Variational Bayesian based robust nonlinear filter for systems with unknown measurement loss and multi-step delay

For nonlinear state estimation of the systems with randomly occurring measurement loss and multi-step delay (MLaMD), this paper investigates a variational Bayesian (VB) based robust cubature Kalman filter (VBRCKF), which does not require prior knowledge of the probabilities or delay steps. The proposed filter is to incorporate the VB framework into the CKF algorithm. Firstly, the randomly occurring MLaMD is modeled by using Bernoulli and categorical variables, thereby formulating a modified measurement model. Subsequently, the joint prior distribution of the system state along with the unknown variables associated with MLaMD is formulated. The joint posterior distribution is then approximately calculated by VB method. The resulting VBRCKF innovatively considers randomly occurring MLaMD without prior information and carries out adaptive estimation of these unknown variables. Finally, two simulation experiments for target tracking demonstrate the effectiveness of the proposed VBRCKF.