Regional variance for multi-object filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the Probability Hypothesis Density (PHD) and the Cardinalized Probability Hypothesis Density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples

Multi-Bernoulli Sensor-Control via Minimization of Expected Estimation Errors

This paper presents a sensor-control method for choosing the best next state of the sensor(s), that provide(s) accurate estimation results in a multi-target tracking application. The proposed solution is formulated for a multi-Bernoulli filter and works via minimization of a new estimation error-based cost function. Simulation results demonstrate that the proposed method can outperform the state-of-the-art methods in terms of computation time and robustness to clutter while delivering similar accuracy

Representation and estimation of stochastic populations

This work is concerned with the representation and the estimation of populations composed of an uncertain and varying number of individuals which can randomly evolve in time. The existing solutions that address this type of problems make the assumption that all or none of the individuals are distinguishable. In other words, the focus is either on specific individuals or on the population as a whole. Theses approaches have complimentary advantages and drawbacks and the main objective in this work is to introduce a suitable representation for partially-indistinguishable populations. In order to fulfil this objective, a sufficiently versatile way of quantifying different types of uncertainties has to be studied. It is demonstrated that this can be achieved within a measure-theoretic Bayesian paradigm. The proposed representation of stochastic populations is then used for the introduction of various filtering algorithms from the most general to the most specific. The modelling possibilities and the accuracy of one of these filters are then demonstrated in different situations

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

Sensor management for multi-target tracking using random finite sets

Sensor management in multi-target tracking is commonly focused on actively scheduling and managing sensor resources to maximize the visibility of states of a set of maneuvering targets in a surveillance area. This project focuses on two types of sensor management techniques: - controlling a set of mobile sensors (sensor control), and - scheduling the resources of a sensor network (sensor selection).​ In both cases, agile sensors are employed to track an unknown number of targets. We advocate a Random Finite Set (RFS)-based approach for formulation of a sensor control/selection technique for multi-target tracking problem. Sensor control/scheduling offers a multi-target state estimate that is expected to be substantially more accurate than the classical tracking methods without sensor management. Searching for optimal sensor state or command in the relevant space is carried out by a decision-making mechanism based on maximizing the utility of receiving measurements.​ In current solutions of sensor management problem, the information of the clutter rate and uncertainty in sensor Field of View (FoV) are assumed to be known in priori. However, accurate measures of these parameters are usually not available in practical situations. This project presents a new sensor management solution that is designed to work within a RFS-based multi-target tracking framework. Our solution does not require any prior knowledge of the clutter distribution nor the probability of detection profile to achieve similar accuracy. Also, we present a new sensor management method for multi-object filtering via maximizing the state estimation confidence. Confidence of an estimation is quantified by measuring the dispersion of the multi-object posterior about its statistical mean using Optimal Sub-Pattern Assignment (OSPA). The proposed method is generic and the presented algorithm can be used with any statistical filter