A new Kalman filter-based recursive method for measuring and tracking time-varying spectrum of nonstationary signals

This paper proposes a new adaptive Kalman filter-based recursive spectrum estimator for measuring time-varying spectrum of nonstationary signals. The nonstationary signal is modeled as a time-varying autoregressive (TVAR) process and the time-varying parameters are described by a smoothness priors model. A new Kalman filter algorithm with variable number of measurements (KFVNM) is employed to recursively compute the TVAR coefficients and then the time-varying spectrum. The number of measurements in the Kalman filter is determined adaptively according to the state estimate derivatives. Furthermore, a fast QR decomposition algorithm is developed to reduce the arithmetic complexity of the proposed KFVNM algorithm. Simulation results show the proposed Kalman filter-based recursive spectrum estimator can achieve a better time-frequency resolution than the conventional parametric spectrum estimations. Its potential application to power quality monitoring is also illustrated.