Joint Kalman Filter for formation moving with wiener process acceleration

Recently, a Joint Kalman Filter (JKF) for tracking targets flying in formation was proposed and implemented for a constant velocity model. In this paper we extend this work and derive a JKF for a Wiener process acceleration target model. In this target model, it is assumed that the acceleration of all formation members is almost the same in its core structure. The closed-form analytical solution for the error state covariance of the JKF is used, gaining insight into the effect of the various parameters of the filter. It is shown that the Joint Kalman Filter has a lower estimation error compared to the case when an individual filter for each formation member is implemented. An advantage of the JKF is in situations when one of the targets is not detected, yet its state can still be estimated.