多目标跟踪英文

observation space
zk
target motion
state space
xk
System Model
fk|k-1(xk| xk-1)
gk(zk| xk)
Markov Transition Density Measurement Likelihood
Objective
pk(xk | z1:k)
Probability Hypothesis Density (PHD) filter Cardinalized PHD filter Multi-Bernoulli filter
Conclusions
The Bayes (single-target) Filter
zk-1
xk-1 state-vector
. . p ( | z ) p ( | z ) prediction
data-update
k|k-1
1:k-1
k
1:k
N . Kalman filter
( ;mk-1, Pk-1)
.N( ;mk|k-1, Pk|k-1)
.N( ;(mk, Pk )
Particle filter
{wk(-i1) , xk(i-)1}iN=1
{wk(|ik)-1,
xk(|ki)-1}
N i=1
{wk(i,)
xk(i)}
N i=1
Multi-target tracking
Multi-target tracking
observation produced by targets
observation space
5 targets
Xk-1
target motion
Random Set/Point Process in Multi-Target Tracking
Ba-Ngu Vo
EEE Department University of Melbourne Australia
Collaborators (in no particular order): Mahler R., Singh. S., Doucet A., Ma. W.K., Panta K., Clark D., Vo B.T., Cantoni A., Pasha A., Tuan H.D., Baddeley A., Zuyev S., Schumacher D.
0
X 0 1
1
True Multi-target state
2 targets
1
X
'
1
0
0
Estimated Multi-target state
2 targets
Estimate is correct but estimation error || X X ' || 2 ???
Remedy: use min || X X ' || 0 perm( X ')
The Bayes (single-target) Filter
zk-1
xk-1 state-vector
observation space
zk
target motion
fk|k-1(xk| xk-1)
gk(zk| xk)
state space
xk
. Bayes filter
pk-1( |z1:k-1)
posterior (filtering) pdf of the state measurement history (z1,…, zk)
The Bayes (single-target) Filter
zk-1
xk-1 state-vector
observation space
zk
target motion
state space
xk
pk-1(xk-1| z1:k-1) fk|k-1(xk| xk-1) dxk-
1
K-1 gk(zk| xk) pk|k-1(xk| z1:k-1)
Bayes filter
pk-1(xk-1 |z1:k-1) prediction pk|k-1(xk| z1:k-1) data-update pk(xk| z1:k)
System Representation
How can we mathematically represent the multi-target state? Usual practice: stack individual states into a large vector! Problem:
System Representation
0 X 0
True Multi-target state
1 target
1
X
'
1
0
0
Estimated Multi-target State
X ?
True Multi-target state
no target
1
X
'
1
Hale Waihona Puke Baidu
0
0
Estimated Multi-target State
Xk
3 targets
state space
Objective: Jointly estimate the number and states of targets Challenges:
Random number of targets and measurements Detection uncertainty, clutter, association uncertainty
SAMSI, RTP, NC, USA, 8 September 2008
Outline
The Bayes (single-target) filter Multi-target tracking System representation Random finite set & Bayesian Multi-target filtering Tractable multi-target filters
What are the estimation errors?
2 targets 2 targets
System Representation
Error between estimate and true state (miss-distance)
fundamental in estimation/filtering & control well-understood for single target: Euclidean distance, MSE, etc in the multi-target case: depends on state representation