Target Tracking and Classification using Collaborative Sensor Networks

Transcription

1 Target Tracking and Classification using Collaborative Sensor Networks Xiaodong Wang Department of Electrical Engineering Columbia University

2 p.1/3 Talk Outline Background on distributed wireless sensor networks Single target tracking A Multiple target tracking and classification

3 Distributed Wireless Sensor Networks p.2/3

4 A sensor network is composed of a large number of sensor nodes, which are densely deployed either inside the phenomenon or very close to it. Random deployment Cooperative capabilities

5 Network Technology Computational Power Sensor Network Sensor Technology

6 MANET WSN High Mobility Peer to Peer model Low number of nodes Energy constraint not too critical No redundancy in data Connected to global network Commercial user end applications Low mobility (most cases!) Peer to peer or masterslave Large number of nodes Very severe energy constraint Some redundancy in data Local network Back end monitoring and data collection

7 Evolution of WSN Characteristic Generation1 Generation 2 Generation3 Timeline Size Large shoe box or bigger Pack of cards Weight Kilograms Grams Negligible Dust particle (MEMS) Node Architecture Separate sensing, processing and communication Integrated sensing, processing and communication Topology Pont to point, star Client server, peer to peer Integrated sensing, processing and communication Peer to peer Power supply lifetime Large batteries, hours to days AA batteries, days to weeks Solar, months to years Deployment Vehicle placed or air drop single sensors Hand emplaced Embedded, sprinkled left behind

8 p.3/3 Single Target Tracking via Collaborative Sensor Network Actual trajectory Estimated trajectory by OPT Estimated trajectory by PNN Estimated trajectory by NN Sensors Y (m) X (m)

9 p.4/3 Sensor network architecture Sensor nodes are scattered in a field. Nodes collect data and route data back to the sink via a multihop wireless medium. Each node has limited energy and only performs on-demand processing tasks upon a query. Otherwise it is a standby mode. Each node extracts relevant summary statistics from the raw data which are stored locally inside the node, and may be transmitted to other nodes upon request. To infer global information, the sensor network must facilitate efficient hierarchical information fusion.

10 p.5/3 Signal model Motion model: x t = {x t,y t,vt x,vy t } x t+ t = I 2 ti 2 0 I 2 x t + t2 2 I 2 ti 2 u t, Σ u = diag(σ 2 x, σ 2 y). Measurement model: Relative Distance Model: h(x t ) = K 10η log 10 ( (yt ȳ t ) 2 + (x t x t ) 2) Relative Angle Model: ( ) yt ȳ t h(x t ) = arctan x t x t

11 p.6/3 Cluttered noise model Measurements: Correct measurement if the target is detected Incorrect measurements from clutters. m f : number of false alarms. P(m f = k) = e λv (λv )m f m f!, k = 0, 1, 2,... V : volume of the observation area λ: number of false alarms per unit volume

12 p.7/3 Problem statement m t : number of measurements from target or false alarms at time t z t = {z m t } m t m=1 : set of measurements at time t Z t = {z j } t j=1 : set of measurements up to t Define events = {z m t is the target oriented measurements}, m = 1, 2,...,m t, θ m t θ 0 t = { none of the measurements at time t is the target oriented} P(θ m t m t ) = P D P G m t, m = 1,...,m t, 1 P D P G, m = 0. Goal: perform online estimation of p(x t Z t ) based on Z t at densely employed sensor nodes.

13 p.8/3 Sensor Selection Suppose at time t, sensor l is the leader node and holds the belief p(x t Z t ). For the new leader node at time t + 1, we select sensor s that achieves the maximum information gain of x t+1 conveyed by the new measurement z t+1,s I(x t+1,z t+1,s Z t ) = H(x t+1 Z t ) H(x t+1 Z t,z t+1,s ) In practice, the new observation z t+1,s is not available yet at time t.

14 p.9/3 Sensor Selection I(x t+1,z t+1,s Z t ) = H(x t+1 Z t ) H(x t+1 Z t,z t+1,s ) Need to estimate the measurement z t+1,s from the predicted belief at time t and use an expected likelihood function ˆp( z t+1,s x t+1 ) Then calculate the entropies using ˆp (x t+1 z t+1,s,z t ) = ˆp ( z t+1,s x t+1 )p(x t+1 Z t ).

15 p.10/3 SMC data fusion Let sensor l be the leader node at time t, which samples {X (j) t 1,w t 1} (j) N j=1 of p(x t 1 Z t 1 ). Let x t be the target state and z t = {z m t } m t m=1 be a set of validated measurements Denote X t = {X t 1,x t } and Z t = {Z t 1,z t }. We are interested in the on-line estimation of the new belief state p(x t Z t ). Use an auxiliary particle filter that resamples at the previous time step, based on some µ (j) t that characterize p(x t X (j) t 1).

16 p.11/3 SMC data fusion 1. For each i = 1,...,N, compute the point estimate of µ i t extended Kalman filter or one step prediction based on x i t For j = 1,...,N, do the following steps: (a) Sample an auxiliary integer variable from the set with probabilities proportional to by the g (i) t w (i) t 1 p(z t µ (i) t ); call the sampled index i (j). (b) Sample a value of the current state vector x (j) t xt 1 i(j). (c) Evaluate the corresponding weight. based on the

17 p.12/3 Entropy calculation Need to calculate the entropy of expected posterior distribution based on the discrete belief state {x (j) t,w (j) t } N j=1. Using the trial distribution q(x t+1 ) = p(x t+1 x (j) t,z t ), draw samples {X (j) t+1,w(j) t+1 )}N j=1 Then {X (j) t+1,w(j) t+1 )}N j=1 respect to p(x t+1 Z t ). with w(j) t+1 = w(j) t. is properly weighted with

18 Entropy calculation The expected posterior belief for sensor s can be represented by the discrete belief state {x (j) t+1, w(j) t+1,s }N j=1 w (j) t+1,s ˆp( z t+1,s x (j) t+1 ) = N Entropy calculation: = ˆp( z t+1,s x (j) t+1 )w(j) t+1 k=1 p (z t+1,s (x (k) t+1 ) x(j) t+1 )w(k) t+1 H(x t+1 Z t,z t+1,s ) = N j=1 w (j) t+1,s log w(j) t+1,s p.13/3

19 p.14/3 Kernel Smoothing Kernel density estimate based on samples: p(x t Z t ) = N w (j) t N ( x t m (j) t,h 2 V t ) j=1 with m (j) t = ax (j) t + (1 a) x t, a = 1 h 2. Instead of resampling from discrete samples, can resample from the continuous approximation, which can mitigate the degeneracy problem. Can collapse mixture components by replacing nearest pairs with a single averaged one reduce communication overhead between sensors.

20 p.15/3 Summary The initial leader node a does the following: 1. Draw initial samples {x (j) 0, w(j) 0 = 1} N j=1 information; 2. Update the belief state {x (j) 1, w(j) 1 }N j=1 measurement z 1 at leader node a; of the target from the prior based on the new 3. Compute the expected posterior belief state {x (j) 2, w(j) 2,i }N j=1 for each neighbor node i; 4. Compute the entropy of the expected posterior belief state {x (j) 2, w(j) 2,i }N j=1 for each neighbor node i, and determine the next best sensor, say b;

21 p.16/3 Summary 5 { Compute the kernel representation } of the belief state {m (j) 1, w(j) 1 }N j=1, h, V t and collapse the kernel smoothed belief state; 6 { Hand off the collapsed kernel representation { m (j) 1, w(j) 1 }K j=1, h, } V 1 to b. Node b takes the role of the leader, and it does the following: 1. Resample the belief state {x (j) 1, w(j) 1 = 1} N j=1 based on the the { collapsed kernel representation { m (j) 1, w(j) 1 }K j=1, h, } V 1 by the kernel-based reampling algorithm;

22 Summary 2 Update the belief state {x (j) 2, w(j) 2 = 1} N j=1 by the sensor fusion algorithm based on the new measurements z 2 and the belief state {x (j) 1, w(j) 1 = 1} N j=1 ; 3 Compute the expected posterior belief state {x (j) 3, w(j) 3,i }N j=1 for each neighbor node i with the weights w (j) 3,i ; 4 Compute the entropy on the expected posterior belief state {x (j) 3, w(j) 3,i }N j=1 for each neighbor node i, and determine the next best sensor, say c; 5 { Compute the kernel representation } of the belief state {m (j) 2, w(j) 2 }N j=1, h, V 2 and collapse it; 6 { Hand off the collapsed kernel representation { m (j) 2, w(j) 2 }K j=1, h, } V 2 to c; p.17/3

23 p.18/3 Simulation Results Localization s6 s6 bias Source Sensor Posterior mean estimate s5 s3 s5 50 Y (m) s1 s4 s2 s X (m) 1480 s s s X (m) X (m)

24 p.19/3 Simulation Results Tracking Actual trajectory Estimated trajectory by OPT Estimated trajectory by PNN Estimated trajectory by NN Sensors Y (m) X (m)

25 Multiple Target Tracking and Classification p.20/3

26 p.21/3 Multi-Target Tracking/Classification Densely scattered sensor nodes able to communicate with their neighbors and to process information. Multiple target tracking: sequential estimation the state of a possibly varying number of objects Classification: identification of those objects down to a given class motion model False detections: measurements arising from the clutter Unknown origin of the measurements complex data association problem

27 Multi-Target Tracking/Classification Sensor collaboration easier, localized tasks single target algorithm with (dis)appearing target Sensors Actual track 1 Actual track 2 Estimation, target 1 Selected sensors (1) Estimation, target 2 Selected sensors (2) Y(m) X(m) p.22/3

28 p.23/3 Leader-based Tracking Operations performed by a leader node [?] in multiple-target tracking and classification:

29 p.24/3 Target Dynamics The dynamic of the system is decomposed into x t,i = F γt,i (x t 1,i,u t,i ), i T t, γ t,i = γ t 1,i, i T t. T t, set of active targets x t,i, position and velocity of the i th target γ t,i, class of the i th target u t,i, independent white noise terms

30 Sensing Model The general model for the measurements is z m t = H t (x t,at (m),v t,m ), m {m a t (m ) 0}, z m t p c (z), m {m a t (m ) = 0}. z m t, m th measurement a t, data association vector H t, measurement function (e.g. power measurement) p c, clutter measurements distribution (e.g. uniform in the power range) The number of clutter measurements, m 0 t, typically arises from a poisson distribution. p.25/3

31 p.26/3 Measurements Likelihood Computation of the conditional distribution of the measurements enumeration of all possible data associations p(z t X t,r t ) = a t p(z t X t,r t,a t )p(a t r t,m t ). Having the dynamic of the system and the conditional distribution of the measurements we can now apply the SMC methodology to solve for the posterior distribution.

32 p.27/3 Single Target Tracking/Classification We compare several classes of dynamic models. 1 st approach: include the class in the state vector Problematic because of the fixed model for the class All particles eventually settle in one class can use a separate filter for each class We propose to modify the resampling scheme

33 Class-based Resampling Draw the number of particles for each class N γ according to { ˆP(γ Z 0:t )} γ Λ. If N γ < N Threshold, set N γ = N Threshold. Reduce the number of particles from the class with the most particles until γ Λ N γ = N. Draw N γ sample streams {X (J) 0:t } from {X (j) 0:t } j {j γ (j ) =γ} t weights {w (j) t } j {j γ (j ) t =γ}. with probability proportional to the Assign equal weight to each new sample within a class i.e. w (J) t = ˆP(γ (J) Z 0:t ) N. γ (J) p.28/3

34 p.29/3 Jump Markov Systems Varying number of targets can be dealt through Hypothesis testing Assuming a dynamic on the number of targets r t We consider a markovian evolution of r t π rt,r t 1 = p(r t r t 1 ) This model is referred as jump Markov Systems (JMS).

35 p.30/3 Choice of the Sampling Density Optimal density is intractable and its approximation are computationally heavy Main problem resides in the density for the number of targets we approximate only the optimal density for the number of targets p(r t X (j) t 1,r(j) t 1,Z t) p(z t X (j) t 1,r(j) t 1,r t)p(r t r (j) t 1 ) q(r t X (j) t 1,r(j) t 1,Z t) p(z t µ (j) t (r t ))p(r t r (j) t 1 ) µ (j) t,i = E[x t,i x (j) t 1,i,γ i]

36 p.31/3 Sensor Selection Scheme Information driven sensor selection s t, sensor chosen at time t s t+1 = arg max s ( Eps (Z t+1 Z 1:t ) [αυ utility (s) + (1 + α)υ cost (s)] ) E[Υ utility (s)] = I s (x t+1,1 ; z t+1 Z 1:t ) Approximation using Monte Carlo Integration from the available samples

37 p.32/3 Simulation Scenario We consider the tracking of two crossing targets from 2 different classes The first is initially tracked The second is initially unknown Probability of detection: 0.95 Average clutter measurements/time step: 1 Field: m 2 covered by 300 randomly scattered sensor nodes Sensing range: [4m, 50m]

38 Tracking Results Actual and estimated trajectories with an unknown target Sensors Actual track 1 Actual track 2 Estimation, target 1 Selected sensors (1) Estimation, target 2 Selected sensors (2) Y(m) X(m) p.33/3

39 p.34/3 Target Detection Results Probabilities of having two targets in the field: (left) first leader node; (right) newly generated second leader node. Probability of having two targets Time Probability of having two targets Generation of the second leader node Time

40 p.35/3 Classification Results Probabilities that the first target of the leader node is from the first class: (left) first leader node; (right) newly generated second leader node. 1 1 Probability of being in class Time Probability of being in class Generation of the second leader node Time

41 p.36/3 Conclusions SMC provides a unique capability for supporting in-network distributed signal processing in non-linear and/or non-gaussian environments. Developed leader-based tracking multi-target tracking and classification algorithm based on SMC filtering. Developed a class-based resampling procedure to avoid the loss of plausible classification hypothesis during the early stage of tracking. Developed an SMC implementation of an optimal sensor selection scheme based on expected information gain.