Signal-to-noise ratio threshold effect in track before detect

Track before detect (TBD) refers to simultaneous detection and tracking using unthresholded sensor responses over time. The motivation for TBD is its capacity to deal with low signal-to-noise ratio (SNR) targets. Previously, the achievable error for TBD has been established using Cramer-Rao analysis. Although computationally simple the Cramer-Rao bound is not useful at low SNR as it does not predict the threshold effect. A more accurate notion of the achievable performance at low SNRs is provided by the computationally more complicated Barankin bound. The computational complexity of the Barankin bound arises from the need to optimise over a number of test points, with the tightness of bound increasing with the number of test points. An approximation to the Barankin bound is proposed which permits the use of multiple test points with reasonable computational expense. The improvements in threshold SNR prediction offered by the proposed bound are demonstrated in numerical examples.