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 2π-period of oscillation. The proposed method is named as Szegö 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 Szegö 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.
Highlights
Estimation is a stochastic method for computing the hidden states of a system from noisy measurements
This paper focuses on improving the estimation accuracy of the Gaussian filtering for oscillatory systems
SIMULATION AND RESULTS the proposed Szego Quadrature Kalman Filter (SQKF) is simulated for two nonlinear filtering problems with oscillatory state dynamics
Summary
Estimation is a stochastic method for computing the hidden states of a system from noisy measurements. An alternative pdf, known as importance density [14], [15], is selected for generating the particles It is a highly accurate filtering method for nonlinear and non-Gaussian systems, which is the most practical scenario. The GHF is introduced, which is possibly the most accurate among all the Gaussian filters It utilizes univariate Gauss-Hermite quadrature rule [17], [22] for approximating the intractable integrals. The GHF is further extended in [21] and [22] by replacing the product rule with computationally efficient methods of extending the univariate quadrature rule in the multivariate domain These extensions reduce the computational burden without harming the accuracy significantly. The aforementioned extensions of the Gaussian filtering, such as the Gaussian-sum filtering and iterated filtering, can be applied over the proposed SQKF as well, to enhance the estimation accuracy further
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