Sensor Networks for the Detection and Tracking of Radiation and Other Threats in Cities
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1 Fakultät Informatik Institut für Systemarchitektur Professur Rechnernetze Sensor Networks for the Detection and Tracking of Radiation and Other Threats in Cities Annie H. Liu, Julian J. Bunn, K. Mani Chandy Presenter: Mariam Zia Supervisor: Dr.-Ing. habil. Waltenegus Dargie Chair of Computer Networks TU Dresden
2 Introduction FUKUSHIMA nuclear reactor raises a threat to the whole man kind. radiation affects even the milk products and the vegetables in Japan. Nuclear radiations can cause Blood cancer Destruction of blood vessels and even DEATH and many more Germany: Nuclear power plants to close by BBC News Folie 2
3 Contribution Approach for detecting and tracking radiation threats Three scenarios Detecting static threats in open fields Bayesian,Parametric and Integrated Algorithm Sensor Threat Folie 3
4 Contribution Approach for detecting and tracking radiation threats Three scenarios Detecting static threats in open fields Bayesian,Parametric and Integrated Algorithm Tracking mobile sources in open fields Integrated Algorithm, Modified Bayesian and parametric algorithm j Sensor Base Station Threat j Folie 4
5 Contribution Approach for detecting and tracking radiation threats Three scenarios Detecting static threats in open fields Bayesian,Parametric and Integrated Algorithm Tracking mobile sources in open fields Integrated Algorithm, Modified Bayesian and parametric algorithm Threat detection in city streets Optimizing number of sensors and speed Optimal strategy for patrolling Folie 5
6 Contribution Approach for detecting and tracking radiation threats Three scenarios Detecting static threats in open fields Bayesian,Parametric and Integrated Algorithm Tracking mobile sources in open fields Integrated Algorithm, Modified Bayesian and parametric algorithm Threat detection in city streets Optimizing number of sensors and speed Optimal strategy for patrolling Algorithm that optimize sensor placement Folie 6
7 Problem definition Network of identical sensors Base station Knows location of sensors M sensors j 1,, M S j = location of sensor PDF = μ, D, S j, t μ = photons/ second D = location of threat n j t = Measurement by sensor j in time interval,0 t- j Determine Threat present or not? Location of threat? Magnitude of threat? Sensor S j = *x, y, z+ n j t = A j Message (n j t, t) Base Station Threat Folie 7
8 Background noise Sources Challenges brick, rocks, concrete,etc. and sensors Two options to model Homogeneous noise background noise uniform Heterogeneous noise Difficult to make a priori estimate about noise Need the knowledge of radioactive materials present Folie 8
9 SCENARIO 1: Detecting static threats in open fields Folie 9
10 Integrated Detection Algorithm Parametric Algorithm Priors construction Bayesian Algorithm Detected? Localized? Parametric Algorithm Ksigma Background noise Threat location Threat Intensity Probability of source present Bayesian Algorithm Takes as input a priori probability Calculates a posteriori probability Requires good prior estimates Parameters estimated by K sigma Algorithm Folie 10
11 K-Sigma Algorithm Dynamic sensor grouping Values from all the sensors are not relevant Grouping of sensors using Delaunay triangulation Partitions the space into triangles Ksigma Priors construction Bayesian Detected? Localized? Folie 11
12 K-Sigma Algorithm Detected? Ksigma Priors construction Bayesian Estimating background radiation Assume that background noise is uniform Break region into quadrilateral cells Cell count: total number of photons count in each cell Cell with minimum average photon count as background count Localized? Folie 12
13 K-Sigma Algorithm Detected? Ksigma Priors construction Bayesian Estimating whether a threat is present Four possible source configurations a,b,c,d Estimate average count from each single sensor, pair of sensors (edge), sensors at corner of triangles and each cell. Compute the number of standard deviations k sigma as ksigma = (N Γ)/ Γ N = groups aggregate radiation count Γ = groups aggregate count form background estimate Localized? Γ = standard deviation of process c b a d Folie 13
14 Estimating threat intensity Photon count from the background at one sensor (Γ) Photons measured at sensor j (n j ) Flux decreases as 1/ s j x 2 Intensity estimate for sensor j for source located at x μ j x x n j Γ = v j where vj x = C μ S j x 2 j x T μ j x = v j x C T = Intensity of source at location x C = Constant of proportionality T = Time interval K-Sigma Algorithm Ksigma Priors construction Bayesian Detected? Localized? Folie 14
15 Estimating source location K-Sigma Algorithm Select quadrilateral with largest value of k sigma Compute v j (x) for all sensors in this quadrilateral for all x Find location x most consistent to threats location by computing the variance estimate m L x = v j x v x j=1 2 Ksigma Priors construction Bayesian Detected? Localized? v 1 (x 1 ) where v j x = (n j Γ) S j x 2 1 x 2 x 3 x 1 2 v 2 (x 1 ) x 4 3 v 3 (x 1 ) x 5 4 v 4 (x 1 ) Folie 15
16 Bayesian Algorithm Detected? Ksigma Priors construction Bayesian Compute a posteriori probability distribution based on a given priori distribution and likely hood values Localized? π θ = L θ; n π 0 (θ) π 0 = prior PDF π = posterior PDF θ = parameters we want to estimate L is the likelihood of observing n = n 1, n 2. n 3,, n m photons at detector j = 1,2,, m If a posteriori exceeds the threshold then we say a source is present or not. Folie 16
17 Simulation static source From Simulation for Detection and localization Radiation sensor used IPRL (Intelligent Portable Radiation Locator) grid 9 sensors Source 1mCi Cesium-137 Folie 17
18 Simulation Results static source T = 9 sec ROC- Detection results 30% of time localizes within 10 m DOCA- Localization results <20% of time localizes within 10 m T = 60 sec 80% of time localizes within 10 m 40% of time localizes within 10 m Folie 18
19 From testbed setup 3 2 grid 6 IPRL-6 sensors Source Cesium-137 Detection threshold= 0.5 Localization computed after detection At T = 60 shielding was removed Testbed Results static source Bayesian algorithm with prior probability of source present = 0.1 Source shielded Detection Results m Localization results Folie 19
20 SCENARIO 2: Tracking mobile sources in open fields Folie 20
21 Modified Parametric Algorithm Integrated Detection Algorithm Priors construction Modifications to parametric algorithm Compute adjusted weighted sum of all measurements Exponentially decay weights of old measurements T W = n t e (t T)/T 0 t=0 Modification to Bayesian Algorithm Kalman filter- used for object tracking Equal probability of moving in all directions Modified Bayesian Algorithm T 0 : decay constant Detected? Localized? Allows for smooth weight transfer by redistributing the weight of current source position estimate x to its neighbor y within radius R Z is the redistribution factor π D = y π D = y + Z π(d = x ) R2 π D = x (1 Z) π(d = x ) Folie 21
22 Simulation Results moving source Trajectory A Trajectory B The integrated algorithm shows slight improvement over parametric method in tracking a weak moving source Slide from [3] Folie 22
23 Testbed Results moving source Trajectory A 3.5 m 15 m Trajectory A Trajectory B 20 m Trajectory B Slide From [3] Folie 23
24 SCENARIO 3: Threat detection in city streets Folie 24
25 Threat Detection in City Street Background data collected by two large NaI scintillators placed in rear of van Simulated Road Side detection Detectors travel city street at constant speed 1mCi unshielded isotropic source placed at random K sigma threshold used to tell if threat present When detected simulation run terminated and record the elapsed time for detection Officers search nearby area Folie 25
26 Threat Detection in City Street How many sensors do we need? How fast should the sensor move? Folie 26
27 Threat Detection in City Street What should be the travelling strategy? Equal probability? Suboptimal Deterministic manner? Can be exploited Probabilistic strategy that specify the probability of given turn. Maximize the minimum flow among all streets Folie 27
28 OPTIMIZING SENSOR PLACEMENT Folie 28
29 Detection function definition Ability of a sensor to make correct detection decision drops as the sensor moves away from anomaly F = TPR map = 1 (1 Φ N (λ x, Γ(s))) x N n=1 dx Φ N = TPR sensor N = total number of sensors λ = f μ, x, s Signal strength Γ = s Noise strength Folie 29
30 Greedy Approximate Algorithm Algorithm for preferred placement of static threats Goal is to maximize detection function F at each step Guaranteed to perform at least a fraction of 1 1/e if function is monotone (preserves the order) Log F N + 1 Log F N 0 ten F N + 1 F(N) 0 submodular (incremental value of object diminishes in a larger context) Folie 30
31 9 seconds 600 seconds Simulation results Non-uniform background The computed placement outperforms the even-spacing placement. Folie 31
32 Comparison Approaches Current approach A Controlled Search for Radioactive Point Sources Sources Static and mobile sources Detection time 100s s Only for Static sources localization error 6.6m m 4.7m 8.6m Folie 32
33 References [1] Annie H. Liu, Julian J. Bunn, K. Mani Chandy Sensor Networks for the Detection and Tracking of Radiation and Other Threats in Cities [2] B Ristic, M Morelande, and A Gunatilaka. A controlled search for radioactive point sources. [3] Slides from talk of Annie H.Liu Folie 33
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