An extension to the Frenet-Serret and Bishop invariant extended Kalman filters for tracking accelerating targets

This paper presents an extension to the original Frenet-Serret and Bishop frame target models used in the invariant extended Kalman filter (IEKF) to account for tangential accelerations for highly-manoeuvrable targets. State error propagation matrices are derived for both IEKFs and used to build the accelerating Frenet-Serret (FSa-LIEKF) and Bishop (Ba-LIEKF) algorithms. The filters are compared to the original Frenet-Serret and Bishop algorithms in a tracking scenario featuring a target performing a series of complex manoeuvres. The accelerating forms of the LIEKF are shown to improve velocity estimation during non-constant velocity trajectory segments at the expense of increased noise during simpler manoeuvres.