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

Optimising exposure for children and adolescents with anxiety, OCD and PTSD: a systematic review

Cognitive-behavioural therapy is an effective treatment for anxiety disorders in children and young people, however, many do not benefit. Behavioural exposure appears to be the critical ingredient in the treatment of anxiety disorders. Research with adults has identified innovative strategies to optimise exposure-based treatments, yet it is not clear how to optimise the effects of exposure for children and young people. This review was a preliminary exploration of the association between potential optimisation strategies and treatment procedures and outcomes for the treatment of child anxiety symptoms/disorders. We searched PsychInfo and Medline databases using a systematic search strategy and identified 29 articles. We found preliminary evidence that some specific strategies may enhance the effects of exposure, such as dropping safety behaviours, parents and therapists discouraging avoidance, and the use of homework. However, not one significant finding was replicated by another study for the same time point using the same methodology. To a large degree, this lack of replication reflects a limited number of studies combined with a lack of consistency across studies around conceptualisations, methodological approaches, and outcome measures making it difficult to make meaningful comparisons between studies and draw firm conclusions. Examination is needed of a wide range of theoretically-driven potential optimisation strategies using methodologically robust, preclinical studies with children and young people. Furthermore, the methods used in future research must enable comparisons across studies and explore developmental differences in the effects of particular optimisation strategies