A Higher-Order Extended Cubature Kalman Filter Method Using the Statistical Characteristics of the Rounding Error of the System Model

Abstract

The cubature Kalman filter (CKF) cannot accurately estimate the nonlinear model, and these errors will have an impact on the accuracy. In order to improve the filtering performance of the CKF, this paper proposes a new CKF method to improve the estimation accuracy by using the statistical characteristics of rounding error, establishes a higher-order extended cubature Kalman filter (RHCKF) for joint estimation of sigma sampling points and random variables of rounding error, and gives a solution method considering the rounding error of multi-level approximation of the original function in the undermeasured dimension. Finally, numerical simulations show that the RHCKF has a better estimation effect than the CKF, and that the filtering accuracy is improved by using the information of the higher-order rounding error, which also proves the effectiveness of the method.

Combined Cubature Kalman and Smooth Variable Structure Filtering Based on Multi-Kernel Maximum Correntropy Criterion for the Fully Submerged Hydrofoil Craft

“…The CKF is derived based on the third-order spherical-radial rule to compute the Gaussian weighted integrals. The cubature rule provides an approximation for m-dimensional integrals with Gaussian weights as detailed below [10]:…”

“…However, the artificial selection of parameters may impact the filtering performance. Recently, the most numerically stable and accurate cubature Kalman filter (CKF) has been introduced [10]. The CKF approximates multi-dimensional integrals in Bayesian filtering under a Gaussian assumption, offering advantages such as rigorous theoretical derivation, third-order filtering accuracy, and reliable stability [11,12].…”