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Particle filter (PF) based multi-target tracking (MTT) methods suffer from the curse of dimensionality. Existing strategies to combat this assume posterior independence between target states, in order to then sample targets independently, or to perform joint sampling of closely spaced targets only. When many targets are in proximity, these strategies either perform poorly or are too computationally expensive. We make two contributions towards addressing these limitations. Firstly, we advocate an alternative view of the use of posterior independence which emphasizes the statistical effect of assuming posterior independence on the Monte Carlo (MC) approximation of posterior density. Our analysis suggests that assuming posterior independence can provide a better MC approximation of the prior distribution at the next time, and therefore the posterior at the next time, without regard for how sampling is performed. Secondly, we present a computationally efficient, measurement directed, joint sampling method to cope with the target coupling and measurement ambiguity when targets are near each other. Consequently, we develop a PF which employs posterior independence while sampling targets jointly. This PF is applicable to both the traditional thresholded and track-before-detect style pixelized models. Simulation results for a challenging tracking scenario show that the proposed PF substantially outperforms existing approaches.