Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

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.

Introduction to the Special Issue on Advances on Modeling and State Estimation for Industrial Processes

“…Specifically, topics across Variational Bayesian Modeling Methods for Industrial Process, Transfer Modeling for Industrial Process, Unsupervised Modeling for Industrial Process, First Principle Modeling for Industrial Process, Non-parametric Bayesian Modeling for Industrial Process, Distributed Multi-Agent Modeling Algorithms and Its Industrial Applications, Robust Modeling Methods for Industrial Process, Supervised Modeling and Its Industrial Applications, Filter-Aided Methods for Industrial Processes, Nonlinear Modeling Methods, and Its Industrial Applications are included. Specifically, "Enhancing the Effectiveness of Trimethylchlorosilane Purification Process Monitoring with Variational Autoencoder" by Wang et al [1], addresses a critically important question regarding the process monitoring of Trimethylchlorosilane Purification Process and proposes a new algorithm based on Variational AutoEncoders (VAE) for the high-dimensional industrial database; "Improved High Order Model-Free Adaptive Iterative Learning Control with Disturbance Compensation and Enhanced Convergence" by Wang et al [2], proposes to employ the compact format dynamic linearization method to improve high-order model-free adaptive iterative control strategy; "State Estimation Moving Window Gradient Iterative Algorithm for Bilinear Systems Using the Continuous Mixed p-norm Technique" by Liu et al [3], develops a novel gradient iterative algorithm by means of the continuous mixed p-norm cost function with the purpose of estimating the parameters of the bilinear systems; "Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference" by Xu et al [4], addresses the state estimation problems for nonlinear systems with unknown statistics of measurement noise by means of the cubature Kalman filter and the skew t distribution; "A Novel Bidirectional Interaction Model and Electric Energy Measuring Scheme of EVs for V2G with Distorted Power Loads" by Cui et al [5], proposes a novel bidirectional interaction model based on modulation theory with nonlinear loads and a novel electric energy measuring scheme of EVs for V2G; "Pattern-Moving-Based Parameter Identification of Output Error Models with Multi-Threshold Quantized Observations" by Li et al [6], addresses a modified auxiliary model stochastic gradient recursive parameter identification algorithm (M-AM-SGRPIA) for a class of single input single output (SISO) linear output error models with multi-threshold quantized observations; "Range-Only UWB SLAM for Indoor Robot Localization Employing Multi-Interval EFIR Rauch-Tung-Striebel Smoother" by Gao et al [7], proposes a multiinterval extended finite impulse response (EFIR)-based Rauch-Tung-Striebel (R-T-S) smoother for the range-only ultra-wideband (UWB) simultaneous localization and mapping (SLAM) for robot localization; "Improved adaptive iterated extended Kalman filter for GNSS/INS/UWB-integrated fixed-point positioning" by Wu et al [8], proposes an adaptive iterated extended Kalman filter for fixed point positioning, which integrates global navigation satellite system, inertial navigation system, ultra wide band; "Change Point Detection for Process Data Analytics Applied to a Multiphase Flow Facility" by Gedda et al [9], utilizes regularisation-based cost functions to handle ill-posed problems of noisy data with aim of improving the performance of process data analyti...…”