Premium
A multi‐tone central divided difference frequency tracker with adaptive process noise covariance tuning
Author(s) -
Brumana Alessandro,
Piroddi Luigi
Publication year - 2020
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3111
Subject(s) - control theory (sociology) , kernel adaptive filter , adaptive filter , kalman filter , extended kalman filter , covariance , invariant extended kalman filter , filter (signal processing) , computer science , mathematics , algorithm , covariance intersection , filter design , artificial intelligence , computer vision , statistics , control (management)
Summary The problem of real‐time frequency estimation of nonstationary multi‐harmonic signals is important in many applications. In this paper, we propose a novel multi‐frequency tracker based on a state‐space representation of the signal with Cartesian filters and the second‐order central divided difference filter (CDDF), which improves the performance of the extended Kalman filter (EKF) by using Stirling's interpolation method to approximate the mean and covariance of the state vector. A crucial element of the method is the adaptive scaling of the process noise covariance matrix appearing in the filter equations, as a function of the innovation sequence, which tunes the accuracy‐reactivity trade‐off of the filter. The proposed solution is evaluated against two approaches from the literature, namely the factorized adaptive notch filter (FANF) and the extended Kalman filter frequency tracker (EKFFT). Several experiments emphasize the estimation accuracy of the proposed method as well as the improved robustness with respect to initial errors and input signal complexity. The presented method appears to be particularly efficient with rapidly varying frequencies, thanks to the update mechanism that adjusts the filter parameters based on the amplitude of the estimation error.