Abstract
The stability of autoregressive (AR) models is an important issue in many applications such as spectral estimation, simulation of EEG, and synthesis of speech. There are methods for AR parameter estimation that guarantee the stability of the model, that is, all roots of the characteristic polynomial of the model have moduli less than unity. However, in some situations, such as EEG simulation, the models that exhibit roots with almost unit moduli are difficult to use. In this paper we propose a method for estimating AR models that guarantees hyperstability, that is, the moduli of the roots are less than or equal to some arbitrary positive number. The method is based on an iterative minimization scheme in which the associated nonlinear constraints are linearized sequentially.
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Juntunen, M., Tervo, J. & Kaipio, J.P. Root modulus constraints in autoregressive model estimation. Circuits Systems and Signal Process 17, 709–718 (1998). https://doi.org/10.1007/BF01206571
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DOI: https://doi.org/10.1007/BF01206571