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Tracking Target Signal Strengths on a Grid using Sparsity

Tracking Target Signal Strengths on a Grid using Sparsity,Computing Research Repository,Shahrokh Farahmand,Georgios B. Giannakis,Geert Leus,Zhi Tian

Tracking Target Signal Strengths on a Grid using Sparsity   (Citations: 1)
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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.
Journal: Computing Research Repository - CORR , vol. abs/1104.5, 2011
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    • ...Alongside the sparsity-aware KF tracker proposed here, a sparsity-cognizant iterated extended KF (IEKF) tracker is developed in [12] which accommodates sparsity by viewing it as an extra measurement...
    • ...1A more accurate covariance update can be found in [12]...
    • ...<{[SECTION]}>k ykk 1. (11) Proof: See [12]...
    • ...the state recursion in (3) holds, and so does the state equation (5a); see [12] for a detailed derivation...
    • ...(The omitted details along with a joint state-vector tracking and track association approach are provided in [12].)...

    Shahrokh Farahmandet al. Sparsity-aware Kalman tracking of target signal strengths on a grid

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