Validation and comparison of coordinated turn aircraft maneuver models

Survey of maneuvering targettracking . part I: dynamic models

“…Virtually all models in the literature (e.g., [95,10,96,97,70,6,98,1,99]) presume explicitly or implicitly that (105) holds. As shown above, a necessary and sufficient condition for its validity is the orthogonality between the linear and angular velocity vectors.…”

Tracking the Frenet-Serret frame associated to a highly maneuvering target in 3D

“…The most prominent work in this direction is, to our best knowledge, the pioneering work of Antoulas and Bishop, see e.g., [7], [17]. If we assume the acceleration of the target is large with respect to the gravity vector field g, which is the case for highly maneuvering targets the NCS-CT model of [7] writes ...…”

“…Moreover, the model (7) is based on a zero torsion assumption. As a result quoting [17] "necessary condition for the model to be an accurate representation of actual trajectories is for the real trajectories to have small torsions". It is easily seen that the retained model (7) does not lend itself very well to extended Kalman filtering due to its strong nonlinearities.…”

“…where exp denote the exponential map of SE(3) (see equation (17) for the detailed formula). In other words, the update of χ t follows directly from [11], whereas the update of z t mimics the one of the conventional EKF.…”

Circular prediction algorithms-hybrid filters

“…In contrast to Berg's augmented adaptive jerk model, the prediction equation becomes non-linear, but does not require the explicit calculation of L, T, p, q, r. This algorithm can be simplified by assuming constant speed during the coordinated turn, which leads to a constant turn rate vector Ω [14,15]. Nabaa and Bishop [16] have shown that the constant speed coordinated turn is a particular subset of the general coordinated turn of Bishop and Antoulas. In general the coordinated turn models are a set of non-linear, coupled equations, which are difficult to solve.…”