Variational adaptive Kalman filter for unknown measurement loss and inaccurate noise statistics

Considering a common situation that the measurements are obtained from independent sensors and the accurate noise statistics are not available, we propose a novel variational adaptive Kalman filter (KF), which can selectively treat measurement loss and adaptively estimate inaccurate state and measurement noise covariance matrices. Firstly, a multiple inverse-Wishart mixture (MIWM) distribution is utilized to modeled state transition probability density function (PDF), which reduces the dependence on the pre-selected nominal state noise covariance matrix (SNCM). Then, a modified measurement model is constructed and a new measurement likelihood PDF is provided, where the measurement losses from different sensors are considered independently and the measurement noise covariance matrix (MNCM) is modeled as an inverse Gamma distribution. Finally, based on the modified state transition and measurement likelihood PDFs, a novel variational adaptive KF is derived by variational Bayesian method, and the feasibility and superiority of the filter are demonstrated by the numerical simulation.