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How to Deal with Parameter Estimation in Continuous-Time Stochastic Systems

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Abstract

In this paper, we present some options to deal with the problem of parameter estimation in continuous-time stochastic systems under white, and coloured noise perturbations using classical methods. Least-squares method (LSM) is one of the most widely used estimation methods, in continuous and discrete time systems, but it presents a bias problem. The instrumental variable method (IV), even though is considered the best option when a noise is present in the system dynamics, cannot completely minimize its effect in continuous time. Here, we propose to combine these algorithms with two auxiliary techniques: the Kalman filter and the equivalent control. These techniques working in parallel with the LSM and IV estimation algorithm will reduce the bias, the noise effect in the estimated parameters, and are very easy to implement. The effectiveness of the proposed methods is illustrated in a numerical example.

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Acknowledgements

Marcos A. González-Olvera acknowledges UACM, Project PI-CCyT-2021-12.

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Authors and Affiliations

  1. Esime Zacatenco-ICE, Instituto Politécnico Nacional, Av. Luis Enrique Erro, Unidad Adolfo Lopez Mateos S/N, 07738, Mexico, Mexico City, Mexico

    Jesica Escobar

  2. Unidad de Investigacion Medica en Enfermedades Metabolicas, Instituto Mexicano del Seguro Social, Cuauhtemoc 330, 03400, Mexico, Mexico City, Mexico

    Ana Gabriela Gallardo-Hernandez

  3. Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, Prol. San Isidro 151, 09790, Mexico, Mexico City, Mexico

    Marcos Angel Gonzalez-Olvera

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  1. Jesica Escobar
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  2. Ana Gabriela Gallardo-Hernandez
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  3. Marcos Angel Gonzalez-Olvera
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Correspondence to Ana Gabriela Gallardo-Hernandez.

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Escobar, J., Gallardo-Hernandez, A.G. & Gonzalez-Olvera, M.A. How to Deal with Parameter Estimation in Continuous-Time Stochastic Systems. Circuits Syst Signal Process 41, 2338–2357 (2022). https://doi.org/10.1007/s00034-021-01862-y

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