MHE under parametric uncertainty -- Robust state estimation without informative data
CoRR(2023)
摘要
In this paper, we study state estimation for general nonlinear systems with
unknown parameters and persistent process and measurement noise. In particular,
we are interested in stability properties of the state estimate in the absence
of persistency of excitation (PE). With a simple academic example, we show that
existing moving horizon estimation (MHE) approaches as well as classical
adaptive observers can result in diverging state estimates in the absence of
PE, even if the noise is small. We propose a novel MHE formulation involving a
regularization based on a constant prior estimate of the unknown system
parameters. Only assuming the existence of a stable estimator, we prove that
the proposed MHE results in practically robustly stable state estimates even in
the absence of PE. We discuss the relation of the proposed MHE formulation to
state-of-the-art results from MHE, adaptive estimation, and functional
estimation. The properties of the proposed MHE approach are illustrated with a
numerical example of a car with unknown tire friction parameters.
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