Random Finite Set Methods for Network-Based Bayesian Estimation

Today and in the future, distributed information processing in agent networkssuch as wireless sensor/actuator networks, robotic networks, intelligent transportation networks, power grids, and social networksis and will be a key technology affecting the daily lives of millions of people. The overall goal of this project is to devise distributed Bayesian estimation methods and message passing algorithms that are based on random finite sets (RFSs), and to study the performance of these techniques in estimation problems involving agent networks. RFS-based techniques are especially suited to situations in which the number of state parameters, measurements, and/or auxiliary parameters is unknown and random. We expect that the distributed estimation methods resulting from the proposed research will outperform existing methods in a wide variety of applications such as localization and tracking, traffic monitoring, robotics, computer vision, and surveillance. Only few distributed RFS-based estimation methods have been proposed so far. Most of them are limited in that they assume a specific network topology, or they require a fusion center, routing protocols, or data flooding, or they do not provide a global estimate to each agent. Furthermore, a systematic analysis of the performance of distributed RFS-based estimation methods has not been performed. Finally, probabilistic graphical models for probability distributions defined on RFSs and corresponding message passing algorithms have not been proposed so far. In particular, message passing algorithms for RFS-based Bayesian estimation are lacking. The project aims to (i) develop distributed (decentralized) RFS-based Bayesian estimation methods that provide a global estimate to each agent, operate under realistic communication and computation constraints, exhibit a performance close to that of centralized schemes, and are robust to transmission errors, synchronization errors, and node and link failures; (ii) develop probabilistic graphical models, message passing algorithms, and parametric message representations for probability distributions defined on RFSs; and (iii) analyze the performance, convergence behavior, and complexity of the devised estimation methods and message passing algorithms both analytically and via simulation. The proposed research will be supported by collaboration partners based at research institutions in Sweden, the United Kingdom, and the United States. The participating researchers have extensive competencies and track records in statistical signal processing, message passing algorithms, RFSs, target tracking and localization, and distributed estimation.

The modeling, measurement, and processing of information-bearing data and signals are key constituents of numerous technical systems. In many cases, important quantities cannot be observed directly but can only be inferred from related observations or measurements. Since this involves some uncertainty, statistical models and methods are often appropriate. The goal of the FWF project "Random Finite Set Methods for Network-Based Bayesian Estimation" was to develop statistical methods for inferring unknown states and conditions from sensor measurements, in order to achieve what may be called "situational awareness." A major focus was on the tracking of one or several moving objects. This is an important problem in a wide range of applications such as air traffic control, autonomous driving, environmental monitoring, robotics, security, and biomedical analytics. When there are several objects, the main difficulty is that in addition to the states (locations) of the objects, also the number of objects is usually unknown, and it is not clear which sensor measurement was generated by which object. To address these challenges, we developed statistical detection and estimation methods in which the object states and measurements are modeled by random finite sets, rather than random vectors. We also developed multiobject tracking methods that use the belief propagation algorithm and are based on a network (graph) representation of statistical dependencies. These multiobject tracking methods remain computationally feasible even for a large number of objects, sensors, and measurements. We are confident that our results will have a lasting impact on multiobject tracking research and implementations. Another focus of the project was on the development of distributed inference methods for use in decentralized sensor networks. In such networks, there is no central unit that collects all the sensor measurements and performs all the necessary computations; instead, the computations are done in a distributed manner by the sensor nodes themselves and each sensor node is able to communicate only with nearby sensor nodes. We developed distributed methods for localizing (tracking) mobile sensor nodes, for simultaneously tracking mobile sensor nodes and noncooperative mobile objects, and for joint network localization and synchronization. We also introduced a distributed cooperative method for joint tracking and control in decentralized sensor/agent networks. This method combines the tracking of time-varying global and local states with an information-seeking control scheme optimizing the behavior (e.g., movement) of the agents. The results of this project were published in a book chapter, in 17 papers in high-quality journals, and in 11 papers in the proceedings of international conferences. The project results also led to the successful application for another FWF project ("Agent Localization and Inference of Dynamic Environments") and for an Erwin Schrödinger Fellowship ("Multiobject Tracking Using Multiple Sensors").