Schizas pi meeting afosr
SPSS, University of Texas at Arlington
Jan. 28, 2016
A Distributed Data Driven Applications System for Multi-Threat Tracking Ioannis D. Schizas and Vasileios Maroulas Dept. of EE, Univ. of Texas at Arlington Dept. of Math, Univ. of Tennessee at Knoxville
Acknowledgment: AFOSR9550-15-1-0103 1
SPSS, University of Texas at Arlington
Project Collaborators PI @ UTA EE:
I. D. Schizas
Co-PI @ UTK Math:
V. Maroulas
Students:
G. Ren @ UTA EE
K. Kang @ UTK Math
2
SPSS, University of Texas at Arlington
Motivation q Ad hoc sensor network employed for tracking multiple targets using nonlinear sensor observations
➢ Perform sensing and tracking only with few informative sensors q Time-varying clusters of correlated sensors 3
SPSS, University of Texas at Arlington
Problem Setting
➢ Network with p sensors ➢ Data model:
: signal emanating from object
: distance of target ρ from sensor j 4
SPSS, University of Texas at Arlington
System Architecture
5
SPSS, University of Texas at Arlington
Sparsity-Based Sensing Adjustments q Set of sensors acquiring information about same object are correlated q Determine the correlated sets of sensors; Controlling active/inactive sensors ➢ Canonical correlation analysis combined with norm-one regularization ➢ Given data sequences
find q x p matrices E and D
ü CCA linearly extracts common features 6
SPSS, University of Texas at Arlington
CCA in Clustering Sensor Data
➢ In
our setting form two sequences: 'past’ of sensor measurements 'present+future’ of sensor measurements
➢ Common components in x(t) and y(t): State vectors sρ(t) ➢ CCA-based clustering:
7
SPSS, University of Texas at Arlington
Regularized CCA Formulation
➢ Norm-one regularization mechanisms [Schizas-Chen’15]
q q
are positive sparsity-controlling coefficients are positive penalty coefficients taking care of whiteness
➢ Employ coordinate descent mechanisms to minimize entry-by-entry
➢ ADMM to obtain distributed implementation 8
SPSS, University of Texas at Arlington
Distributed Sparse CCA ➢ Each sensor applied K ADMM iterations during coordinate cycle k to find estimates
➢ for k=1,2,3,... (coordinate cycle) ➢ ➢ for j=1,...,p
end for end for
q Convergence to a stationary point as iterations K and k go to infinity
➢ Communication cost proportional to t,
and M
9
SPSS, University of Texas at Arlington
Drift Homotopy Particle Filtering q Particle filters need a lot of particles when tracking multiple targets in order to approximate accurately the targets’ state distribution
q Introduce one extra MCMC step to move samples in statistically significant regions
q A drift homotopy/relaxation algorithm (Maroulas and Stinis ‘12)
10
SPSS, University of Texas at Arlington
Drift Homotopy Process
11
SPSS, University of Texas at Arlington
Drift Homotopy Algorithm
12
SPSS, University of Texas at Arlington
Remarks
13
SPSS, University of Texas at Arlington
Target’s State Model ➢ For target ρ the state (position+velocity) evolves according to:
➢ Data covariance matrix contains sparse factors that indicate which groups
of sensors acquire measurements about the same target 14
SPSS, University of Texas at Arlington
Tracking Multiple Targets q 120 sensors and 12 targets
q S-CCA and PF significantly improves tracking performance 15
SPSS, University of Texas at Arlington
RMSE Performance
q Our novel approach achieves the smallest root mean-square error 16
SPSS, University of Texas at Arlington
Number of Active Sensors
q No more than 18% of sensors are utilized; Selective sensing
SPSS, University of Texas at Arlington
Sensor Mobility q Exploit sensor mobility
q Design kinematic strategies
q DDDAS to move informative sensors
➢ Canonical Preliminary results: EKF/S-CCA combined with modified barrier method 18
SPSS, University of Texas at Arlington
Learning Unknown Models q Constantly changing state/observation models; E.g., maneuvering targets q Learning the time-varying models via online convex optimization
➢ Construct proper loss functions sequences; Quantify effectiveness of used model ➢ Acquired data will be used as feedback in model accuracy
SPSS, University of Texas at Arlington
1.
Publications
G. Ren, V. Maroulas, and I. D. Schizas, '' Distributed Spatio-Temporal Association and Tracking of Multiple Targets Using Multiple Sensors,'' IEEE Transactions on Aerospace and Electronic Systems, 2016.
2. G. Ren, V. Maroulas, and I. D. Schizas, '' Decentralized Sparsity-Based Multi-Source Association and State Tracking,'' Elsevier Signal Processing, vol. 120, pp. 627--643, March 2016 3.
G. Ren, V. Maroulas and I. D. Schizas, “Exploiting Sensor Mobility and Sparse Covariances for Distributed Tracking of Multiple Targets,” EURASIP Journal on Advances in Signal Processing, under review Oct. 2015.
4. V. Maroulas, K. Kang and I. D. Schizas, “Drift Homotopy and Likelihood Bridging Particle Filter.,” Elsevier Computational Statistics and Data Analysis, submitted Jan.2016 5. I. D. Schizas and V. Maroulas, “Dynamic Data Driven Sensor Network Selection and Tracking,” Elsevier Procedia Computer Science, vol. 51, pp. 2583– 2592, 2015. 6. G. Ren, I. D. Schizas and V. Maroulas, “Sparsity Based Multi-Target Tracking Using Mobile Sensors,” IEEE Intl. Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, 2016. 7. V. Maroulas, K. Kang, I. D. Schizas and M. W. Berry, “A Learning Drift Homotopy Particle Filter,” Proc. of the Intl. Conf. on Information Fusion, Washington, DC, pp. 1930–1937, July 6-9, 2015. 8. G. Ren, I. D. Schizas and V. Maroulas, “Distributed Spatio-Temporal Multi-Target Association and Tracking,”Proc. of IEEE Intl. Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia, pp. 4010–4014, 2015
SPSS, University of Texas at Arlington
Thank You! Questions? Comments?
SPSS, University of Texas at Arlington
Prior Art q Related sparse CCA formulations [Hardoon etal'08, Witten etal'09, Chen etal'12, Wiesel'08] ➢ Maximize correlation between two data sets and perform variable selection ➢ Not decentralized approaches q Sensor selection and clustering
➢ Data model parameters should be known/available; Find sleeping intervals [Gupta etal'06, Krishnamurthy etal'08, Fuemmeler etal'10, Joshi etal'09]
➢ Linear data models and memoryless sources [Schizas'13]
22
Jan. 28, 2016
A Distributed Data Driven Applications System for Multi-Threat Tracking Ioannis D. Schizas and Vasileios Maroulas Dept. of EE, Univ. of Texas at Arlington Dept. of Math, Univ. of Tennessee at Knoxville
Acknowledgment: AFOSR9550-15-1-0103 1
SPSS, University of Texas at Arlington
Project Collaborators PI @ UTA EE:
I. D. Schizas
Co-PI @ UTK Math:
V. Maroulas
Students:
G. Ren @ UTA EE
K. Kang @ UTK Math
2
SPSS, University of Texas at Arlington
Motivation q Ad hoc sensor network employed for tracking multiple targets using nonlinear sensor observations
➢ Perform sensing and tracking only with few informative sensors q Time-varying clusters of correlated sensors 3
SPSS, University of Texas at Arlington
Problem Setting
➢ Network with p sensors ➢ Data model:
: signal emanating from object
: distance of target ρ from sensor j 4
SPSS, University of Texas at Arlington
System Architecture
5
SPSS, University of Texas at Arlington
Sparsity-Based Sensing Adjustments q Set of sensors acquiring information about same object are correlated q Determine the correlated sets of sensors; Controlling active/inactive sensors ➢ Canonical correlation analysis combined with norm-one regularization ➢ Given data sequences
find q x p matrices E and D
ü CCA linearly extracts common features 6
SPSS, University of Texas at Arlington
CCA in Clustering Sensor Data
➢ In
our setting form two sequences: 'past’ of sensor measurements 'present+future’ of sensor measurements
➢ Common components in x(t) and y(t): State vectors sρ(t) ➢ CCA-based clustering:
7
SPSS, University of Texas at Arlington
Regularized CCA Formulation
➢ Norm-one regularization mechanisms [Schizas-Chen’15]
q q
are positive sparsity-controlling coefficients are positive penalty coefficients taking care of whiteness
➢ Employ coordinate descent mechanisms to minimize entry-by-entry
➢ ADMM to obtain distributed implementation 8
SPSS, University of Texas at Arlington
Distributed Sparse CCA ➢ Each sensor applied K ADMM iterations during coordinate cycle k to find estimates
➢ for k=1,2,3,... (coordinate cycle) ➢ ➢ for j=1,...,p
end for end for
q Convergence to a stationary point as iterations K and k go to infinity
➢ Communication cost proportional to t,
and M
9
SPSS, University of Texas at Arlington
Drift Homotopy Particle Filtering q Particle filters need a lot of particles when tracking multiple targets in order to approximate accurately the targets’ state distribution
q Introduce one extra MCMC step to move samples in statistically significant regions
q A drift homotopy/relaxation algorithm (Maroulas and Stinis ‘12)
10
SPSS, University of Texas at Arlington
Drift Homotopy Process
11
SPSS, University of Texas at Arlington
Drift Homotopy Algorithm
12
SPSS, University of Texas at Arlington
Remarks
13
SPSS, University of Texas at Arlington
Target’s State Model ➢ For target ρ the state (position+velocity) evolves according to:
➢ Data covariance matrix contains sparse factors that indicate which groups
of sensors acquire measurements about the same target 14
SPSS, University of Texas at Arlington
Tracking Multiple Targets q 120 sensors and 12 targets
q S-CCA and PF significantly improves tracking performance 15
SPSS, University of Texas at Arlington
RMSE Performance
q Our novel approach achieves the smallest root mean-square error 16
SPSS, University of Texas at Arlington
Number of Active Sensors
q No more than 18% of sensors are utilized; Selective sensing
SPSS, University of Texas at Arlington
Sensor Mobility q Exploit sensor mobility
q Design kinematic strategies
q DDDAS to move informative sensors
➢ Canonical Preliminary results: EKF/S-CCA combined with modified barrier method 18
SPSS, University of Texas at Arlington
Learning Unknown Models q Constantly changing state/observation models; E.g., maneuvering targets q Learning the time-varying models via online convex optimization
➢ Construct proper loss functions sequences; Quantify effectiveness of used model ➢ Acquired data will be used as feedback in model accuracy
SPSS, University of Texas at Arlington
1.
Publications
G. Ren, V. Maroulas, and I. D. Schizas, '' Distributed Spatio-Temporal Association and Tracking of Multiple Targets Using Multiple Sensors,'' IEEE Transactions on Aerospace and Electronic Systems, 2016.
2. G. Ren, V. Maroulas, and I. D. Schizas, '' Decentralized Sparsity-Based Multi-Source Association and State Tracking,'' Elsevier Signal Processing, vol. 120, pp. 627--643, March 2016 3.
G. Ren, V. Maroulas and I. D. Schizas, “Exploiting Sensor Mobility and Sparse Covariances for Distributed Tracking of Multiple Targets,” EURASIP Journal on Advances in Signal Processing, under review Oct. 2015.
4. V. Maroulas, K. Kang and I. D. Schizas, “Drift Homotopy and Likelihood Bridging Particle Filter.,” Elsevier Computational Statistics and Data Analysis, submitted Jan.2016 5. I. D. Schizas and V. Maroulas, “Dynamic Data Driven Sensor Network Selection and Tracking,” Elsevier Procedia Computer Science, vol. 51, pp. 2583– 2592, 2015. 6. G. Ren, I. D. Schizas and V. Maroulas, “Sparsity Based Multi-Target Tracking Using Mobile Sensors,” IEEE Intl. Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, 2016. 7. V. Maroulas, K. Kang, I. D. Schizas and M. W. Berry, “A Learning Drift Homotopy Particle Filter,” Proc. of the Intl. Conf. on Information Fusion, Washington, DC, pp. 1930–1937, July 6-9, 2015. 8. G. Ren, I. D. Schizas and V. Maroulas, “Distributed Spatio-Temporal Multi-Target Association and Tracking,”Proc. of IEEE Intl. Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia, pp. 4010–4014, 2015
SPSS, University of Texas at Arlington
Thank You! Questions? Comments?
SPSS, University of Texas at Arlington
Prior Art q Related sparse CCA formulations [Hardoon etal'08, Witten etal'09, Chen etal'12, Wiesel'08] ➢ Maximize correlation between two data sets and perform variable selection ➢ Not decentralized approaches q Sensor selection and clustering
➢ Data model parameters should be known/available; Find sleeping intervals [Gupta etal'06, Krishnamurthy etal'08, Fuemmeler etal'10, Joshi etal'09]
➢ Linear data models and memoryless sources [Schizas'13]
22
