Persistent excitation is often recognized as a sufficient condition to exponentially converge in the field of parameter estimation. But in fact, this condition is strict even impractical where each stage is required to hold. Therefore, recent attention has shifted towards achieving exponential convergence under finite excitation. This paper presents a novel estimator that combines filtering and a second-order Newton algorithm to achieve Q-superlinear convergence, which is able to maintain exponential convergence even in the presence of finite excitation. Moreover, a time-varying forgetting factor is introduced to ensure the estimator remains bounded. The proposed estimator is analyzed for convergence properties under different excitation conditions and demonstrated through numerical simulations.

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