文档介绍：NOMENCLATURE
v(S) Lebesgue measure of set S (IIB6)
1 x S
Multitarget Bayes Filtering S( ) Indicator function of set (IIIA)
±w(x) Dirac delta function concentrated
via First-Order Multitarget at w
±X (x) Sum of Dirac deltas at elements of
Moments X (IVC2)
¢w(S) Dirac measure concentrated at w
(VIA)
hX Product of h(x)withx in X (IIIA)
x Single-target state-vector (IIB1)
RONALD P. S. MAHLER
Lockheed Martin X Random state-vector
X Single-target state space (IIB1)
[j]
x,x State of jth sensor (VD)
z,zk Single observation collected at
The theoretically optimal approach to multisensor-multitarget time-step k (IIB2)
[j]
detection, tracking, and identification is a suitable generalization z Single observation from jth
of the recursive Bayes nonlinear filter. Even in single-target sensor (IIB2)
problems, this optimal filter is putationally challenging Z Random observation-vector
[j]
that it must usually be approximated. Consequently, multitarget Z Observation space for jth sensor
(IIB2)
Bayes filtering will never be of practical interest without the
X Finite set of target state-vectors
development of drastic but principled approximation strategies.
Z,Z Finite set of observations collected
In single-target problems, putationally fastest approximate k
at time-step k
filtering approach is the constant-gain Kalman filter. This Z[j] Observation-set collected by jth
filter propagates a first-order statistical moment—the posterior sensor (IIB2)
expectation—in the place of the posterior distribution. The k
Z : z1,:::,zk Time-sequence of observations
purpose of this paper is to propose an analogous strategy for (k)
Z : Z1,:::,Zk Time-sequence of observation-sets
multitarget systems: propagation of a first-order statistical ¥ Random state-set (finite subset of
moment of the multitarget posterior. This moment, the probability state space) (IIB8)
hypothesis density (PHD), is the function whose integral in any § Random observat