Projectile trajectory estimation: performance analysis of an Extended Kalman Filter and an Imperfect Invariant Extended Kalman Filter

This paper compares two nonlinear Kalman filters to estimate a projectile trajectory: an Extended Kalman Filter (EKF) and an Imperfect Right-Invariant Extended Kalman Filter (Imperfect R-IEKF). For this purpose, only an Inertial Measurement Unit (IMU), composed by an accelerometer and a gyrometer embedded in the projectile is considered. In addition, a misalignment between the IMU and the projectile is used as an observation. Both filters share the same evolution and measurement models.A nonlinear observability analysis is performed and suggests that the EKF creates a false observability contrary to the Imperfect R-IEKF. Furthermore, evaluated on 100 mortar fire simulations, the Imperfect R-IEKF is considerably more accurate than the EKF to estimate a projectile trajectory. These observations on accuracy and observability are explained by the Imperfect R-IEKF design, i.e. an EKF based on a nonlinear error and an update step based, in part, on an exponential application.