多目标跟踪英文ppt

Multi-target Bayes Filter
Multi-target Bayes filter

pk-1(Xk-1|Z1:k-1)
prediction
pk|k-1(Xk|Z1:k-1) data-update pk(Xk|Z1:k)
g k ( Z k | X k ) pk|k 1 ( X k | Z1:k 1 )
perm ( X ')
min || X X ' || 0
is a distance for sets not vectors
System Representation
observation produced by targets
observation space
state space
target motion
Remedy: use
perm ( X ')
X X ' || 2 ???
min || X X ' || 0
System Representation
0 X 0
True Multi-target state
1 1 X ' 0 0
X X
Bayesian: Model state & observation as Random Finite Sets [Mahler 94]
pk-1(Xk-1|Z1:k-1)
prediction
pk|k-1(Xk|Z1:k-1)
data-update
pk(Xk|Z1:k)

K 1gk (Zk | X k ) pk|k 1 ( X k | Z1:k 1 )
Probability Hypothesis Density (PHD) filter Cardinalized PHD filter Multi-Bernoulli filter
Conclusions
The Bayes (single-target) Filter
zk zk-1
state space target motion observation space
For multi-target state:
vector representation doesn’t admit multi-target miss-distance finite set representation admits multi-target miss-distance: distance between 2 finite sets In fact the “distance”
5 targets
Xk-1
Xk
3 targets
Number of measurements and their values are (random) variables
Ordering of measurements not relevant!
Multi-target measurement is represented by a finite set
Vo et. al. (2005)
b (T ) =
T f (X)dX
Set integral
Conventional integral
Multi-target Motion Model
Xk = Sk|k-1(Xk-1)Bk|k-1(Xk-1)k
motion
x
death
x’
X’
fk|k-1(Xk|Xk-1 )
Point Process Theory (1950-1960’s)
Choquet (1968)
Probability density of p : F(E) [0,) P (T ) =
T p (X)m(dX)
Belief “density” of f : F(E) [0,)

f
k|k 1
( X k | X ) pk 1 ( X | Z1:k 1 ) m s (dX )
g
k
( Z k | X ) pk|k 1 ( X | Z1:k 1 ) m s (dX )
Computationally intractable in general
来自百度文库
0 0 X 1 1
True Multi-target state
1 1 X ' 0 0
2 targets
Estimated Multi-target state
2 targets
Estimate is correct but estimation error ||
1 target
Estimated Multi-target State
2 targets
X ?
True Multi-target state
1 1 X ' 0 0
no target
Estimated Multi-target State
2 targets
Zk = Qk(Xk) Kk(Xk)
z
x
misdetection

gk(Zk|Xk)
Multi-object likelihood
x

state space
clutter
observation space
Observation process for each element x of a given multi-object state Xk
xk
xk-1
state-vector
System Model
fk|k-1(xk| xk-1)
Markov Transition Density
gk(zk| xk)
Measurement Likelihood
Objective
pk(xk | z1:k)
posterior (filtering) pdf of the state measurement history (z1,…, zk)
gk(zk| xk)
state space
xk-1
state-vector
fk|k-1(xk| xk-1)
xk
Bayes filter

pk-1(. |z1:k-1)
prediction
pk|k-1(. | z1:k-1)
data-update
pk(. | z1:k)

Kalman filter
What are the estimation errors?
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
The Bayes (single-target) Filter
zk zk-1
state space target motion observation space
xk
xk-1
state-vector
pk-1(xk-1| z1:k-1) fk|k-1(xk| xk-1) dxk1
K-1 gk(zk| xk) pk|k-1(xk| z1:k-1)
Need suitable notions of density & integration
RFS & Bayesian Multi-target Filtering
state space
E

random finite set or random point pattern
S
state space

N(.;mk-1, Pk-1)
(i) {wk1, xk-1}i=1 (i) N
N(.;mk|k-1, Pk|k-1)
{wk|k-1, xk|k-1} i=1
(i) (i) N
N(.;(mk, Pk )
(i) (i) {wk , xk } i=1 N

Particle filter


Random Set/Point Process in Multi-Target Tracking
Ba-Ngu Vo
EEE Department University of Melbourne Australia
http://www.ee.unimelb.edu.au/staff/bv/
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. SAMSI, RTP, NC, USA, 8 September 2008
System Representation
How can we mathematically represent the multi-target state? Usual practice: stack individual states into a large vector! Problem:
Multi-target tracking
Multi-target tracking
observation produced by targets
observation space
state space
target motion
5 targets
Xk-1
Xk
3 targets
Objective: Jointly estimate the number and states of targets Challenges: Random number of targets and measurements Detection uncertainty, clutter, association uncertainty
Belief “distribution” of b (T ) = P( T ) , T E
Mahler’s Finite Set Statistics (1994)
Probability distribution of P (T ) = P( T ) , T F(E)
E
N(S) = | S|
point process or random counting measure
RFS & Bayesian Multi-target Filtering
Collection of finite subsets of E
F(E) T
E
State space
T
RFS & Bayesian Multi-target Filtering
Reconceptualize as a generalized single-target problem [Mahler 94]
observations observed set
Z
targets target set
Bayes filter

pk-1(xk-1 |z1:k-1)
prediction
pk|k-1(xk| z1:k-1)
data-update
pk(xk| z1:k)

The Bayes (single-target) Filter
zk zk-1
target motion observation space
Multi-object transition density
x
spawn
x
X’
creation
Evolution of each element x of a given multi-object state Xk-1
Multi-target Observation Model
likelihood
Outline
The Bayes (single-target) filter Multi-target tracking
System representation
Random finite set & Bayesian Multi-target filtering Tractable multi-target filters