Detecting a Small Boat using Histogram PMHT

The conventional tracking paradigm is to sequentially apply a single frame detector to each sensor frame and then employ a tracking algorithm to determine which detector outputs originate from targets and which are false alarms. The tracker associates detections from a particular target and estimates parameters of interest for the target [3], [1]. The obvious shortcoming of this approach is that it is impossible for the tracker to recover a target if there are no detector outputs. For low signal strength targets, this implies that the detector threshold must be low and the tracker must attempt to suppress a large number of false alarms. In practice, the tracker can only do so much and for very low signal strength targets, conventional tracking fails [8]. In contrast, track-before-detect (TkBD) algorithms supply the whole predetection sensor frame to the tracker. In essence the tracking problem remains the same, but the measurement function is different. What makes TkBD challenging is that the relationship between the sensor frame and the target state is non-linear and often non-Gaussian, whereas point measurements may often be treated as linear and Gaussian. Apart from a small number of special cases, non-linear nonGaussian estimation problems cannot be solved with a closed form algorithm. Instead, TkBD algorithms generally use a numerical approximation to make the problem tractable. The numerical approximation may take the form of a fixed discrete grid in state space [17], [2], [21], or a stochastic sampling method may be used (i.e., a particle filter) [19], [4], [18]. Alternatively, the data likelihood ratio may be viewed as an increasing function and the likelihood given a particular state sequence approximated by incoherent or binary integration [14], [20]. The Histogram Probabilistic Multi-Hypothesis Tracker (H-PMHT) is an exception: it is a TkBD algorithm that does not use numerical approximation [22], [24]. H-PMHT uses a unique histogram interpretation of the sensor frame and expectation maximisation (EM) to treat the TkBD problem as one of mixture fitting. The algorithm has the advantage of being capable of handling multiple targets whereas the numerical methods usually assume a single target. In addition, it does not require an assumed statistical distribution for the amplitude of the scene background, which may be difficult to adequately approximate in a realistic application. Despite its advantages, little work has been published on H-PMHT besides the original algorithm development [22], [24] and its extension to spectral data [23]. Pakfiliz and Efe presented marginalised expressions for a two-dimensional filtering problem and compared H-PMHT with a conventional tracking approach (Interacting Multiple Model Probabilistic Data Association with Amplitude Information) [16]. They showed that H-PMHT provided lower estimation errors. However, the comparison used two independent simulated