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Multi-target tracking is mainly challenged by the nonlinearity present in themeasurement equation, and the difficulty in fast and accurate data association.To overcome these challenges, the present paper introduces a grid-based modelin 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 viasparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity ofthe novel model, two types of sparsity-cognizant TSSG-KF trackers aredeveloped: one effects sparsity through $\ell_1$-norm regularization, and theother invokes sparsity as an extra measurement. Iterative extended KF andGauss-Newton algorithms are developed for reduced-complexity tracking, alongwith accurate error covariance updates for assessing performance of theresultant sparsity-aware state estimators. Based on TSSG state estimates, moreinformative target position and track estimates can be obtained in a follow-upstep, ensuring that track association and position estimation errors do notpropagate back into TSSG state estimates. The novel TSSG trackers do notrequire knowing the number of targets or their signal strengths, and exhibitconsiderably lower complexity than the benchmark hidden Markov model filter,especially for a large number of targets. Numerical simulations demonstratethat sparsity-cognizant trackers enjoy improved root mean-square errorperformance at reduced complexity when compared to their sparsity-agnosticcounterparts.

Tracking Target Signal Strengths on a Grid using Sparsity