Multi-object estimation refers to applications where there are unknown
number of objects with unknown states, and the problem is to estimate both the number
of objects and their individual state vectors, from observations acquired by sensors.
The solution is usually called a multi-object filter. In many modern complex systems,
multi-object estimation is one of the most challenging problems to be solved for
satisfactory performance of the dedicated tasks by the system. A wide range of
practical applications involve multi-object estimation, from multi-target tracking in
radar to visual tracking in sport, to cell tracking in biomedicine, to data clustering in
big data analytics. In the past decade, a new generation of multi-object filters has been
developed and rapidly adopted by researchers in various fields, that is based on using
stochastic geometric models and approximations. In such methods, the multi-object
entity is treated as a random finite set (RFS) variable (with random variations in its
cardinality and elements), and the stochastic geometric-based notions of density and
integration, developed in the new theory of finite set statistics (FISST), are used to
formulate Bayesian filters for estimation of cardinality (number of objects) and state of
the multi-object RFS variable. Examples of such solutions include PHD filter, CPHD
filter and the recent trend of multi-Bernoulli filters. In many applications, the
observations are acquired through a controlled sensing procedure, either by controlling
a mobile sensor (e.g. in radars and visual surveillance) or by selecting a sensor node
(e.g. in sensor networks). This chapter reviews the most recent developments in sensor
management (control or selection) solutions devised for multi-Bernoulli solutions in
various applications. It first presents basics of random set theory and formulation of the
cardinality-balanced and labeled multi-Bernoulli filters. The most recent sensor-control
and sensor-selection solutions that have been proposed by the authors and other
researchers active in the field are then presented and comparative simulation results are
discussed.
Keywords: Stochastic Geometry, Random Sets, Point Process, Finite Set
Statistics, Multi-Target Tracking, Sensor Management, Sensor Selection, Sensor
Control, Multi-Bernoulli Filter, OSPA, PEECS.