  Multi-target tracking is mainly challenged by the nonlinearity present in the
measurement equation, and the difficulty in fast and accurate data association.
To overcome these challenges, the present paper introduces a grid-based model
in which the state captures target signal strengths on a known spatial grid
(TSSG). This model leads to \emph{linear} state and measurement equations,
which bypass data association and can afford state estimation via
sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of
the novel model, two types of sparsity-cognizant TSSG-KF trackers are
developed: one effects sparsity through $\ell_1$-norm regularization, and the
other invokes sparsity as an extra measurement. Iterative extended KF and
Gauss-Newton algorithms are developed for reduced-complexity tracking, along
with accurate error covariance updates for assessing performance of the
resultant sparsity-aware state estimators. Based on TSSG state estimates, more
informative target position and track estimates can be obtained in a follow-up
step, ensuring that track association and position estimation errors do not
propagate back into TSSG state estimates. The novel TSSG trackers do not
require knowing the number of targets or their signal strengths, and exhibit
considerably lower complexity than the benchmark hidden Markov model filter,
especially for a large number of targets. Numerical simulations demonstrate
that sparsity-cognizant trackers enjoy improved root mean-square error
performance at reduced complexity when compared to their sparsity-agnostic
counterparts.
