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

Abstract

Abstract-In this paper we consider the problem of tracking a maneuvering aircraft. The dynamical model used is based on assumptions of nearly constant tangential velocity, curvature, and torsion, of the target trajectory. Using the Frenet-Serret frame, that is, an element of the special orthogonal group SO(3) we cast the tracking problem into a filtering on Lie groups framework. We then use an invariant extended Kalman filter to estimate the various quantities involved. The resulting filter is simple to implement, and shown to gracefully accomodate some realistic target trajectories.

Fully adaptive update rate for non‐linear trackers

“…To be able to express the covariance matrix evolution, the evolution of the linearization of this double error has to be derived. To achieve this, see the preliminary conference 13 paper [9] that presents the explicit computations in 3D. Let us call ξ χ t and ξ ζ t the linearized errors associated to η χ t and η ζ t respectively.…”

Particle observers for state estimation and adaptation in deterministic systems with random piecewise constant inputs

“…Regarding the weight update, particles are sampled using the prior and the weights are classically defined as w ( j) n = p(y n | θ ( j) n , y 1:n−1 )w ( j) n−1 , see Algorithm 1. As x(0) is known (and thus considered as a fixed parameter), given the sequence θ ( j) n of changepoint times and parameters, the state corresponds to the integration of system (11), that is x ( j) n as defined by (15). Using that x…”

“…One such instance is target tracking using one particular model of the nonlinear deterministic models with random piecewise constant inputs proposed in [7]. For a 3D target model inspired by [7], an invariant extended Kalman filter based on the work [14] was shown in [15] to yield good tracking performance, and might be used as a building block in a particle observer approach.…”

Drone Tracking Using an Innovative UKF

“…The IEKF and l-UKF algorithms can be adapted to 3D range, bearing and elevation measurements. The 3D IEKF for the target tracking problem is for example presented in [13]. In the model (1), the tangential and angular velocities (u and ω) were supposed constant.…”