A generalized acceleration model for Kalman filter trackers

Kalman filter trackers used for radar tracking typically model target accelerations as plant noises that are assumed to last for the entire sample interval. That assumption is so ubiquitous that it is rarely stated explicitly. In this paper we present a generalized model in which accelerations endure less than the sample interval, and derive a new formula for plant noise covariance that is a function of the interval length and the acceleration's endurance and start time. We explore the limiting behavior of this formula as acceleration endurance vanishes, and also show that position and velocity gains can be traded off by simply moving the acceleration earlier or later in the sample interval.