Track-before-detect Bernoulli filters for combining passive and active sensors

This paper is concerned with the implementation of track-before-detect (TkBD) algorithms for a range of single-target multi-sensor scenarios with only intermittently visible targets. Visible targets generate measurements from sensors characterised by data rate and clutter density. Bernoulli filters implementing multiple hypothesis tracking (MHT) strategies are deployed to infer both the target location and existence probability. Various Bernoulli filter configurations are compared, including integrated probabilistic data association filters (IPDAF) and integrated expected likelihood particle filters (IELPF) using both prior and Gaussian mixture proposal distributions for the latter. Performance is evaluated against the clutter density in scenarios featuring one low data rate active sensor or two sensors, complimenting the former with a high data rate passive sensor with opposing measurement resolutions. The performance measures used are the area under the receiver operating characteristic (ROC) curve, localisation root mean squared error (RMSE) compared with the posterior Cramér-Rao lower bound (PCRLB), and computation time. Simulation results show that Kalman filters provide an effective solution at low computational expense in less cluttered and comparatively easy scenarios, whereas particle filters implementing Gaussian mixture proposal distributions provide performance benefits relative to computational costs as scenarios become more cluttered and comparatively challenging.