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NEAR-Lab - 1040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Multi-static Active Target Tracking using an Invariance Constraint
Northwest Electromagnetics & Acoustics Research Lab Electrical & Comp. Eng. Dept, Portland State Univ.
Chensong He, Jorge Quijano, Lisa M. Zurk
Funded by
Office of Naval Research (ONR)
NEAR-Lab - 2040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
A significant challenge in tracking targets in multi-static active geometries is the large dimensionality and inherent uncertainty of the track hypothesis space. Traditional tracking approaches (such as Bayesian state estimators) rely on prescribed target kinematics to describe track evolution, but cannot easily incorporate the effects of shallow water multipath. The objective of the proposed research is to improve the capability and robustness of tracking algorithms for Navy multi-static active sonar systems with a physics-based processing technique that relies on the invariance principle and is incorporated into the tracker framework.
Although the invariance principle is approximately invariant to details of the ocean environment, it still provides a useful relationship between source frequency, frequency offset, target range, and target range rate. For a broadband waveform, the invariance principle suggests a method to constrain the track- hypothesis space by relating the frequency dependent signal characteristics to physically realizable target range rates. This effort is a three year effort (2005- 2008).
NEAR-Lab - 3040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Multi-static Sonar Systems
• Sensor network of underwater acoustic sources and receivers– Acoustic pulses illuminate and scatter from underwater targets– Received pulses provide information on time dependent range and Doppler
• Objective: Determine target track (location vs. time) from observations
• Challenges– Underwater propagation physics and bottom reverberation– Multi-dimensional solution space
)( 0tRij )( 1tRij)( 2tRkj
ith rcvr
jth src = pulse from t0
= pulse from t1= pulse from t2
= receiver
= source
= target
NEAR-Lab - 4040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Active Sonar Signal Contributions
• Acoustic waves travel via discrete modes – Environment-dependent propagation paths and velocity
(hence multiple arrival times and angles)
• Reverberation from (rough) ocean bottom– Dominant source of noise for active sonar
Acoustic source
Target scatter
Bottom reverberation
Θm
mth mode
Mode functions Ζm (z)
Dep
th (m
)
020406080
100120140160180200
m=2m=1
m=3 m=4
020406080
100120140160180200
Hypothesis: Moving target time-frequency structure can be separated from reverberation using its invariant structure
NEAR-Lab - 5040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Time-Frequency Intensity Variation Invariance Principle
10 dB
Range (km)
Soun
d in
tens
ity (d
B)
Sound intensity versus range(from Brehkovskikh & Lysanov)
300 Hz
307.5 Hz
Invariant time-frequency structure described by Brekhovskikh in terms of normal mode interference• Invariance parameter β
approximately unity• Principle applied to interpretation of lofargrams
Question: is there an invariant structure in active (bi-static) sonar? Can it be exploited?
Figure from D’Spain & Kuperman, 1999
NEAR-Lab - 6040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Contacts2=Oil rig3=Moored tanker4=Wreck 18=Wreck 29=Wreck 3
TracksRed=East/WestBlue=DiagonalGreen=Ridge geometry
Geographic Details
Shallow Water Active Classification (SWAC) Characterization & Reduction of Active False Tracks*
Variable ValueSignal processing
Sampling rate 222 to 666 S/sPulse length 1.2 to 2 s
Broadband source
Bandwidth 70 to 400 HzCenter frequency
495 to 600 Hz
Kinematics Receiver depth 66.5 mShip’s speed 4.9 knots
Experiment specifications
*NUWC-NPT Tech Memo 04-054, 2004; Comeau & Petersen
1515 1520 1525 1530 1535
0
50
100
Sound speed profile of the channel
Dep
th(m
)
Sound Speed(m/s)
Channel specifications(135 m depth)
NEAR-Lab - 7040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Active Spectrograms from Malta Plateau
Note appearance of striation patterns indicative of target track
Linear
Contact 03/track 56: moored tank
Bathtub
Contact 09/track 03:Wreck=missing data
dB
from GPS
from GPS
NEAR-Lab - 8040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Active Sonar Simulation
• Received (bi-static) pressure:
• Environment values (bathymetry, sound speed, etc.) from NUWC– Mode functions computed with KRAKEN
• Scattering matrix: assume no mode coupling (diagonal matrix)
∑∑⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
=m n
rik
rntnmnm
rik
tmsmn rk
ewzwzGrk
ewzwzCwzrpnm
21
21
),(),(),(),(),,( ψψψψ
=mnG
=),( wzmψwhere: mth mode function in the water column.=mk
=21 , rrhorizontal wavenumber of mth mode
Scattering matrix defined by the targetNormalizing constant
Source/target and target/receiver ranges
=C=),,( wzrp Pressure due to a point source of frequency ω
Source to target Target to receiver
NEAR-Lab - 9040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Measured versus Simulated Spectrograms for Contact 3 (Moored Tank )
Contact 03/track 56: moored tank
Spectrogram(Data)
Tim
e(m
in)
Frequency(Hz)
450 500 550
20
40
60
80
100
120
140
160
dB
-25
-20
-15
-10Spectrogram(Simulation)
Frequency(Hz)
450 500 550
20
40
60
80
100
120
140
160
-25
-20
-15
-10
-5
16 18 20 22 24 26
20
40
60
80
100
120
140
160
Range vs time
Range(km)
Simple scattering matrix: no inter- mode coupling
from GPS
NEAR-Lab - 10040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Contact 08/track 23:wreck
Measured versus Simulated Spectrograms for Contact 8 (Wreck )
Spectrogram(Data)
Tim
e(m
in)
Frequency(Hz)
500 600 700
10
20
30
40
50
60
70
80
90
100
dB
-25
-20
-15
-10Spectrogram(Simulation)
Frequency(Hz)
500 600 700
10
20
30
40
50
60
70
80
90
100 -25
-20
-15
-10
-5
10 12 14
10
20
30
40
50
60
70
80
90
100
Range vs time
Range(km)
Simple scattering matrix: no inter- mode coupling
from GPS
NEAR-Lab - 11040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Tracking using the Invariance Features
⎥⎦
⎤⎢⎣
⎡=
t
t
state vx
X
γ11
][−−
Δ=
Δtt rr
ff
= detectionTarget track
=)(tf m Frequency of striationttt rrr 21 +=
Bistatic range
⎥⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡=
bt
rt
t
t
nn
bearingrange
V
Standard Kalman Filter (SKF): Tracking based only on kinetics
Physics-based Invariance with KF: Additional time- frequency constraint imposed to decrease allowable detections
State vector Observations vector
Def.
Invariant: 1)1()( 1
1+
−=
−
−
t
tmm r
TvTfTf γ
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)(Tfvx
X
m
t
t
inv⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
+⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
ft
bt
rt
m
t
t
inv
nnn
Tfbearingrange
V)(
New set of equations:
NEAR-Lab - 12040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Conventional Extended Kalman Filter (CEKF) for Bistatic Geometries
• State vector (position & velocity)
• Nearly constant velocity (NCV) dynamics model
[ ]Tnnnnn yxyxX =
Bistatic geometry:
r1
r2
xs ,ys
xr ,yr
xn =x(tn ), yn =y(tn )
nn tttt
t
wXX nn
−=Δ
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡Δ
Δ
=
+
+
=+
1,
10000100
010001
F
F ,n1
F = state transition matrix; wn = zero mean, white Gaussian noise
NEAR-Lab - 13040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
CEKF Observations and Measurement Model
• System measures bistatic range, r, and bearing angle w.r.t. receiver:
• Measurement model:
,)()()()(
)(2222
)( 21
rnrnsns
n
yyxxyyxx
trrr
n
ntn
−+−+−+−=
+=
[ ] ,)(),( Tnnn tmtmm r φ=, tan)( 1 ⎥
⎥
⎦
⎤
⎢⎢
⎣
⎡=
−
−−
rn
rnn
xxyy
rXh
n
[ ]Tnnn rZ φ=
nnn mXhZ += )(
Bistatic geometry:
r1
r2
xs ,ys
xr ,yr
xn , yn
Measurement:
Measurement noise:
NEAR-Lab - 14040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Invariance EKF (IEKF) State Transition
• State space vector includes time dependent frequency
Determine state transition, F, from definition of invariance
[ ]Tnnnnnn fyxyxX =
γ)1()1( −
Δ=
−Δ
Trr
Tff
,n1 )F( nn wXX +=+
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
⎥⎦
⎤⎢⎣
⎡ Δ++
Δ+Δ+
=
n
nnn
n
n
nn
nn
rtyxf
yx
ytyxtx
X
)(1
)F( n
Invariance relation
Relates new frequency to previous value using invariance
NEAR-Lab - 15040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
IEKF Observations & Measurements
• System measures frequency for each pulse – For now, assume single value representing the maximum frequency– Add to measurement vector
• Measurement model becomes:
• Proceed with Kalman prediction and update as before
[ ]Tnnnn frZ φ=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=−
−−
n
rf
xxyy
r
Xhn
rn
n
n
1tan)(
[ ] ,)(),(),( Tnfnnn tmtmtmm r φ=
Measurement noise:
NEAR-Lab - 16040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Tracker Logic
• Confirm: If M contacts are associated
• Discarded: If less than M contacts are associated with N scans
• Terminated: If it’s confirmed and after K consecutive missed detections
• Validated contacts are those that satisfy the following threshold condition
( ) ( ) ( ) 21'' )1()()()1()()1()( χ<−−+−−−− iiXiCZRiCiiPiCiiXicZ ijiij
Where the parameter is the association gate parameter2χ
NEAR-Lab - 17040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Tracker Performance
• Addition of invariance constraint improves tracker performance– Eliminates false detections using frequency (in addition to
kinetics)– Average range error decreases 34% to 117 m (averaged over 100
realizations)
NEAR-Lab - 18040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Future Work
• Extend frequency measurement to spectral information– Use family of frequencies representing striations– Need transition relationship and estimation (Hough? Radon?)– Add uncertainty due to gamma
• Improve tracker formulation– Multiple tracks, increased tracker logic (track initiation,
confirmation, and elimination– More realistic reverberation environment
• Apply to real data
NEAR-Lab - 19040123, lmz
NEAR-Lab Northwest Electromagnetics &
Acoustics Research
Publications
• J. Quijano, L. M. Zurk, D. Rouseff, Demonstration of the invariance principle for monostatic active sonar, Journal of the Acoustical Society of America, May 2007, submitted for publication
• L.M. Zurk and C. He, Active target tracking using the bistatic invariance principle, invited for presentation Acoustical Society of America, Salt Lake City, Utah, June 2007
• L. M. Zurk, J. Quijano, and M. Velankar, D. Rouseff, Bistatic invariance for active sonar systems, Acoustical Society of America, Vol. 120, No. 5, p. 3221. November 2006
• J. Quijano, L. M. Zurk, D. Rouseff, Use of the invariance principle for target tracking in active sonar geometries, IEEE Oceans Conference, Boston, MA, September 2006
• L.M. Zurk, J. Quijano, D. Rouseff, Bistatic Invariance Principle for Multi- Static Active Geometries, Acoustical Society of America, Providence, RI, June 2006
• L. M. Zurk, D.Rouseff, J. Quijano, G. Greenwood, Bistatic Invariance Principle for Active Sonar Geometries, European Conference on Underwater Acousics (ECUA), Carvoviero, Portugal, June 2006