A second-order PHD filter with mean and variance in target number

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

Multi-object filtering with second-order moment statistics

The focus of this work lies on multi-object estimation techniques, in particular the Probability Hypothesis Density (PHD) filter and its variations. The PHD filter is a recursive, closed-form estimation technique which tracks a population of objects as a group, hence avoiding the combinatorics of data association and therefore yielding a powerful alternative to methods like Multi-Hypothesis Tracking (MHT). Its relatively low computational complexity stems from strong modelling assumptions which have been relaxed in the Cardinalized PHD (CPHD) filter to gain more flexibility, but at a much higher computational cost. We are concerned with the development of two suitable alternatives which give a compromise between the simplicity and elegance of the PHD filter and the versatility of the CPHD filter. The first alternative generalises the clutter model of the PHD filter, leading to more accurate estimation results in the presence of highly variable numbers of false alarms; the second alternative provides a closed-form recursion of a second-order PHD filter that propagates variance information along with the target intensity, thus providing more information than the PHD filter while keeping a much lower computational complexity than the CPHD filter. The discussed filters are applied on simulated data, furthermore their practicality is demonstrated on live-cell super-resolution microscopy images to provide powerful techniques for molecule and cell tracking, stage drift estimation and estimation of background noise

Joint Registration and Fusion of an Infra-Red Camera and Scanning Radar in a Maritime Context

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

Marker-Less Stage Drift Correction in Super-Resolution Microscopy Using the Single-Cluster PHD Filter

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

Joint estimation of telescope drift and space object tracking

With the proliferation of low-cost CCD-based sensors used on telescopes by amateur astronomers, there is potential to exploit these within an infrastructure for space surveillance. Observations may be corrupted by an undesirable drift of the telescope due to mount jittering and uncompensated diurnal motion of stars. This work presents an approach for drift compensation based on a joint estimation of the sensor drift and the states of the objects and stars observed by the telescope. It exploits a recent development in multi-object estimation, known as the single-cluster Probability Hypothesis Density filter, that was designed for group tracking. The sensor drift is obtained by estimating the collective motion of the stars, which is in turn used to correct the estimation of moving objects. The proposed method is illustrated on simulated and real data

Marker-less stage drift correction in super-resolution microscopy using the single-cluster PHD filter

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