The tracking filter plays a key role in accurate estimation and prediction of maneuvering the vessel’s position and velocity. Different methods are used for tracking. However, the most commonly used method is the Kalman filter and its modifications. The α- β - γ filter is one of the special cases of the general solution provided by the Kalman filter. It is a third order filter that computes the smoothed estimates of position, velocity, and acceleration for the nth observation, and predicts the next position and velocity. Although found to track a maneuvering target with good accuracy than the constant velocity α - β filter, the α - β - γ filter does not perform impressively under high maneuvers, such as when the target is undergoing changing accelerations. This study aims to track a highly maneuvering target experiencing jerky motions due to changing accelerations. The α - β - γ filter is extended to include the fourth state that is, constant jerk to correct the sudden change of acceleration to improve the filter’s performance. Results obtained from simulations of the input model of the target dynamics under consideration indicate an improvement in performance of the jerky model, α - β - γ - η algorithm as compared to the constant acceleration model, α - β - γ in terms of error reduction and stability of the filter during target maneuver.