Nonlinear Kalman Filters Comparison for GARCH Clutter Parameter Estimation

J.P. PASCUAL; C.H. MURAVCHIK; N. VON ELLENRIEDER; J.A. ARETA

IET CONTROL THEORY AND APPLICATIONS

INST ENGINEERING TECHNOLOGY-IET

Año: 2019 vol. 13 p. 603 - 613

1751-8644

Abstract: In this work we analize the estimation of the GARCH process conditional variance based on three nonlinear filtering approaches: extended (EKF), unscented (UKF) and cubature (CKF) Kalman filters.We present a statemodel for a GARCH process and derive an EKF including second order nonlinear terms for simultaneous estimation of state and parameters. Using synthetic data we evaluate the consistency and the correlation of the innovations for the three filters, by means of numerical simulations. We also study the performance of smoothed versions of the nonlinear Kalman filters using real clutter data in comparison with a conventional quasi-maximum likelihood estimation method for the GARCH process coefficients. We show that with all methods the process coefficients estimates are of the same order and the resulting conditional variances are commensurable. However, the nonlinear Kalman filters greatly reduce the computational load. These kind of filters could be used for the radar detector based on a GARCH clutter model that uses an adaptive threshold that demands the conditional variance at each decision instant.