SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation

Kulikova, Maria V.; Tsyganova, Julia V.; Kulikov, G. Yu.

doi:10.1016/j.cam.2019.112487

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…Additionally, some numerically robust SVD-based Kalman filter implementations were explored in [9]. For some extensions of classical state-space models, i.e., linear time-invariant multipleinput, multiple-output systems, and linear pairwise Markov models with the related pairwise KF, the SVD-based state, and parameter estimation approach were proposed in [10].…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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Section: Introductionmentioning

confidence: 99%

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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“…Therefore, SVD factorization-based modifications of the Kalman filter (KF) have the same improved numerical robustness to machine roundoff errors as all known square-root modifications [1,6]. In addition, as mentioned in [7], SVD filters have additional advantages such as:…”

Section: Introductionmentioning

confidence: 99%

SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization

Tsyganov,

Tsyganova

2023

Mathematics

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The paper addresses a parameter identification problem for discrete-time stochastic systems models with multiplicative and additive noises. Stochastic systems with additive and multiplicative noises are considered when solving many practical problems related to the processing of measurements information. The purpose of this work is to develop a numerically stable gradient-free instrumental method for solving the parameter identification problems for a class of mathematical models described by discrete-time linear stochastic systems with multiplicative and additive noises on the basis of metaheuristic optimization and singular value decomposition. We construct an identification criterion in the form of the negative log-likelihood function based on the values calculated by the newly proposed SVD-based Kalman-type filtering algorithm, taking into account the multiplicative noises in the equations of the state and measurements. Metaheuristic optimization algorithms such as the GA (genetic algorithm) and SA (simulated annealing) are used to minimize the identification criterion. Numerical experiments confirm the validity of the proposed method and its numerical stability compared with the usage of the conventional Kalman-type filtering algorithm.

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Reliability and maintenance modeling for a production system by means of point process observations

Ahmadi

2022

Ann Oper Res

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SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation

Cited by 6 publications

References 36 publications

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

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

SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization

Reliability and maintenance modeling for a production system by means of point process observations

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