A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants
Journal of Multivariate Analysis
Asymptotic behavior of maximum likelihood estimates of superimposedexponential signals
IEEE Transactions on Signal Processing
Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra
IEEE Transactions on Information Theory
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Tracking of an unknown frequency embedded in noise is widely applied in a variety of applications. Unknown frequencies can be obtained by approximating generalized spectral density of a periodic process by an autoregressive (AR) model. The advantage is that an AR model has a simple structure and its parameters can be easily estimated iteratively, which is crucial for online (real-time) applications. Typically, the order of the AR approximation is chosen by information criteria. However, with an increase of a sample size, model order may change, which leads to re-estimation of all model parameters. We propose a new iterative procedure for frequency detection based on a regularization of an empirical information matrix. The suggested method enables to avoid the repeated model selection as well as parameter estimation steps and therefore optimize computational costs. The asymptotic properties of the proposed regularized AR (RAR) frequency estimates are derived and performance of RAR is evaluated by numerical examples.