Robust Gaussian Approximate Fixed-Interval Smoother With Outlier Detection

Abstract

We consider that existing nonlinear state estimators cannot always yield a satisfactory performance when the distribution of the measurement noise deviates from the assumed Gaussian distribution. This letter investigates the non-linear robust fixed-interval smoothing problem where the measurement vectors are partially disturbed by outliers. The proposed smoother employs a binary indicator variable modelled with a beta-Bernoulli distribution to determine whether the measurement vector is an outlier. Moreover, to address the inaccurate process noise covariance matrix, an inverse Wishart distribution was chosen as the conjugate prior of the process noise covariance matrix. Then, the variational Bayesian inference method was applied to estimate the state trajectory, inaccurate process noise covariance matrix, and a set of binary indicator variables. Traditional target tracking simulation results indicate the effectiveness and stability of the derived smoother, and the proposed smoother has demonstrated a marked improvement in estimation accuracy and robustness.