EKF-SINDy: Empowering the extended Kalman filter with sparse identification of nonlinear dynamics
arxiv(2024)
摘要
Observed data from a dynamic system can be assimilated into a predictive
model by means of Kalman filters. Nonlinear extensions of the Kalman filter,
such as the Extended Kalman Filter (EKF), are required to enable the joint
estimation of (possibly nonlinear) system dynamics and of input parameters. To
construct the evolution model used in the prediction phase of the EKF, we
propose to rely on the Sparse Identification of Nonlinear Dynamics (SINDy). The
numerical integration of a SINDy model leads to great computational savings
compared to alternate strategies based on, e.g., finite elements. Indeed, SINDy
allows for the immediate definition of the Jacobian matrices required by the
EKF to identify system dynamics and properties, a derivation that is usually
extremely involved with physical models. As a result, combining the EKF with
SINDy provides a computationally efficient, easy-to-apply approach for the
identification of nonlinear systems, capable of robust operation even outside
the range of training of SINDy. To demonstrate the potential of the approach,
we address the identification of a linear non-autonomous system consisting of a
shear building model excited by real seismograms, and the identification of a
partially observed nonlinear system. The challenge arising from applying SINDy
when the system state is not accessible has been relieved by means of
time-delay embedding. The great accuracy and the small uncertainty associated
with the state identification, where the state has been augmented to include
system properties, underscores the great potential of the proposed strategy,
paving the way for the development of predictive digital twins in different
fields.
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