COMP 5900B Wireless Ad Hoc Networking

Instructor: Professor Ivan Stojmenovic (SITE, U of O )

Target Tracking in Wireless Sensor Networks

Prepared by –Tahsin Arafat Reza

4 March 2010

Carleton University University of Ottawa

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Contents

• Topic background • Target tracking in WSN• Challenges• Research approach• Tracking moving objects• Kalman Filter

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Background

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Tracking

• Tracking involves updating static locationestimates using a motion model

(Logical module)

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Target Tracking in WSN

• Distributed observation and control of mobile objects via static (relative) wireless sensors

• Exposure is directly related to coverage in that it is a measure of how well an object, moving on an arbitrary path, can be observed by the sensor network over a period of time

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Applications

• Incrementally track spatiotemporal changes of objects in the environment

• Location based communication• Surveillance• Emergency response• Industrial settings

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Challenges• Real time decision making• High frequency sampling• Multi-model sensing• Complex signal processing• Energy consumptions• Fault tolerant• Load balancing• Data fusion• Determining the location• Localization or positioning• Tracking• Accuracy

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Research Approaches

• Probabilistic Coverage• Radio Interferometry• Active / Passive mobile devices• Binary Detection • Agent based• Fuzzy Inference• Model free (training data)

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Assumptions

• Target is roaming in a WSN• We do not worry about how we get the

location information of the sensors them selves

• We do not worry message propagation or routing within the network

• We only care about tracking the moving object in a distributed manner

• Moving object is not an actuator

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Tracking an Object in WSN• Agent based (master-

slave agents)• Determining the

position using trilateration

• Selection of next node to be assigned as the master (based on estimating the motion if the moving object).

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Particle Filters: State Estimation

• Bayesian estimation• Alpha-Beta Filters• Markov Model• Gaussian Probability Model• Kalman Filter• Hybrid Models

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Kalman Filter

• Rudolph E.Kalmanin 1960

• Recursive data processing algorithm that estimates the state of a noisy linear dynamic system

• Stochastic estimation from noisy sensor measurements

• State-Space Model

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Assumptions for linear KF

• Noise distribution is assumed to be Gaussian

• Process noise has zero mean

State t State t+1 State t+3State t+2

State Transition Process

State Transition Process

State Transition Process

Measurement Measurement Measurement Measurement

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Kalman Filter (linear)State Transition:

A – State transition matrix (m x m matrix where m is the number of parameters that describe the state)

wt – Noise term (assumed to be independent of state xt )

Q – Process noise covariance matrix (accounts for change in process between t and t+1)

States are connected to each other through the physics underlying object motion

ttt wAxx 1

),0()( QNwp

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Kalman Filter (linear)

Measurement Model:

C – matrix relating State and Measurement (m x n matrix, estimated noise free measurement at a given state. n is the number of measured parameters)

vt – Noise term

R – Measurement noise covariance matrix

ttt vCxy

),0()( RNvp

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Kalman Filter: Recursive Algorithm

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KF Simulation Example

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Variations of KF

• Extended Kalman Filter (EKF) – non-linear model

• Multiple model Kalman Filters: Interacting Multiple Model (IMM)

• Unscented Kalman Filter (non-linear)• Ensemble Kalman Filter (allows millions of

state parameters)

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Application of Kalman Filter

• Autonomous or assisted navigation• Control systems• Tracking in interactive computer graphics• Motion prediction• Statistical decision

theory

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References• Moaveni-Nejad, K. & Li, X.; Nayak, A & Stojmenovic, I (Editors) (2008). Handbook of

Applied Algorithms: CHAPTER 14 - Path Exposure, Target Location, Classification, and Tracking in Sensor Networks. Wiley-IEEE Press.

• Funk, N. (December, 2003). A Study of the Kalman Filter applied to Visual Tracking. Project for CMPUT 652, University of Alberta.

• Gu, Y. & Veloso, M. (2006). Multi-Model Motion Tracking under Multiple Team Member Actuators.AAMAS’06 May 8–12 2006, Hakodate, Hokkaido, Japan.

• Rudy N. (September, 2003). Robot Localization and Kalman Filters On finnding your position in a noisy world. Thesis submitted for the degree Master of Science, Utrecht University.

• Kusy, B. et al. (2007). Radio Interferometric Tracking of Mobile Wireless Nodes. MobiSys ’ 07, June 11-14, 2007, San Juan, Puerto Rico, USA.

• Smith, A., Balakrishnan, H., Goraczko, M., & Priyantha, N. (2004). Tracking Moving Devices with the Cricket Location System. MobiSys'04, June 6.9, 2004, Boston, Massachusetts, USA.

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Questions?

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Thank you

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Question: Kalman filter uses a finite set of parameters to describe the state of an Object? What could be the possible parameters to describe the state of a Robot moving on the ground?

Answer: A simple example of the parameters necessary for tracking are the x and y coordinates as well as the u and v velocity components (required for motion).

Reference:Euclidean vector: http://en.wikipedia.org/wiki/Euclidean_vector

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Question: Can variable acceleration be represented by linear model of Kalman filter?

Answer:No. Acceleration is measured in meter/second2. In a linear model acceleration must be incorporated as a constant. Measuring variable acceleration would require the non-linear model. Non- linear model supports maneuvering objects.

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Question: The following diagram outlines the recursive Kalman filter algorithm:

If process and measurement noises are always zero, which part of the above process flow can be omitted?

Answer: If noise is zero then Q and R are both zero in the above equations and there is no need of updating the Covariance. (Please refer to slides 14, 15, 16)

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Please email me @ treza@connect.carleton.ca if you have any question.