Kalman filter for radio astronomy dynamic imaging based on empirical covariances

Traditional Kalman filters are not immediately suitable for the estimation of state parameters with sample covariance matrices as observations. This comes from the fact that the observations must be first expressed as a linear function of sample covariance matrices. The primary objective of this work is to enable the calculation of both the mean and covariance of the observation model noise, which is here correlated with the state vector. Any signal distribution is considered, revealing the multivariate kurtosis of the signal in the measurement noise covariance matrix. The proposed method is evaluated on simulated data representative of a dynamic radio astronomy framework. The results show that our method is capable of effectively tracking moving sources in complex scenes with theoretical guaranties when the signal multivariate kurtosis is known.