An innovative nonlinear filter for radar kinematic estimation of maneuvering targets in 2D

Abstract

In this paper we consider the problem of tracking a target in a 2D space whose model is based on a constant velocity assumption (up to a process noise) in the Frenet-Serret frame (or intrinsic coordinates). This model is particularly suited to straight lines and coordinated turn motions. Then, we adapt the Invariant Extended Kalman Filter (I-EKF), as in [1], a novel variant of the EKF on Lie groups, to suit this dynamical model. Numerical experiments inspired by real fighter trajectories confirm the validity of our approach.

Fully adaptive update rate for non‐linear trackers

“…Its motion is described by piecewise constant control commands in a frame that is attached to the aircraft. The idea of expressing the state of the target in a frame attached to it is now a common idea, see [27], [20,7], see also [28] for robotics applications. For the radar application, and to take into account 3D motions, but accounting for the fact that rotations of the target on itself are unobservable, the Frenet-Serret frame seems most appropriate.…”

Drone Tracking Using an Innovative UKF

“…We thus need to use a 2D model to derive the evolution equation of the drone. They are presented in [9] for instance, and they read:…”

“…We apply to this model the methodology of the IEKF, as explained in [1] and [10] for instance. The method for the particular model (1) is also developed in [9].…”

“…Let us define the augmented covariance as P a n = diag(P n , N). We then construct a set of 2L + 1 sigma points (in our model L = 7, it is the dimension of the augmented state) as in (9), and where λ is a scaling factor.…”

“…In Section 2 the kinematic model is presented. In Section 3 we recall the IEKF equations for this model, as described in [9]. In Section 4 we develop the UKF update step and adapt it to fit our IEKF propagation step, the filter obtained will be called the left-UKF.…”