Basic tracking using nonlinear continuous-time dynamic models [Tutorial]

Physicists generally express the motion of objects in continuous time using differential equations, whereas the majority of target tracking algorithms use discrete-time models. This paper considers the use of general, nonlinear, continuous-time motion models for use in target tracking algorithms that perform measurements at specific, discrete times. The basics of solving/simulating deterministic/stochastic differential equations is reviewed. The difference between most direct-discrete and continuous-discrete tracking algorithms is the prediction step. Consequently, a number of continuous-time state prediction techniques are presented, focusing on derivative-free techniques. Consistent with common filtering techniques, such as the cubature Kalman filter, Gaussian approximations are used for the propagated state. Three dynamic models are considered for evaluating the performance of the algorithms: a highly nonlinear spiraling motion mode, a multidimensional geometric Brownian model, which has multiplicative noise, and an integrated Ornstein-Uhlenbeck process. Track initiation is also discussed.