TY - JOUR
T1 - How to Deal with Parameter Estimation in Continuous-Time Stochastic Systems
AU - Escobar, Jesica
AU - Gallardo-Hernandez, Ana Gabriela
AU - Gonzalez-Olvera, Marcos Angel
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/4
Y1 - 2022/4
N2 - 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.
AB - 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.
KW - Equivalent control
KW - Instrumental variables
KW - Kalman filter
KW - Least-squares method
UR - http://www.scopus.com/inward/record.url?scp=85116843647&partnerID=8YFLogxK
U2 - 10.1007/s00034-021-01862-y
DO - 10.1007/s00034-021-01862-y
M3 - Artículo
AN - SCOPUS:85116843647
SN - 0278-081X
VL - 41
SP - 2338
EP - 2357
JO - Circuits, Systems, and Signal Processing
JF - Circuits, Systems, and Signal Processing
IS - 4
ER -