  Feature aided tracking can often yield improved tracking performance over the
standard multiple target tracking (MTT) algorithms with only kinematic
measurements. However, in many applications, the feature signal of the targets
consists of sparse Fourier-domain signals. It changes quickly and nonlinearly
in the time domain, and the feature measurements are corrupted by missed
detections and mis-associations. These two factors make it hard to extract the
feature information to be used in MTT. In this paper, we develop a
feature-aided nearest neighbour joint probabilistic data association filter
(NN-JPDAF) for joint MTT and feature extraction in dense target environments.
To estimate the rapidly varying feature signal from incomplete and corrupted
measurements, we use the atomic norm constraint to formulate the sparsity of
feature signal and use the $\ell_1$-norm to formulate the sparsity of the
corruption induced by mis-associations. Based on the sparse representation, the
feature signal are estimated by solving a semidefinite program (SDP) which is
convex. We also provide an iterative method for solving this SDP via the
alternating direction method of multipliers (ADMM) where each iteration
involves closed-form computation. With the estimated feature signal,
re-filtering is performed to estimate the kinematic states of the targets,
where the association makes use of both kinematic and feature information.
Simulation results are presented to illustrate the performance of the proposed
algorithm in a radar application.
