Szego quadrature kalman filter for oscillatory systems

Abstract

Filtering problems with oscillatory system dynamics commonly appear in real-life. However, the existing Gaussian filters, like the unscented Kalman filter (UKF), cubature Kalman filter CKF, Gauss-Hermite filter (GHF) and cubature quadrature Kalman filter (CQKF), are accurate for the nonlinear systems with a particular order of polynomials only. This manuscript introduces a new Gaussian filter, which is accurate for oscillatory systems with 2-period of oscillation. The proposed method is named as Szego Quadrature Kalman Filter (SQKF). The SQKF transforms the intractable integrals that appear during the filtering over a unit circle. The transformed integral is approximated using the univariate Szego quadrature rule. The univariate quadrature rule is extended in a multivariate domain using the product rule. Simulation results reveal an improved estimation accuracy for the SQKF in an oscillatory environment. The computational burden of the SQKF is similar to the GHF and higher than the UKF, CKF and CQKF. © 2020 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.