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

• Published in: Signal processing 2023-11, Vol.212, p.109184, Article 109184
• Main Authors: Fu, Hongpo, Cheng, Yongmei
• Format: Article
• Language: English
• Subjects: adaptive Kalman filter; inaccurate noise statistics; measurement loss; State estimation; variational Bayesian method
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2023.109184

•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. 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.