1. International Technology Alliance In Network & Information Sciences International Technology Alliance In Network & Information Sciences 1 A framework for QoI-inspired analysis for sensor network deployment planning Sadaf Zahedi EE Department, UCLA Chatschik Bisdikian T. J. Watson Research Center, IBM US

2. 2 Problem Statement Observation field Sensor deployment field S1S1 S2S2 S3S3 S4S4 S5S5 Event S * (t) designer Sensor-collected data Is QoI good enough? d1d1 d2d2 d3d3 d4d4 d5d5 Objective Goal: Evaluate, and ultimately optimize the quality of information (QoI) of the sensor networks, which support sensor-based applications QoI Definition: QoI is the collective effect of the (accessible) knowledge, derived from the sensor-collected data, to determine the degree of accuracy Event Detection is common in most of the sensor–based applications such as: surveillance and intelligence gathering, detecting presence of enemy weaponry, hostile activities (e.g., gunfire, explosion), and etc QoI attributes of importance for event detection class of applications are: Detection probability (P d ), of correctly detecting the occurrence of an event False alarm probability (P f ), of declaring the occurrence when it did not occur Error probability (P e ), of making any kind of error in decision

3. 3 detection subsystem event signature: signal s*(t) fusion subsystem fusion subsystem Fusion subsystem noise n(t) Communications M L signal propagation sensor subsystem (sampler) sensor subsystem Sensor subsystem Communications E?E? E?E? signal measurements y Samples of the Projection of the event signal s * (t) Anchored on the core analysis engine, a system-level analysis framework can be developed that contains the required system parameters, to provide the knowledge of the signal projections at the sensor locations. Core fusion & detection analysis engine Reference Detection System

4. 4 topology, cost constraints topology, cost constraints samplin g policy others propagation/ attenuation model sampling policy integration (e.g., averaging) optimization (e.g., select best deployment plan) signal s(t) signal(s) s * (t) measurement error model(s) core QoI analysis engine core QoI analysis engine propagation/ attenuation model(s) sampling policy(ies) integration (e.g., averaging) Planner provides deployment topology, QoI objectives, cost constraints, application domains, etc. Designer provides sample policies, and system models (libraries) Planner provides deployment topology, QoI objectives, cost constraints, application domains, etc. Designer provides sample policies, and system models (libraries) Deployment plan optimization (e.g., select best deployment plan) Detection Test Tools Input Pre-processing Output Post-processing noise model(s ) Good enough? What if scenarios …. Good enough? What if scenarios …. QoI Analysis Framework/Toolkit Architecture

5. 5 Core QoI Analysis Engine Binary Hypothesis testing: –Hypothesis H 1 : r i = s i +n i i=1,2,…,N event occurrence –Hypothesis H 0 : r i = n i i=1,2,…,N no event The Likelihood Ratio Test (LRT): –f R N |Hi (r N ) represents the pdf conditionen on H i – η=P 0 /P 1 Bayesian threshold Decision Test: –where C is the noise covariance matrix C=E{n T n} –n=[n 1,n 2,….,n N ]

6. 6 Fully Distributed Detection (L=M) vs. Centralized (L=1) Sensor Subsystem 1 Communication Fusion Subsystem 1 Make decision Based on the detection policy (Q) Local Decision 1 Sensor Subsystem 2 Sensor Subsystem M Fusion Subsystem 2 Communication Fusion Subsystem M Local Decision 2 Local Decision M Noise Fully distributed detection (L=M) Fusion Subsystem Make decision Centralized detection (L=1) system level QoI metrics local QoI metrics iterative calculation of QoI parameters

7. 7 Performance Comparison η=2 η=1 η=0.5 event S1 S2 S3 S4 d1d1 d3d3 d4d4 d2d2 Sampling Policy Same number of samples from each sensor Same sampling rate Signal Signature S*(t)=1-t 2 Attenuation Model a k =1/(1+d k 2 ) Delay Modelτ k =d k /v k Propagation Model S k (t)=a k S*(t- τ k ) η=P0/P1η=P0/P1

8. 8 Conclusion QoI-based framework for analyzing rather non-homogenous systems –For a finite number of sensors, transient signals, arbitrary sensor deployment, and different noise level at each sensor Framework facilitates –Decoupling of analysis approach in three steps (input preprocessing, QoI core analysis, output post processing) –Mix-and-match of different analysis, and modeling approaches Compared the centralized vs. distributed detection architectures with respect to QoI Influence of the priori knowledge on selection of the best detection policy for distributed schemes Future work Deployment algorithm which optimize both QoI and cost subject to constraints Extension of the noise models to models with spatio-temporal correlation Consider the measurement error models (i.e., errors from the faulty sensors, …)