Autoregressive frequency detection using Regularized Least Squares

Abstract

a b s t r a c tTracking 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.

Real time prediction of irregular periodic time series data

“…In spite of its simplicity, the time‐varying ARMA model is flexible enough to describe the periodic pattern of the time series data with unknown frequency cases. The frequency estimation problem based on the time‐constant ARMA model is discussed in Zhang, Ng, and Na (), B. Chen and Gel (), Stoica, Friedlander, and Soderstrom (), and Platonov, Gajo, and Szabatin ().…”

“…The frequency estimation problem based on the time-constant ARMA model is discussed in Zhang, Ng, and Na (2018), B. Chen and Gel (2010), Stoica, Friedlander, andSoderstrom (1987), andPlatonov, Gajo, andSzabatin (1992).…”