iccs schizas
SPSS, University of Texas at Arlington
June 2, 2015
Dynamic Data Driven Sensor Network Selection and Tracking Ioannis D. Schizas and Vasileios Maroulas Dept. of EE, Univ. of Texas at Arlington Dept. of Math, Univ. of Tennessee at Knoxville http://www.uta.edu/faculty/schizas Acknowledgment: AFOSR9550-15-1-0103 1
SPSS, University of Texas at Arlington
Motivation Ad hoc sensor network employed for tracking multiple targets using nonlinear sensor observations.
➢
Only a few sensors are informative
2
SPSS, University of Texas at Arlington
Problem Setting ➢ Network with m sensors
➢ Targets spatially scattered ➢ Sensor j acquires
3
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 ➢ Canonical correlation analysis is enhanced here with norm-one regularization
to identify target-informative sensors and control the sensing process
4
SPSS, University of Texas at Arlington
Canonical Correlation Analysis ➢ Given
data sequences
CCA linearly extracts
common features
➢ Find
q x p matrices E and D such that
➢ Sample-average
covariance matrices
➢ Uncovering common targets present in both x(t) and y(t) 5
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
➢ Controlling memory length is possible ➢ Common components in x(t) and y(t): State vectors sρ(t) ➢ CCA based clustering:
6
SPSS, University of Texas at Arlington
Regularized CCA Formulation ➢ Enhance CCA with norm-one regularization mechanisms
➢ Sample-average expectation vectors
are positive sparsity-controlling coefficients are positive penalty coefficients taking care of whiteness
➢ Employ coordinate descent mechanisms to minimize entry-by-entry ➢ Consensus-averaging to obtain distributed implementation 7
SPSS, University of Texas at Arlington
Prior Art 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 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]
8
SPSS, University of Texas at Arlington
Algorithmic Matters ➢ Sparse CCA formulation
Utilize 'average-like' quantities
➢ dj and ej denote the jth column of D and E respectively; Updated at sensor j ➢ Replacing at coordinate cycle k-1 D and E in last two black terms with
9
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
Termination when e.g., Convergence to a stationary point as iterations K and k go to infinity
➢ Communication cost proportional to t,
and M 10
SPSS, University of Texas at Arlington
Drift Homotopy Particle Filtering Particle filters need a lot of particles when tracking multiple targets in order to approximate accurately the targets’ state distribution
Introduce one extra step to move samples in statistically significant regions
A drift homotopy/relaxation algorithm
11
SPSS, University of Texas at Arlington
Drift Homotopy Process
12
SPSS, University of Texas at Arlington
Drift Homotopy Algorithm
13
SPSS, University of Texas at Arlington
Remarks
14
SPSS, University of Texas at Arlington
Joint Sensor Selection and Tracking
15
SPSS, University of Texas at Arlington
Tracking Multiple Targets
16
SPSS, University of Texas at Arlington
RMSE Performance
Our novel approach achieves the smallest root mean-square error 17
SPSS, University of Texas at Arlington
Concluding Remarks ➢ Sensor selection clustering via CCA and norm-one regularization
➢ Determining groups of correlated data; Multiple tracking processes
➢ Improved drift homotopy algorithms for tracking
Thank You! 18
June 2, 2015
Dynamic Data Driven Sensor Network Selection and Tracking Ioannis D. Schizas and Vasileios Maroulas Dept. of EE, Univ. of Texas at Arlington Dept. of Math, Univ. of Tennessee at Knoxville http://www.uta.edu/faculty/schizas Acknowledgment: AFOSR9550-15-1-0103 1
SPSS, University of Texas at Arlington
Motivation Ad hoc sensor network employed for tracking multiple targets using nonlinear sensor observations.
➢
Only a few sensors are informative
2
SPSS, University of Texas at Arlington
Problem Setting ➢ Network with m sensors
➢ Targets spatially scattered ➢ Sensor j acquires
3
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 ➢ Canonical correlation analysis is enhanced here with norm-one regularization
to identify target-informative sensors and control the sensing process
4
SPSS, University of Texas at Arlington
Canonical Correlation Analysis ➢ Given
data sequences
CCA linearly extracts
common features
➢ Find
q x p matrices E and D such that
➢ Sample-average
covariance matrices
➢ Uncovering common targets present in both x(t) and y(t) 5
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
➢ Controlling memory length is possible ➢ Common components in x(t) and y(t): State vectors sρ(t) ➢ CCA based clustering:
6
SPSS, University of Texas at Arlington
Regularized CCA Formulation ➢ Enhance CCA with norm-one regularization mechanisms
➢ Sample-average expectation vectors
are positive sparsity-controlling coefficients are positive penalty coefficients taking care of whiteness
➢ Employ coordinate descent mechanisms to minimize entry-by-entry ➢ Consensus-averaging to obtain distributed implementation 7
SPSS, University of Texas at Arlington
Prior Art 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 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]
8
SPSS, University of Texas at Arlington
Algorithmic Matters ➢ Sparse CCA formulation
Utilize 'average-like' quantities
➢ dj and ej denote the jth column of D and E respectively; Updated at sensor j ➢ Replacing at coordinate cycle k-1 D and E in last two black terms with
9
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
Termination when e.g., Convergence to a stationary point as iterations K and k go to infinity
➢ Communication cost proportional to t,
and M 10
SPSS, University of Texas at Arlington
Drift Homotopy Particle Filtering Particle filters need a lot of particles when tracking multiple targets in order to approximate accurately the targets’ state distribution
Introduce one extra step to move samples in statistically significant regions
A drift homotopy/relaxation algorithm
11
SPSS, University of Texas at Arlington
Drift Homotopy Process
12
SPSS, University of Texas at Arlington
Drift Homotopy Algorithm
13
SPSS, University of Texas at Arlington
Remarks
14
SPSS, University of Texas at Arlington
Joint Sensor Selection and Tracking
15
SPSS, University of Texas at Arlington
Tracking Multiple Targets
16
SPSS, University of Texas at Arlington
RMSE Performance
Our novel approach achieves the smallest root mean-square error 17
SPSS, University of Texas at Arlington
Concluding Remarks ➢ Sensor selection clustering via CCA and norm-one regularization
➢ Determining groups of correlated data; Multiple tracking processes
➢ Improved drift homotopy algorithms for tracking
Thank You! 18
