Abstract
This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise. Based on the cubature Kalman filter, we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise. The system states and the statistics of skew t noise distribution, including the shape matrix, the scale matrix, and the degree of freedom (DOF) are estimated jointly by employing variational Bayesian (VB) inference. The proposed method is validated in a target tracking example. Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.
Highlights
State estimation serves as an important role in various elds, such as control, signal processing, fault detection and diagnosis, and many more [1,2,3,4,5,6,7]
Due to its effectiveness and optimality, the Kalman lter (KF) is the state estimation method of the most widespread used for linear systems with Gaussian noise distribution [8,9,10]
A skew t cubature Kalman lter is proposed, in which the states, shape matrix, scale matrix and degree of freedom (DOF) are simultaneously estimated by using variational Bayesian (VB) approach
Summary
State estimation serves as an important role in various elds, such as control, signal processing, fault detection and diagnosis, and many more [1,2,3,4,5,6,7]. Due to its effectiveness and optimality, the Kalman lter (KF) is the state estimation method of the most widespread used for linear systems with Gaussian noise distribution [8,9,10]. A recursive state estimation method was presented with unknown Gaussian noise covariance for linear systems [20]. A skew t variational Beyasian lter was designed for measurement noise with heavy-tails and skewness in [30] and the estimation accuracy was improved by covariance matrix approximation in [31]. A new skew t cubature Kalman lter (STCKF) is proposed for nonlinear system with heavy-tailed and skewed measurement noise. The statistics of skew t distribution including the shape matrix, the scale matrix and the DOF are unknown and need to be estimated together with the system states by using VB inference
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