Root tracking using time-varying autoregressive moving average models and sigma-point Kalman filters

Abstract

Root tracking is a powerful technique that provides insight into the mechanisms of various time-varying processes. The poles and the zeros of a signal-generating system determine the spectral characteristics of the signal under consideration. In this work, time-frequency analysis is achieved by tracking the roots of time-varying processes using autoregressive moving average (ARMA) models in cascade form. A cascade ARMA model is essentially a highorder infinite impulse response (IIR) filter decomposed into a series of first-and second-order sections. Each section is characterized by real or conjugate pole/zero pairs. This filter topology allows individual root tracking as well as immediate stability monitoring and correction. Also, it does not suffer from high round-off error sensitivity, as is the case with the filter coefficients of the direct-form ARMA structure. Instead of using conventional gradient-based recursive methods, we investigate the performance of derivative-free sigma-point Kalman filters for root trajectory tracking over time. Based on simulations, the sigma-point estimators provide more accurate estimates, especially in the case of tightly clustered poles and zeros. The proposed framework is applied to real data, and more specifically, it is used to examine the time-frequency characteristics of raw ultrasonic signals from medical ultrasound images.

Using linear parameter varying autoregressive models to measure cross frequency couplings in EEG signals

“…14 and x L was defined as the scheduling variable. The main motivation behind this procedure was the use of a persistently exciting signal for AR fitting, since AR modeling provides more robust and stable estimates on a broad spectral structure (Hall et al, 1983;Kostoglou and Lunglmayr, 2020). After model estimation, the conditional power spectral density of the model, which essentially describes the power changes of y in different frequencies with respect to the scheduling variable, was used in conjunction with the Kullback-Leibler divergence metric and the low frequency phase to quantify the CFC (similarly as in the MI method).…”

“…Apart from controlling model complexity, regularization ensures stability [i.e., poles inside the unit circle (Ljung, 1998)]. Narrowband signals are known to induce temporal instabilities on the AR models, because the roots of the signal generating system are located very close to the unit circle (Hall et al, 1983;Kostoglou and Lunglmayr, 2020). By applying regularization, the chances of obtaining unstable estimates are low.…”

Estimation of Farmgate Rice Price Using Temporal Causal Modeling and Kalman Filtering

“…One such algorithm is the Kalman filter. Kalman filtration has found recent applications in time-varying brain networks (7) , root tracking (8) , chaotic oscillators (9) , rice price estimation (10) , ultrasonic signals (11) , biological systems (12) , rice production (13) , coffee price (14) and among many others. Results of the studies show that Kalman filter-embedded models provide superior estimates than the original model.…”