our knowledge, apart from our previous work [24][25][26], this approach is novel on its own. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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State Space Modeling of Event Count Time Series

Moontaha,

Arnrich,

Galka

2023

Entropy

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This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definiteness of covariance matrices is preserved by a square-root filtering approach, based on singular value decomposition. Non-negativity of the count data is ensured, either by an exponential observation function, or by a newly introduced “affinely distorted hyperbolic” observation function. The resulting algorithm is applied to time series of the daily number of seizures of drug-resistant epilepsy patients. This number may depend on dosages of simultaneously administered anti-epileptic drugs, their superposition effects, delay effects, and unknown factors, making the objective analysis of seizure counts time series arduous. For the purpose of validation, a simulation study is performed. The results of the time series analysis by state space modeling, using the dosages of the anti-epileptic drugs as external control inputs, provide a decision on the effect of the drugs in a particular patient, with respect to reducing or increasing the number of seizures.

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Section: Independent Components Linear State Space (Ic-lss) Modelsmentioning

confidence: 99%

Section: Singular Value Decomposition Iterated Extended Kalman Filter...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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State Space Modeling of Event Count Time Series

Moontaha,

Arnrich,

Galka

2023

Entropy

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“…For example, it was used to solve the problem of identifying parameters for linear discrete-time stochastic systems [18], as well as the problems of Kalman filtering for inertial measurement unit readings [19], research of MIMU/GPS integrated navigation [20], adaptive KF filtering for some engineering applications [21], and an indoor positioning and tracking based on angle-of-arrival using a dual-channel array antenna [22]. It was also used to determine attitude and angle rate of gyroless spacecraft only using a star sensor [23], estimate GARCH-in-Mean(1,1) models [10], model epileptic seizures count time series with external inputs [24], and identify parameters of convection-diffusion transport models [25].…”

Section: Introductionmentioning

confidence: 99%

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

Tsyganov,

Tsyganova

2024

Mathematics

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This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known.

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“…Motivated by the advanced functionality of any SVDbased filter, the goal is to derive the first SVD-based CKF algorithms. By now, the existing SVD-based estimators are restricted by linear dynamic systems, only [26,30,45]. Here, we propose two nonlinear estimators: (i) the filter based on the traditionally used Euler-Maruyama discretization scheme of order 0.5; (ii) the estimator based on advanced Itô-Taylor expansion of order 1.5 for discretizing the underlying stochastic differential equations (SDEs).…”

Section: Introductionmentioning

confidence: 99%