A general theory of multitarget extended Kalman filters
Ronald Mahler · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
The conventional extended Kalman filter (EKF) is based on Taylor's series approximation of nonlinear motion and measurement models. The EKF cannot be directly generalized to multitarget situations since the multitarget state variable X = {x1,...,xn} exhibits discontinuous jumps in target number: X = 0, X = {x1}, X = {x1, x2}, etc. However, it is possible to extend X to a continuous multitarget state X = {x1,..., xn} via the concept of a point target-cluster x = (a,x) where x is interpreted as multiple targets co-located at target-state x, the expected number of which is a. We generalize the EKF to multitarget problems. We illustrate the approach by deriving predictor and corrector equations for a single-sensor, single-target EKF that integrates the functions of detection and tracking in the presence of missed detections and false alarms.