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

•The MIWM distribution is utilized to model the SNCM. The distribution is suitable for describing the state noise with rough prior information via learning adaptively the mixing probability vector, which can achieve direct estimation of the state noise and reduce the dependence on the pre-selected nominal SNCM.•In the modified measurement model, to selectively treat the measurement loss for different sensor measurements, a diagonal matrix, whose diagonal elements are Bernoulli random variables, is introduced. By assigning an indicator to each sensor measurement, the model can describe the situation where different sensor measurements loss are random and independent, which can enhance the utilization of measurement information.•For the sake of derivation, all distributions are converted into exponential family form, the hierarchical Gaussian model about the state transition and measurement likelihood PDFs is built. A robust filter is deduced by means of the VB technology, in which the state vector, unknown loss probability, inaccurate SNCM and MNCM are jointly estimated.