Citation preview
Hopfield-Tank
China Institute of Technology
Email: elaine@cc.chit.edu.tw
Abstract
The problem of tracking multiple targets in the presence of clutter
is addressed. Data association is the most critical part in
multi-target tracking; erroneous data as- sociations can result in
lost tracks. The joint probabilistic data association (JPDA) and
multiple hypotheses tracking (MHT) algorithm have been previously
reported to be suitable for this problem. However, the complexity
of this algorithm increases rapidly with the number of targets and
returns. The computation for probabilities of enormous feasible
events becomes very heavy burden. For real-time processing and
tracking performance, it seems that parallel structure is a
suitable approach. A Hop- field-Tank Network, which consists of
many connected processing elements, is ca- pable of parallel
computation, and it is suitable for a solution to the data
association problem.
- 143 -
Tracking (MHT)Hopfield-Tank Neural Network (HTN)
(Nearest Neighbor Standard Filter; NNSF)[3,4]
"1" "0"(Innovation)
(Maximum Likelihood Function)
Y. Bar-Shalom Tse 1975 (Probabilistic Data Association; PDA)[7](All
Neighbor)
(Validation Region; Gating)
Y. Bar-Shalom Fortmann 1983
(Joint Probabilistic Data Association; JPDA)[9]
144
Roecker JPDA
"AD HOC JPDA"[10]Emre and Seo [11]
Y. Bar-Shalom Chang [12] JPDA
JPDA
(Neural Network)
JPDA SOFM
-(Hopfield-Tank; HTN) JPDA HTN
”
JPDA : km
[] (Validation Matrix) Gate
[ ] , 1, 2, , , 0,1, 2, ,jt kj m tω = =L TL (1)
jtw t ’1’
’0’
j
m
j jt
145
ˆ ( ) 0,
jt jt
0
jt k t
jt j
≤ =∑ θ L
[] (1) (Binary M
146
(5) 1
ˆ( ) ( ) T
j t
τ ω =
θ t
[] ( )kθ
1 11{ ( ) } { ( ) ( ), } [ ( ) ( ), ] { ( ) }k k kP k Z P k Z k Z p
Z k k Z P k Z c
− −= = ⋅θ θ θ θ 1k− (8)
1 1 1 2
j jt j
p Z k k Z p z k z k z k k Z
p z k k Zθ
− −
−
=
=
=∏
1 1
j
N z k if k p z k k Z
V if
τ θ
θ (10)
ˆ[ ( )] [ ( ); ( 1), ( )]j jt t tj j j j jN z k N z k z k k S
k−
)1(ˆ −kkz jt j : jt
)(kS jt j : jt
( )1 ( )
1
[ ( ) ( ), ] [ [ ( )]] k
j
=
(Prior Probability) ( )kθ
{ ( )} { ( ), ( ), ( )} { ( ) ( ), ( )} { ( ), ( )}P k P k P k Pδ φ
δ φ δ φ= = ⋅θ θ θ θ θ θ θ θ θ (12)
{ ( ) ( ), ( )}P k δ φθ θ θ :
km : k
( )φ θ : θ
−= ⋅ − =θ θθ θ θ θ (13)
{ ( ), ( )} { ( ) ( )} { ( )}P P Pδ φ δ φ φ= ⋅θ θ θ θ θ (14)
{ ( ) ( )}P δ φθ θ : ( )φ θ
∏ =
DP−
tj j D D F j tk
P k Z V N z k P P c m
τ δ δφφ t µ φ−−
= =
= −∏ ∏θ (16)
PMF )(φµF { ( )} ( )FP φ µ φ=θ Possion
! )()(
P k Z N z k P P c
φ τ ttδ δλ −
[] t j
ˆ{ } { } (t k k j jt jtP Z P Z wβ θ
= =∑ θ
i i j j i
j i
148
) iE A X W X xθ ≠
= − ⋅ = − −∑ (20)
1 1( ) ( )2 2i i i ij j i i j i i
E A X X W X iXθ ≠
= − ⋅ = − +∑∑ ∑ (21)
A W x )iθ ≠
= ∑ − (Firing Function)HTN
(1)(2) (3) N
51 52 53 55
0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0
1 2 3 4 5
=
xiX 1xiX =
X X ≠
X X ≠
X N N−∑∑ (25)
: , 1 , 1)(xy xi y i y i x i y x
dist X X X+ ≠
2 2
[( ) ] ( ) 2 2
xi xj xi yi x i j i x i y x
xi xy xi y i y i x i x i y x
A BE X X X X
C DX N dist X X X
≠ ≠
+ − ≠
= ⋅ + ⋅
+ − + ⋅ ⋅ +
∑∑∑ ∑∑∑
xy
W A x y i j B i j x y
C D dist j i j i
δ δ δ δ
TSP
})({)( kZkiPki θβ
−= − k
1 22 ( ) (1 ) /D G Db S k P P Pλ π= − (32)
1 0
τ ≠
i t j i X X
≠
⋅∑∑∑
t i X )−∑ ∑
i t X β−∑∑
[] JPDA
2 2( 1) ( 2 2 2
t t t t DAP i i i j i i i
i t t i t j i t i i t
A B DE X X X X X Xτ
τ
[JPDA ]
: O O 1 2 3(3.3, 2.1) , (1.4, 2.5) , (2.4, 2.225)T T
: TT PP )45.2,0.2(,)0.2,8.2( 21 ==
: 99.0=GP
2χ : Prob 2( ) 0.01 , 9.χ γ γ> = = 21
(1) 2 jtd 2χ
151
0 16.667 0.1 O P d
− ⇒ = = <
1 0 0 θ
1 0 0 θ
1 0 0 θ
0 1 0 θ
0 0 1 θ
1 0 0 θ
0 0 1 θ
0 1 0 θ
1 1exp[ ] exp[ ] 2 2(2 ) (2 )
t t t j j j jt
M Mt t j j
v S v d
1}{1}{0}{1}{ 4321 0
1 ×+×+×+×= kkkk ZPZPZPZP θθθθβ 1}{0}{0}{1}{ 8765 ×+×+×+× kkkk
ZPZPZPZP θθθθ
55566.0,3967.0,0,0
t
t
+ = +
= +
k (38)
( )tx k t ( ) ( )t Tx k x x y y= & &
( )tF k t t ( )tG k
153
2
2
01 0 0 2 0 1 0 0 0 1 0 0 0
( ) , ( ) , ( ) 0 0 1 0 0 1 00 20 0 0 1
0
= = =
k σ
x y kmk k sσ σ= =
PDA : 0.95GP = 2χ
9.2γ = 0.95DP =
: 20.2km−
( )x km ( )y km ( )x km s& ( )y km s&
1 1.5 3.5 0.4 0.56 2 1.0 4.0 0.6 0.44 ()()() PDAJPDAHTNPDA
PDA
HTN-JPDA
(Cluster)
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