Adaptive High Dimensional Data Fusion and Sensing for ... · Collaboration/Summer Faculty Program...

Adaptive High Dimensional Data Fusion and Sensing

for Dynamic Target Detection and Tracking

Dr. Ruixin Niu

Department of Electrical and Computer EngineeringVirginia Commonwealth University

Richmond, VA, USA

AFOSR PI’s meeting, DDDAS Program

September 19, 2018

Ruixin Niu (VCU) Adaptive High Dimensional Data Fusion September 19, 2018 1 / 21

Summary

Summary of EffortAF Relevance: information fusion, target detection/tracking are crucial forsurveillance and situational awarenessAFRL POC: Peter Zulch

Key Focus of Scientific ResearchDevelop efficient approaches for high dimensional data fusion for targettracking, joint sequential detection & tracking, and adaptive sensing.

RF Sensors

Sequential Detection

/Tracking

Acoustic

Sensors

Video

Cameras

Data Stream

Fusion.

.

.


Summary

Challenges:

highly nonlinear systems/measurementsheterogeneous/asynchronous sensor datalimited resources in distributed networked systems

AccomplishmentsNew Theory/Results

Joint sequential detection and trackingPreliminary results on sparsity based data fusionPreliminary results on fault tolerant source localization

Transition - DOD/Industry/Toolboxes

Collaboration/Summer Faculty Program with AFRL (mentors: Zulchand Huie)Collaboration with a company (IFT) on an Air Force STTR projectResearch Collaboration with Army Research Lab

Other performers on project

will recruit a student/post-doc


THEORY and Results: Joint Sparsity Based Data Fusion

Novelty: a new heterogeneous data-level fusion approach

Targets are sparse in discretized state space −→ joint sparse representationsof targets

Does not require knowledge of number of targets

Non-parametric and data driven: flexible and requires minimum priorinformation

Can handle non-linearity and discrete-time data (RF sensor and image data)

RF

Signals Joint Sparsity

Based Grid

Computation

for

Heterogeneous

Data Fusion

Joint Target Detection

& Estimation

FFT

Video

Images

Background

Subtraction

Intensity

Normalization

& Vectorization

Dim. Reduction

via Random

Projection

Magnitude

Normalization

Figure: Overview of the JSDLF fusion approach



At a reference time, target’s state is denoted as

x = [x0 y0 vx0 vy0 ]T

State space is discretized into NG grid points, and each grid point: a hypothesizedtarget stateHeterogeneous data are linked through target state grids:θ: RF signal amplitude in frequency domain; β: intensity of background-subtractedimage

Figure: Hypothesized target states and corresponding measurement representations. k:time, l : index for RF sensors.



Frequency domain signal amplitude and image intensity correspond to the sametargets −→ joint sparse signals

Θ = {θlk ,βk} (k = 1, · · · ,K ; l = 1, · · · , L− 1), a NG × (KL) matrix, has the

same non-zero support or is jointly sparse

Reconstruct Θ or its support (S-OMP, AMP, l1-l2 minimization, etc.)

Θ = {θlk ,βk} =

0 0 0 · · · 0∅ ∅ ∅ · · · ∅0 0 0 · · · 00 0 0 · · · 0∅ ∅ ∅ · · · ∅0 0 0 · · · 0...

......

. . ....

0 0 0 · · · 0

NG×(KL)

(There are 2 targets with 2nd and 5th hypothesized states.)



rlk : sampled signal at l-th RF sensor at time k (N × 1 vector)

rlk = F

−1B

lkθ

lk + n

lk

Blk : N × NG frequency selection matrix

Blk(i , j) = 1 if Doppler shift for the j-th hypothesized state corresponds to

i-th DFT frequency binF−1: inverse DFT matrix

βk : vectorized image data at time k (M × 1 vector)

yk = Akβk + wk

image data are large −→ use a N ×M random compression matrix

zk = Φkyk = ΦkAkβk +Φkwk

Based on {rlk , zk} over l and k, recover Θ or its support


Joint Sparsity Based Data Fusion: Numerical Results

Numerical examples (Niu et al., SPIE’17, Aerospace’18)

100 150 200 250 300 350 400 450 500

−5

−4

−3

−2

−1

0

1

2

3

4

Frame Number

Po

sit

ion

Err

or

Ea

st

(m)

100 150 200 250 300 350 400 450 500

−4

−2

0

2

4

6

8

Frame Number

Po

sit

ion

Err

or

No

rth

(m

)

(a) (b)

Figure: (a)A testing scenario with 4 RF sensors and 1 video camera (b) Targetposition estimation errors.


Joint Sparsity Based Data Fusion: Future Work

Extend from non-Bayesian parameter estimation to Bayesian target tracking

Instead of using uniform grid, adaptively quantize state space with aparticle/particle flow filter

Find analytical performance for proposed approach

RF Sensors

Target State

Information

Acoustic

Arrays

Video

Camera

Data Fusion

via JSDLF.

.

.

Particle

Filter

Propagated

Particles

Figure: Adaptive state space discretization based on particle filtering.


Joint Sequential Detection and Tracking: Motivation

For moving objects with very weak SNRs, the detector based on a single samplecannot deliver acceptable detection performance

The joint object detection and tracking approach has the potential to significantlyimprove the detection of extremely weak moving objects

Different from the existing algorithms, the proposed algorithm works in continuousstate space, without the knowledge of possible object trajectories, and does notrequire very informative prior knowledge

Sequential detector vs. fixed sample size (FSS) detector


Joint Sequential Detection and Tracking: Related Work

Joint object detection and tracking problem can be viewed as a special case of thegeneral joint detection and estimation problem.

Middleton and Esposito, IEEE T-IT, 1968.Baygun and Hero, IEEE T-IT, 1995.Fredriksen, Middleton, and VandeLinde, IEEE T-IT, 1972.Moustakides, Jajamovich, Tajer, and Wang, IEEE T-IT, 2012.Jajamovich, Tajer, and Wang, IEEE T-SP, 2012.

Existing joint detection and tracking approaches:

Track-before-detect algorithms, along-track integration, probabilityhypothesis density (PHD) filter and Bernoulli filter.

Our previous work on joint detection and tracking:

Niu, WPMC, 2013, which provides the optimal FSS detector.


Problem Formulation

Under hypothesis H1, state sequence xk is a first-order Markov process

xk+1 = Fxk + Γvk

F: state transition matrix, vk : independent white process noise with zero meanand variance Q, Γ: gain matrix for vk .

Observations are obtained according to the measurement equation

zk = Hxk + wk

H: measurement matrix, wk : independent white measurement noise with zeromean and variance Rw .

Under hypothesis H0, the measurement is purely noise

zk = uk

uk : i.i.d. Gaussian distributed with mean µ and covariance Ru.


Likelihood Ratio

Using chain rule, the likelihood function p(z1:K |H1) is

p(z1:K |H1) = p(z1|H1)

K−1∏

k=1

p(zk+1|z1:k ,H1)

If z1, · · · , zk are independent under H0, the likelihood function p(z1:K |H0) is

p(z1:K |H0) =

K∏

k=1

p(zk |H0)

The optimal test statistic, the likelihood ratio, is

Λ(z1:K ) =p(z1:K |H1)

p(z1:K |H0)=

p(z1|H1)∏K−1

k=1 p(zk+1|z1:k ,H1)∏K

k=1 p(zk |H0)


Log-likelihood Ratio

In the Kalman filter, p(zk+1|z1:k ,H1) is:

p(zk |z1:k−1,H1) = N (Hx̂k|k−1,Sk)

where Sk is the observation residue covariance provided by the KF

Under hypothesis H0,p(zk |H0) = N (µ,Ru)

The log-likelihood ratio can be written in the summation form

Λ(z1:K ) =K∑

k=1

logp(zk |z1:k−1,H1)

p(zk |H0)=

1

2t(z1:K )

in which

t(z1:K ) =

K∑

k=1

[

log|Ru|

|Sk |+ (zk − µ)TR−1

u (zk − µ)− (zk −Hx̂k|k−1)TS−1k (zk −Hx̂k|k−1)

]


Wald’s SPRT

Since the observations are dependent over time under hypothesis H1, in this casethe optimum detector is in the form of a generalized sequential probability ratiotest (GSPRT) 1.

Λ(z1:K )

≥ AK stop and decide H1

≤ BK stop and decide H0

otherwise continue

where AK and BK : thresholds that are functions of K . However, the determinationof AK and BK is still an open problem.

1Cochlar and Vrana, Kybernetika, 1978; Eisenberg, Ghosh, and Simons, The Annals of Statistics, 1976


Expected Values of the Test Statistic

Proposition

The expectation of test statistic t(z1:K ) under hypothesis H1 when using the KF is

provided as follows

E [t(z1:K )|H1]

=

K∑

k=1

{log|Ru|

|Sk |+ tr[R−1

u HFkP0|0(HF

k)T

+ R−1u

k−1∑

i=0

HFiΓQ(HF

iΓ)T + R

−1u Rw ]

+(

HFkx̂0|0 − µ

)T

R−1u

(

HFkx̂0|0 − µ

)

− nz}

(1)


Expected Values of the Test Statistic

Proposition

The expectation of test statistic t(z1:K ) under H0 when using the KF is

E [t(z1:K )|H0]

=K∑

k=1

{

log|Ru|

|Sk |+ nz

− tr

[

S−1k Ru + S

−1k

k−1∑

i=1

Bk,iWk−iRu(Bk,iWk−i )T

]

−

[(

I−k−1∑

i=1

Bk,iWk−i

)

µ− Bk,k x̂0|0

]T

S−1k

·

[(

I−k−1∑

i=1

Bk,iWk−i

)

µ− Bk,k x̂0|0

]}

(2)

where Bk,i = HF∏i−1

j=1 [(I−Wk−jH)F].


SPRT detector vs. FSS detector

10−4

10−3

10−2

10−1

100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of false alarm

Pro

ba

bili

ty o

f d

ete

ctio

n

Figure: ROC Curves for FSS detector (Meng and Niu, Fusion’15).

When SNR is −20dB, Pfa = 6.1× 10−4 and Pm = 1.4× 10−4.The ASN|H1 ≈ 10 and ASN|H0 ≈ 5 by using SPRT detector.To achieve the same or better performance, FSS detector needs 19 samples.


Conclusion

A new joint object detection and tracking algorithm based on Wald’s SPRT andthe Kalman filter has been proposed.

The first and second moments of the test statistic under H1 and H0 have beenderived, respectively.

The expected values of the test statistic are monotone functions of the number ofsamples, and they cross the threshold in a few samples.

The sequential detection approach detects a moving object with a small ASN andlow probabilities of error even under low SNR conditions, and it outperforms theoptimal FSS detector significantly.

A terminative joint sequential object detection and tracking approach: twohypothesis testing statistics cooperate with each other to guarantee that theWald’s SPRT procedure will eventually terminate

Future Work: extend to nonlinear settings


Accomplishments

Accomplishments

A journal paper on joint sequential detection and tracking, nearcompletion, to be submitted to IEEE Trans. on Information Theory

Transitions

Theories and algorithms will be transitioned to STTR program, AFRL,and ARL

Coordination/Synergy

Collaboration with Other PIs (Drs. Varshney and Chen from SyracuseUniversity)Ongoing collaboration with AFRL, ARL, and a small company


Appendix: Fault Tolerant Source Localization

Ongoing work, preliminary results published in Fusion’18


Source Location with Quantized Sensor Data Corruptedby False Information

Maitham Al-Salman and Ruixin Niu

Department of Electrical and Computer EngineeringVirginia Commonwealth University

Richmond, VA, USA

FUSION’18, University of Cambridge, UK

July 11, 2018

M. Al-Salman and R. Niu (VCU) Source Location with Quantized Sensor Data Corrupted by False InformationJuly 11, 2018 1 / 20

1 Motivation

2 Related Work

3 System Model

4 MLE-QRSS-GMM

5 CRLB Derivation

6 Simulation ResultsRMSE vs. Attack ProbabilityRMSE vs. Number of SensorsMLE-QRSS-GMM with Parameter Mismatch

7 Conclusion


Motivation

Sensor network measurement reliability issues

Crucial role of sensor networks’ applications

Secure state estimation in sensor networks under false informationinjection attacks (spoofing attack) is an important topic, which hasbeen studied recently

Sensor data can be corrupted due to natural interference, sensorfailure, or intentional false information injection by an adversary tomislead the fusion center (FC)


Related Work

Quantized received signal strength (Q-RSS)Niu and Varshney, IEEE T-SP, 2006.

Gaussian mixture model (GMM) in localizationYin et al., IEEE T-SP, 2015.Pfaf, Plagemann, and Burgard, IEEE ICRA , 2008.Zhang et al., IEEE Communications Letters, 2017.

False information injection attacks on state estimation (spoofingattacks)

Niu and Lu, CISS’15Lu and Niu, Fusion’14


System Model

We assume an isotropic signal attenuation model:

a2i =P0

(di )n(1)

ai : signal amplitude at the ith sensor.P0: radiated power by the target at a reference distance d0n: attenuation exponentdi : Euclidean distance.

di =√

(xi − xt)2 + (yi − yt)2 (2)

(xi , yi ) and (xt , yt): coordinates of the ith sensor and the targetrespectively.

Corrupted measurements of the attacked sensor:

ri = ai + bi (3)

bi : false information injected at the ith sensor.M. Al-Salman and R. Niu (VCU) Source Location with Quantized Sensor Data Corrupted by False InformationJuly 11, 2018 5 / 20

System Model

We assume bi follows a GMM:

bi ∼2∑

k=1

ωi ,kN (bi ; 0, σ2k)

ωi ,1 = 1− pa: probability of not being attackedωi ,2 = pa: attack probability, and σ22 > σ21


MLE-QRSS-GMM

Quantization process:

Di =

0 −∞ ≤ ri < ηi1

1 ηi1 ≤ ri < ηi2

: :

: :

L− 1 ηL−1 ≤ ri <∞

(4)

Quantized data vector D = [D1, · · · ,DN ]T .Di ∈ {0, · · · , 2M − 1}.M: number of quantization bits (L = 2M)


MLE-QRSS-GMM

Denoting the parameter vector as θ = [P0, xt , yt ]T , the MLE

problem is:θ̂ = arg max

θp(D|θ)

According to GMM :

pil(ηi ,θ) =2∑

k=1

ωi ,k

[Q

(ηil − aiσk

)− Q

(ηil+1 − ai

σk

)](5)

Joint probability:

p (D|θ) =N∏i=1

L−1∏l=0

[pil(ηi ,θ)]δl, Di (6)


MLE-QRSS-GMM

Log-likelihood :

log p(D|θ) =N∑i=1

L−1∑l=0

δl ,Dilog pil(ηi ,θ) (7)

where δi ,j is Kronecker delta function:

δi ,j =

{1 if j = i0 o.w.

MLE-QRSS-GMM:

θ̂ = arg maxθ

log p(D|θ) (8)


CRLB Derivation

Theorem

For an unbiased estimator θ̂(D), the CRLB is given by

E{

[θ̂(D)− θ][θ̂(D)− θ]T}≥ J−1 (9)

where J is the 3× 3 Fisher information matrix (FIM).

FIM elements:

j11 =N∑i=1

βid−2ni a−2

i

j12 = j21 = nN∑i=1

βid−(n+2)i (xi − xt)

j13 = j31 = nN∑i=1

βid−(n+2)i (yi − yt)

(10)


CRLB Derivation

j22 = n2N∑i=1

βia2i d

−4i (xi − xt)

2

j23 = j32 = n2N∑i=1

βia2i d

−4i (xi − xt)(yi − yt)

j33 = n2N∑i=1

βia2i d

−4i (yi − yt)

2

(11)

βi =1

8π

L−1∑l=0

1

pil(ηi ,θ)

[K∑

k=1

wi ,kγi ,l ,kσk

]2

γi ,l ,k = e− (ηil−ai )

2

2σ2k − e

− (ηil+1−ai )2

2σ2k


RMSE of MLE-QRSS-GMM vs. pa

10−2

10−1

100

2000

4000

6000

8000

10000

12000

14000

Attack probability pa

RM

SE

of P

0

nominal MLE

Q−RSS−GM

CRLB

10−2

10−1

100

2

4

6

8

10

12

14

16

18


RM

SE

of x

t in m

nominal MLE

Q−RSS−GM

CRLB

Figure: RMSE of MLE-QRSS-GMM vs. pa


RMSE of MLE-QRSS-GMM vs. pa

10−2

10−1

100

2

4

6

8

10

12

14

16

18


RM

SE

of y

t in m

nominal MLE

Q−RSS−GM

CRLB

Figure: RMSE of MLE-QRSS-GMM vs. pa


RMSE of MLE-QRSS-GMM vs. Number of Sensors(pa = 0.03)

8 10 12 14 16 18 201000

1500

2000

2500

3000

3500

4000

4500

5000

Square Root of Sensor Number

RM

SE

of P

0

nominal MLE

Q−RSS−GM

CRLB

8 10 12 14 16 18 202

3

4

5

6

7

8

9

Square Root of Sensor numberR

MS

E o

f x

t in m

ete

r

nominal MLE

Q−RSS−GM

CRLB

Figure: RMSE of MLE-QRSS-GMM vs. Number of Sensors (pa = 0.03)



8 10 12 14 16 18 202

3

4

5

6

7

8

9

Square Root of Sensor number

RM

SE

of y

t in m

ete

r

nominal MLE

Q−RSS−GM

CRLB

Figure: RMSE of MLE-QRSS-GMM vs. number of sensors (pa = 0.03)



8 10 12 14 16 18 201500

2000

2500

3000

3500

4000

4500

5000

5500

6000

Square Root of Sensor Number

RM

SE

of P

0

nominal MLE

Q−RSS−GM

CRLB

8 10 12 14 16 18 202

3

4

5

6

7

8

9

10

11

12

Square Root of Sensor numberR

MS

E o

f x

t in m

ete

r

nominal MLE

Q−RSS−GM

CRLB




8 10 12 14 16 18 202

3

4

5

6

7

8

9

10

11

12

Square Root of Sensor number

RM

SE

of y

t in m

ete

r

nominal MLE

Q−RSS−GM

CRLB



MLE-QRSS-GMM with Parameter Mismatch

Mismatches exist between true parameters and nominal parameters.MLE-QRSS-GMM is designed assuming pan = 0.05, but a different pa(pat ) is used by the attacker.

Table: RMSE of P0 for the Q-RSS-GM estimator with a mismatched pa

N pat = 0 pat = 0.01 pat = 0.05 pat = 0.1

144 2505.1 2505.6 2594.9 2714.0

256 1827.2 1847.0 1912.2 2026.6

400 1449.6 1460.3 1493.2 1571.1

Table: RMSE of xt for the Q-RSS-GM estimator with a mismatched pa

N pat = 0 pat = 0.01 pat = 0.05 pat = 0.1

144 4.0614 4.1942 4.4723 4.6697

256 3.0083 3.0859 3.3337 3.4781

400 2.3707 2.4047 2.7200 2.8098M. Al-Salman and R. Niu (VCU) Source Location with Quantized Sensor Data Corrupted by False InformationJuly 11, 2018 18 / 20

MLE-QRSS-GMM with Parameter Mismatch

Table: RMSE of yt for the Q-RSS-GM estimator with a mismatched pa

N pat = 0 pat = 0.01 pat = 0.05 pat = 0.1

144 4.1767 4.1357 4.4543 4.7472

256 3.0306 3.0286 3.2758 3.5819

400 2.4028 2.4592 2.4864 2.7359


Conclusion

1 Target localization in WSNs based on quantized RSS in the presenceof false information injection attacks studied.

2 Using Gaussian mixture model, we developed a maximum likelihoodestimator.

3 The proposed estimator is much more robust and efficient comparedto nominal MLE which ignores the possible attacks.

4 The corresponding CRLB has been derived to evaluate the estimationperformance.

5 Proposed method is robust to injected false information andparameter mismatch, and its performance reaches the CRLB as thenumber of sensors increases.

6 Ongoing work: an estimator that works with much less knowledgeabout the attacks.


Date post:	18-Mar-2020
Category:	Documents
Upload:	others
View:	4 times
Download:	0 times

Adaptive High Dimensional Data Fusion and Sensing for ... · Collaboration/Summer Faculty Program...

Documents