The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget 
detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable 
for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of 
this filter based on propagation of a first-order multitarget moment called the probability hypothesis density 
(PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which 
remains first-order in the states of individual targets, but which is higher-order in target number. In this paper 
we show that this and much more is possible. We derive a closed-form cardinalized PHD (CPHD), filter, which 
propagates not only the PHD but also the entire probability distribution on target number.

A theory of PHD filters of higher order in target number

THE multi-object filtering problem is a logical and fundamental generalization of the ubiquitous single-object vector filtering problem. Multi-object filtering essentially concerns the joint detection and estimation of the unknown and time-varying number of objects present, and the dynamic state of each of these objects, given a sequence of observation sets. This problem is intrinsically challenging because, given an observation set, there is no knowledge of which object generated which measurement, if any, and the detected measurements are indistinguishable from false alarms. Multi-object filtering poses significant technical challenges, and is indeed an established area of research, with many applications in both military and commercial realms. The new and emerging approach to multi-object filtering is based on the formal theory of random finite sets, and is a natural, elegant and rigorous framework for the theory of multiobject filtering, originally proposed by Mahler. In contrast to traditional approaches, the random finite set framework is completely free of explicit data associations. The random finite set framework is adopted in this dissertation as the basis for a principled and comprehensive study of multi-object filtering. The premise of this framework is that the collection of object states and measurements at any time are treated namely as random finite sets. A random finite set is simply a finite-set-valued random variable, i.e. a random variable which is random in both the number of elements and the values of the elements themselves. Consequently, formulating the multiobject filtering problem using random finite set models precisely encapsulates the essence of the multi-object filtering problem, and enables the development of principled solutions therein. The central thesis of this dissertation is that the random finite set framework not only is a natural, elegant and rigorous foundation, but also leads to practical, efficient and reliable algorithms for Bayesian multi-object filtering. In support of this thesis, the following fundamental contributions are established within the random finite set framework. The first key contribution is a mathematically rigorous derivation and practical implementation of a novel algorithm for the important case of single-object Bayesian filtering, with multiple measurements generated by the object, state dependent sensor field of view and clutter. The performance of the proposed algorithm is demonstrated in simulated scenarios, and shown at least in simulation to dramatically outperform traditional single-object filtering in clutter approaches. The second iv key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on moment approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is also demonstrated in practical scenarios, and shown to considerably outperform traditional multi-object filtering approaches. The third key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on functional approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is compared with the previous, and shown to appreciably outperform the previous in certain classes of situations. The final key contribution is the definition of a consistent and efficiently computable metric for multi-object performance evaluation. It is shown that the finite set theoretic state space formulation permits a mathematically rigorous and physically intuitive construct for measuring the estimation error of a multi-object filter, in the form of a metric. This metric is used to evaluate and compare the multi-object filtering algorithms developed in this dissertation.

Random finite sets in Multi-object filtering

Data and information fusion (DIF) involves a process of combining data from multiple inputs (from one or more sources such as sensors and textual reports).1 The aim is to obtain information that is better (more useful and meaningful) than that would be derived from each of the sources individually (that is, without fusing). DIF is emerging as an important field of multidisciplinary study [113, 316]. This is due to increase in data and information flow, as well as improvement in communication, computing and sensor technology. The first applications of DIF techniques were in the military arena [177, 179, 455]. The use of DIF techniques for problem-solving has extended to many non-military applications in the commercial and industrial sectors [177, 179, 199, 228]. In general, data and information fusion can provide enhancement to the outcomes of processes for solving various application problems. Some advantages of carrying out DIF include [316]: 2 improvement in the accuracy of data, as well as reduction in uncertainty and ambiguity within data, and 2 improvement in situation awareness (SAW) and inference that lead to better decision making.

High-level Information Fusion: An Overview.

A blueprint for higher-level fusion systems

https://www.csc.kth.se/~hedvig/publications/if_07.pdf

An information fusion demonstrator for tactical intelligence processing in network-based defense

The paper discusses a recently developed demonstrator system where new ideas in tactical information fusion may be tested and demonstrated. The main services of the demonstrator are discussed, and essential experience from the use and development of the system is shared.

Göran Neider

Papers

An information fusion demonstrator for tactical intelligence processing in network-based defense

The IFD03 Information Fusion Demonstrator

The IFD03 Information Fusion Demonstrator -- requirements, methodology, design, and experiences