Target Tracking in Distributed Sensor Networks

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Target Tracking in Distributed Sensor Networks

• Ahtasham Ashraf

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Presentation Outline

• Objective Approach
• Elements of a Basic MTT System
• Target Dynamics Estimation
• Alpha-Beta Filters, Kalman Filter
• Multiple Target Tracking
• Gating, Data Association, NN, JPDA, MHT.
• References

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Objective Approach

• The idea is to track multiple targets moving
  through a distributed sensor network using
  multiple modalities.
• The whole Sensor Network is divided into regions
  which can be dynamically created may overlap
  with each other.
• Each sensor of the active regions performs the
  native detections for the targets emanating
  different modality signals.

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Approach Continued..

• The time series data is used to classify the
  targets into various predefined categories, which
  can be used to assist the multiple target
  tracking case.
• The detection classification results are used
  by the Localizer in the Manager Nodes to perform
  target position estimation after region
  detection.
• The tracking algorithm is being used to process
  the Localizer output to generate tracks make
  accurate predictions for the future target
  positions.
• New regions are created as the target escapes the
  current regions surveillance area.
• In this way the target moves through the network
  regions are created.

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Elements of a Basic MTT System

• The figure shows the functional elements of a
  simple recursive Multi-Target Tracking system
• It shows a convenient partitioning of the overall
  system for introduction but there is a
  considerable overlap of the functions of these
  elements. The distinction between individual
  elements becomes less apparent when recently
  developed techniques like MHT are used.
• Assume this recursive processing is being used
  tracks have been formed on previous scans.
• Now the Detection Localization Algs do the
  necessary Sensor Data Proc hence produce a set
  of Observations.
• First of all, these observations are gated with
  current tracks so as to simplify the later
  association process. Then more refined Data
  Association Alg are used to determine the final
  assignments.

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Continued

• Observations not assigned to existing tracks can
  initiate new Tentative Tracks. A tentative track
  becomes a Confirmed Track when it satisfies some
  quality number of observation tests.
• Similarly Low quality Tracks, as determined by
  the update history, are deleted.
• Finally the Track Update Alg is used to predict
  the track in the future time.
• The Uncertainty in Covariances is used to make
  the gates for next Data Assoc recursion.

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Target Dynamics Estimation

• The objective of this block is to use the current
  measurements give an accurate estimate of the
  position of vehicle also to predict where the
  target would be after certain time T.
• The state estimation has its basics in the
  principles of Least Squares Estimation. LSE is
  basically a batch processing method that uses
  multiple scans of data to estimate parameters
  that are assumed constant over the data
  collection interval. However a recursive form of
  LSE can be derived it leads to Kalman
  Filtering.
• (70s) Alpha-Beta (80s) Adaptive Kalman
• (90s) Interactive Multiple Model (IMM) (00s )
  Non-linear filtering?
• Advantage of KF is to provide a convenient manner
  to introduce Process noise to model random target
  motions.

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Continued

• KF gain is chosen automatically based on assumed
  target maneuver measurement noise model.
• Provides a convenient measure of estimation
  accuracy through Covariance Matrix. This is
  helpful in data association stage.
• Can compensate partially for effects of
  miss-detections by increasing the Prediction Cov
  Matrix elements to reflect the expected error
  association with uncertain data. (JPDA)
• Can use interacting multiple KF in parallel to to
  track maneuvering targets.

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Kalman Filter

• The Kalman filter can be used to addresses the
  general problem of trying to estimate the state
  of a discrete-time process that is governed by
  the linear stochastic difference equation
• where the State Transition Matrix A is given by
• Its a Constant Velocity model the target
  acceleration is modeled as white noise w(k)
• The measurement model
•  z(k) HX(k) v(k)
• The random variables w(k) and v(k) represent the
  process and measurement noise respectively.
• They are assumed to be independent (of each
  other), white and with normal probability
  distributions
• p(w) N(0,Q) p(v) N(0,R)  

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• Q The process noise covariance matrix
• R The measurement noise covariance matrix
• The Process noise Covariance Matrices for the
  constant velocity filter is given by
• where sm is the std dev of maneuver T is the
  observation interval.
• These can be easily derived from the equations of
  motion
• S vit ½ at2
• Vf Vi at

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• The Measurement Covariance for the constant
  velocity filter is given by
• To start the Filter we have to specify the State
  Vector X(k) .This can be specified by proper
  track Initiation procedures e.g. M/N rule.
• So once the track is established every incoming
  localization result is used to update the
  recursive Kalman Filter to generate an estimate
  of the current (Filtered) position the
  Predicted position after some time T.
• We keep on monitoring when the target is about to
  escape the current region when that time comes
  a new region is created the track is handed
  over to the next region.
• In this way the Track ID, State vector Process
  Covariance matrices are propagated along the
  network as the target moves.
• If we dont get observations for a track till
  certain number of observation intervals, we can
  drop the track.

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Multiple Target Tracking

• In case of multiple targets, in the same region,
  the detection localization algorithms should be
  capable enough to sense the presence of multiple
  targets hence give proportional number of (x,y)
  observations to the tracking algorithm. Also the
  classifier should also be able to identify the
  vehicles based on their signatures in order to
  help the tracker in updating their respective
  tracks.
• This gives rise to the Data Association Problem.
  Update Which Track with Which Observation?
• This problem can be solved by the help of
  Classifier OR certain Probabilistic techniques.

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Data Association

• GATING This is the process of specifying a
  region within which we are expecting the next
  observation. This helps in eliminating the false
  observations to a large extent. For those
  observations which fall within the gates, Data
  Association Algs are used.
• Different types of gates can be used depending
  upon the data behavior e.g Circular, Elliptical
  V Gates.
• The size of the gate is calculated at each
  recursion from the Prediction Covariance Matrix.
  So gates grow shrink in size due to
  miss-detections.
• Those Tracks which share observations with each
  other are grouped together are called
  Clusters.
• Data Association Algs are run on these Clusters.

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Data Association ( Techniques.. )

• -- Nearest Neighborhood Assoc.
• It is the simplest method and maintains the
  single most likely hypothesis. A Hypothesis is an
  assignment from a set of Observations to a set of
  Tracks.
• O1, O2, O3 ? T1, T2
• But the NN approach chooses only one of the many
  hypothesis discards the others without giving
  any measure of the correctness of the decision,
  which may be wrong sometimes due to the
  measurement accuracy.
• X(k1) X(k) K(k1)z(k) HX(k)
• Not good with multiple observations case within a
  gate.
• Auction Alg can be used for solving this problem.

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JPDA (Joint Probabilistic Data Association)

• Its a multiple hypothesis data association
  technique developed to handle multiple targets
  (as opposed to PDA which was for single targets),
  in which the probability of each hypothesis is
  calculated by
•  
• ß False Alarm density Pfa/Vg
• x y no of tracks in the hypoth
• xno of tracks that get obs assigned
• y no of tracks that dont get obs assigned
• So no observation is discarded all of them are
  used to update the track but with some
  probabilistic weights.
• Residue ? pijz(k) Hxi(k)
• X(k1) X(k) K(k1)Residue

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MHT (Multiple Hypothesis Testing)

• JPDA has the disadvantage in case of very close
  hypothesis.
• A better approach is to use a Delayed Decision
  Logic so that hypothesis are propagated in
  anticipation that subsequent data will resolve
  the uncertainty.
• The Track Oriented MHT Approach deals with the
  tracks adds or deletes(prunes) tracks on each
  scan.
• One should expect a potential combinatoric
  explosion of hypothesis , but there are different
  techniques to prune them at each scan.
• Its computationally expensive but can work in
  complex cases.

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References

• Estimation Tracking Principles Techniques.
  By Yaakov Bar-Shalom and Xiao-Rong Li
• Design and Analysis of Modern Tracking Systems.
  By Blackman and Robert Popoli
• Applied Optimal Estimation. By Arthur Gelb
• Bayesian Multiple Target Tracking By Stone,
  Barlow Corwin
• Multitarget-Multisensor Tracking Principles
  Techniques By Yaakov Bar-Shalom Xiao-Rong Li
• Multi-Sensor Fusion By Brooks and Iyengar