Abstract
Cubature Kalman filter (CKF) is widely used for non-linear state estimation under Gaussian noise. However, the estimation performance may degrade greatly in presence of heavy-tailed measurement noise. Recently, maximum correntropy square-root cubature Kalman filter (MCSCKF) has been proposed to enhance the robustness against measurement outliers. As is generally known, the square-root algorithms have the benefit of low computational complexity and guaranteed positive semi-definiteness of the state covariances. Therefore, MCSCKF not only possesses the advantages of square-root cubature Kalman filter (SCKF), but also is robust against the heavy-tailed measurement noise. Nevertheless, MCSCKF is prone to the numerical problems. In this paper, we propose a new maximum correntropy square-root cubature Kalman filter (NMCSCKF) based on a cost function which is obtained by a combination of weighted least squares (WLS) to handle the Gaussian process noise and maximum correntropy criterion (MCC) to handle the heavy-tailed measurement noise. Compared to MCSCKF, the proposed method is more time-efficient and most importantly, it avoids the numerical problem. A univariate non-stationary growth model and a multi-rate vision/IMU integrated attitude measurement model are used to demonstrate the superior performance of the proposed method.
Highlights
Measuring the attitude of moving objects is important in many fields such as aerospace and industry manufacturing
By using Variational Bayesian (VB) method to approximate the posterior state at each time step, VB-based Kalman filters (VBFs) can deal with state estimation problem under non-Gaussian noise effectively [9]–[11]
Inspired by [24]–[26], we propose a new square-root maximum correntropy criterion (MCC)-based Cubature Kalman filter (CKF), denoted as new maximum correntropy square-root cubature Kalman filter (NMCSCKF)
Summary
Measuring the attitude of moving objects is important in many fields such as aerospace and industry manufacturing. By using VB method to approximate the posterior state at each time step, VB-based Kalman filters (VBFs) can deal with state estimation problem under non-Gaussian noise effectively [9]–[11]. Based on the form of MCKF and its non-linear extension, maximum correntropy square-root cubature Kalman filter (MCSCKF) was newly proposed in [20]. Maximum correntropy criterion Kalman filter (MCCKF) and its square-root form were developed in [24], [25] to overcome the numerical problem. They are only applicable to linear systems. SQUARE-ROOT CUBATURE KALMAN FILTER Considering a non-linear dynamic system with state and measurement equations expressed as follows: xk = fk−1(xk−1) + wk−1.
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