Stability and stationarity in target kinematic modeling

This paper analyzes a Mixed Ornstein-Uhlenbeck (MOU) process that has a number of appealing properties as a target motion model. Relevant earlier models that have been proposed include the standard nearly constant velocity motion model (unbounded long-term position and velocity), the Ornstein-Uhlenbeck process (bounded position, but no defined velocity), and the Integrated Ornstein-Uhlenbeck process (bounded velocity, but unbounded position). The Mixed Ornstein-Uhlenbeck (MOU) process exhibits drift terms in both position and velocity, and thus has a well-behaved limit for both. The initial target state can be defined in a natural way based on the steady-state characteristics of the MOU process, leading to a stationary stochastic process. Similarly, multi-target stationarity is achieved by choosing the initial target birth distribution according to the steady-state distribution on the number of targets. The MOU process can be used both in simulations and, correspondingly, in Kalman-based recursive filtering as part of multi-target tracking solutions.¹²