Regional variance for multi-object filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the Probability Hypothesis Density (PHD) and the Cardinalized Probability Hypothesis Density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples

Tracking Target Signal Strengths on a Grid using Sparsity

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.Comment: Submitted to IEEE Trans. on Signal Processin