The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters.

The number of nodes in sensor networks is continually increasing, and maintaining accurate track estimates inside their common surveillance region is a critical necessity. Modern sensor platforms are likely to carry a range of different sensor modalities, all providing data at differing rates, and with varying degrees of uncertainty. These factors complicate the fusion problem as multiple observation models are required, along with a dynamic prediction model. However, the problem is exacerbated when sensors are not registered correctly with respect to each other, i.e. if they are subject to a static or dynamic bias. In this case, measurements from different sensors may correspond to the same target, but do not correlate with each other when in the same Frame of Reference (FoR), which decreases track accuracy. This paper presents a method to jointly estimate the state of multiple targets in a surveillance region, and to correctly register a radar and an Infrared Search and Track (IRST) system onto the same FoR to perform sensor fusion. Previous work using this type of parent-offspring process has been successful when calibrating a pair of cameras, but has never been attempted on a heterogeneous sensor network, nor in a maritime environment. This article presents results on both simulated scenarios and a segment of real data that show a significant increase in track quality in comparison to using incorrectly calibrated sensors or single-radar only.

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Fluorescence microscopy is a technique which allows the imaging of cellular and intracellular dynamics through the activation of fluorescent molecules attached to them. It is a very important technique because it can be used to analyze the behavior of intracellular processes in vivo in contrast to methods like electron microscopy. There are several challenges related to the extraction of meaningful information from images acquired from optical microscopes due to the low contrast between objects and background and the fact that point-like objects are observed as blurred spots due to the diffraction limit of the optical system. Another consideration is that for the study of intracellular dynamics, multiple particles must be tracked at the same time, which is a challenging task due to problems such as the presence of false positives and missed detections in the acquired data. Additionally, the objective of the microscope is not completely static with respect to the cover slip due to mechanical vibrations or thermal expansions which introduces bias in the measurements. In this paper, a Bayesian approach is used to simultaneously track the locations of objects with different motion behaviors and the stage drift using image data obtained from fluorescence microscopy experiments. Namely, detections are extracted from the acquired frames using image processing techniques, and then these detections are used to accurately estimate the particle positions and simultaneously correct the drift introduced by the motion of the sample stage. A single cluster Probability Hypothesis Density (PHD) filter with object classification is used for the estimation of the multiple target state assuming different motion behaviors. The detection and tracking methods are tested and their performance is evaluated on both simulated and real data.