IEEE Robotics & Automation Magazine - June 2014 - 77
Multiple-Object State Est imation
Multiple-object estimation is a joint estimation problem that
consists of estimating the number of objects and the state of
each object. Just as in single-object estimation, in multipleobject estimation all of the detections are corrupted by noise.
However, there are additional characteristics that further
complicate the estimation problem.
For each object, the probability of detection is less than
one. In practice, this means that we cannot know for certain
whether or not an object caused any detection. There may
also be false alarms called clutter detections. Furthermore, the
detection origin is unknown: We do not know which detections are clutter and which are caused by actual objects, and
we do not know which object caused which detection. A
final characteristic of multiple-object estimation is that we do
not know how many objects there are inside the sensor's surveillance area.
Let N x, k denote the unknown number of objects present at
(i)
time k, and let x k denote the state of object i at time k. At
time k the set X k of all present objects is given by
x, k
(i)
X k = " x k ,i = 1 .
N
Each sensor scan gives N z, k detections z . Let the set of
detections at time k be denoted
N
zk
(4)
and let z k be all sets of measurements from time 1 to time k,
i.e., Z k = " Z i ,ki = 1 . The objective of MOT is to estimate X k
given Z k, i.e., to determine how many objects there are, and
for the objects that are present, to estimate the object states
x (ki) . This is illustrated in Figure 3(b).
Just as in single-object estimation, each individual estimate
needs to be both time updated and measurement updated. In
addition to this, classical approaches to MOT have included
data handling and data association. In the next two sections,
we will briefly review these two problems.
Data Handling
Data handling means to handle the fact that the number of
objects in the sensor's surveillance area changes over time. This
includes new targets appearing and old targets disappearing,
referred to in MOT literature as object birth and object death.
Approaches to handle birth and death include M/N logic and
the score-based approach; see [1].
Data Association
Using multiple detections to estimate the states of multiple
objects requires an approach to the data association, or correspondence, problem. Data association means to associate
each detection to one of the detection generating sources, i.e.,
either to an object or a clutter source. Correct data association is very important because an incorrect association solution can result in disastrous estimation performance. In each
time step, each detection is assumed to be either clutter or
State Space
Target Motion
xk+1
xk
(a)
(3)
zk
(2)
zk
(1)
zk
(2)
xk
(1)
(3)
zk+1 Observation Space
(4)
zk
(2)
zk+1
(1)
zk+1
(5)
Target Motion
zk+1
xk+1
(3)
xk+1
(1)
(4)
xk+1 xk+1
xk
(6)
zk+1
State Space
(2)
(3)
xk
(b)
Observation
Space
zk+1
zk
(3)
( j)
k
(j) z, k
Z k = " z k ,j = 1,
Observation Space
zk+1
xk
Meta Target
Motion
State
Space
xk+1
(c)
Figure 3. The objects' states x belong to a state space, and the
detections z are generated in an observation space. (a) There is a
one-to-one correspondence between the detection and the state.
(b) Generalization of the single-object case where the detectionto-state correspondence is unknown. (c) The multiple objects are
treated as an RFS whose set members all belong to the same state
space, and the detections are treated as an RFS whose set members
all belong to the same observation space. There is a one-to-one
correspondence between the object set X and the detection set Z.
generated by an object. For the detections that are generated
by objects, a decision has to be made as to which measurements belong to already existing objects and which measurements belong to newly appeared objects. Note that if it is
known that there can be at most one object; cf. the singleobject cases in Table 2, the data association problem becomes
somewhat easier.
In a multiple-point object scenario, at most one detection
can be caused by each source, since a point object by definition
may cause at most one detection. For multiple-point object
estimation, solutions to the data association problem in MOT
literature include global nearest neighbor (gNN), joint probabilistic data association (JpDA), and multiple hypothesis tracking (MHT). A comprehensive overview of these methods is
given in [1]. In sLAM literature, the joint compatibility branch
and bound (JCbb) algorithm can be found [9].
In contrast to point objects, an extended object by definition may cause more than one detection, and thus in a multiple extended target scenario at most one cell of detections
can be caused by each source. In this context, a cell of detections is a nonempty subset of the full set of detections. A partition of the set of detections is a set of cells, such that the
June 2014
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IEEE ROBOTICS & AUTOMATION MAGAZINE
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