Methods for Data and Information Fusion

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Methods for Data and Information Fusion
Institute for Parallel Processing - Bulgarian
Academy of Science

• Kiril Alexiev, Iva Nikolova
• alexiev_at_bas.bg
• Tel [phone] 616
• 25A, Acad.G.Bonchev Str., Sofia 1113, Bulgaria

NATO ARW, Velingrad, Bulgaria, 2006
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Institute for Parallel Processing - Bulgarian
Academy of Sciences

• Correct decision making (taking) in the
  security sector mainly depends on information,
  received from multiple sources. Often, the
  information is insufficient, unreliable and
  contradictive.

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Architecture of sensor network
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sensor node
Communication
routing data
sensor data
query
sensor data
sensor node
user
routing data
sensor data
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Definition of Data and Information Fusion
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Academy of Sciences

• Wikipedia
• Sensor fusion is the combining of sensory data
  such that the resulting information is in some
  sense better than would be possible when these
  sources were used individually.
• Better more accurate, more complete, or more
  dependable

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Definition of Data and Information Fusion
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• Authors remark
• In definition
• combination of data is not very suitable
  phrase. We have to find better one, for example
  simultaneously processed data

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Benefits from Fusion Process
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• The first and the most important remark is that
  fusion process is necessary most of all to reduce
  (to filter) input information through its
  integration (merging) and generalization.
• Fusion process is necessary to improve accuracy.
• Fusion process is necessary to reduce
  uncertainty.

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Structure of Data and Information Fusion (JDL)
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• Level 0 Preliminary data processing pixel or
  signal level data association and
  characterization.
• Level 1 Data alignment, association, tracking
  and identification.
• Level 2 Situation assessment.
• Level 3 Threat assessment.
• Level 4 Process Refinement includes adaptive
  processing through performance evaluation and
  decision or resource and mission management.

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Institute for Parallel Processing - Bulgarian
Academy of Sciences
Methods for Data and Information Fusion
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Institute for Parallel Processing - Bulgarian
Academy of Sciences
Methods for Data and Information Fusion
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• Level 1
• Temporal data fusion Sensor data fusion

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Institute for Parallel Processing - Bulgarian
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Data association methods

• The Nearest Neighbor method associates the
  nearest measurement to the track prediction. The
  more complicated Global Nearest Neighbor
  minimizes cluster cost function in measurement
  distribution.
• The probabilistic data association filter (PDAF)
  and its extension to multiple targets joint
  PDAF (JPDAF), solve the same task of measurement
  identification in a simpler way. In the JPDAF
  hypotheses are built for the measurements and
  targets only for the current scan. In this way
  the number of hypotheses is additionally reduced
  but the chance of combinatorial explosion in
  dense target and clutter scenarios still remains.

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Institute for Parallel Processing - Bulgarian
Academy of Sciences
Data association methods

• In Multiple Hypothesis Tracking approach all
  measurements received at a scan are assigned to
  initialized targets, new targets or false alarms.
  A number of hypotheses are generated. Every one
  supposes a possible assignment scheme between
  measurements, received in all scans, and the
  targets - confirmed, new ones or false. Pruning
  and gating techniques are used to retain the most
  likely hypotheses and in this way to reduce their
  number
• Finite Set Statistics considers all measurements
  as measurements from a generalized sensor and all
  targets as a generalized target of interest.
  Fusion of information from one and the same
  sensor but from different moments of time

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Identification
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• Two types of identification
• Structural identification more difficult
• Define structure (model), which in the best
  way corresponds to the observed system (process).
  
• Parametrical identification a lot of
  algorithms
• Find (calculate) values of parameters, which
  characterize entirely considered system
  (process).

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Parameter identificationMathematical description
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• Linear dynamic system (Markovian presentation)
• Kalman filter gives optimal solution for Gaussian
  noises

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Description
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• Markovian - semi Markovian
• Linear - non-linear dynamic system
• Additive - non additive system noise
• Gaussian - non Gaussian system noise
• Additive - non additive measurement noise
• Gaussian - non Gaussian measurement noise

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• The simplest tracking filter, considered in the
  paper, is alpha-beta filter. It is suitable for
  tracking of moving with constant velocity targets
  without steady-state error. The alpha-beta-gamma
  filter has ability to track even accelerating
  targets without steady-state error.
• Kalman filter is a classical optimal estimating
  algorithm for dynamical linear system with
  Gaussian measurement and system noise. The
  modification of Kalman filter - Extended Kalman
  filter is developed for non-linear systems. The
  EKF gives particularly poor performance on highly
  non-linear functions because only the mean is
  propagated through the non-linearity. The
  unscented Kalman filter (UKF) uses a
  deterministic sampling technique to pick a
  minimal set of sample points (called sigma
  points) around the mean.

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Institute for Parallel Processing - Bulgarian
Academy of Sciences

• The theoretically most powerful approach for
  manoeuvring targets tracking is known to be
  Interacting Multiple Models estimator.
  Generalized Pseudo-Bayesian (GPB) estimators
  different orders, Fixed structure IMM, Variable
  Structure IMM, Probabilistic Data Association IMM
  are variants. The most important feature is that
  all these estimators use in parallel several
  models for modelling of the estimated system.
• Particle filters, also known as Sequential Monte
  Carlo methods (SMC), are sophisticated model
  estimation techniques based on simulation.
  Particle filters generate a set of samples that
  approximate the filtering distribution to some
  degree of accuracy. Sampling Importance
  Resampling (SIR) filters with transition prior as
  importance function are commonly known as
  bootstrap filter and condensation algorithm.

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Temporal data fusion (Alan Steinberg)
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NN Nearest Neighbor PF Particle
Filter F Alpha-Beta Filter PDAF Probabilistic
Data Association Filter KF Kalman
Filter JPDAF Joint Probabilistic Data
Association Filter EKF Extended Kalman
Filter FISST Finite Set Statistics IMM Interacti
ng Multiple Model filter Y/N Good/Poor Choice
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Institute for Parallel Processing - Bulgarian
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Alan Steinberg
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Fully Centralized Measurement Fusion Architecture
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Fully Centralized Trajectory Fusion Architecture
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Distributed Decision Fusion Architecture
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Simple Example
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• When both sources are reliable, there is a
  consensus and it is reasonable to find solution
  in the cross-section of and - sets of
  corresponding sources . If
  the two sources do not agree, we have
  . The hypothesis for reliability sources
  is no longer credible and three other hypotheses
  appear 1) First source is correct, the second is
  incorrect 2) First source is incorrect, but
  second is incorrect 3) Both sources are
  incorrect. How to find the correct hypothesis? As
  a precaution, all available information is kept
  and we hold up .

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Example continue
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• It is obvious that the first fusion method is
  the most informative because the information is
  refined to the intersection of sets given by each
  source. It is also the most risky approach
  because the real value of is assumed to be
  inside a smaller set than the two initial sets.
  The second fusion method is more reliable since
  all the information given by the two sources is
  preserved. The drawback of such an approach is a
  loss of accuracy since the set assumed to contain
  , is larger than each of the initial sets.

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Homogeneous sensor fusion
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• AND Operator. This method transforms the output
  of the sensors in a binary yes/no consensus
  operating with logical AND. After that thresholds
  are applied to find the result. The procedure is
  very simple, intuitive and fast, if the values of
  thresholds are determined in advance. The method
  does not take into account the degree of
  confidence of each sensor.
• Weighted Average. This method takes a weighted
  average of available sensor data and uses it as
  the fused value. Usually the weights are
  proportional to accuracy of sensors or to
  credibility of sensor information.
• Voting. The voting schemes main advantage is
  computation efficiency. Voting involves the
  derivation of an output data object from a
  collection of n input data objects, as prescribed
  by the requirements and constraints of a voting
  algorithm. The voting algorithms can be quite
  complex in terms of content and structure of the
  input data objects and how they handle the votes
  (weights) at input and output.

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Sensor fusion
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Academy of Sciences

• Bayesian Theory. The use of Bayesian inference
  theory is widely spread for the fusion of
  redundant information. The most known method is
  the Kalman Filter, that is optimal in a
  statistical sense (it presents the least square
  error). Bayesian theory is also used to establish
  the weights linking the sensors in a weighted
  average fusion architecture. Moreover, some
  reductions of superbayesian methods to
  probabilistic evidence combination formulas have
  been provided. Some problems arise in a Bayesian
  framework I) it does not distinguish between
  lack of evidence and disbelief ii) practical
  difficulties in setting the apriori
  probabilities noninformative priors can cause a
  wrong bias of further reasoning iii) it assumes
  that the knowledge sources are consistent.

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Sensor Fusion
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Academy of Sciences

• Information Theory. Mutual information, in the
  form of the Kullback-Leiber divergence, has been
  used in 12 as a way of combining probabilistic
  masses (sensor outputs). This is yet another
  method of fusing two probabilities, this time
  with a non-bayesian law, adding some information
  on average image values (e.g. depending on
  lighting conditions). The local maximum of the
  mutual information is then taken as the fused
  value.

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Sensor Fusion
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Academy of Sciences

• Belief Theory. Dempster-Shafer evidential
  reasoning is used to compute the belief of a
  given event from two or more assessments provided
  by different knowledge sources at a symbolic
  level. This theory is based on the premise that
  each source of information provides only a
  partial belief about a proposition. Problem
  redistribution of conflicts.
• Dezert Smarandache Theory(DSmT). DSmT is
  analogous to Dempster-Shafer evidential reasoning
  theory but overcomes some drawbacks of this theory

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Sensor fusion
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Academy of Sciences

• Fuzzy Reasoning. Fuzzy sets and variables are
  used to deal with real-world models where the
  usual ideal mathematical assumptions are
  inappropriate. Under the fuzzy framework, the
  possibility theory has emerged to represent
  imprecision in terms of fuzzy sets and to
  quantify uncertainty through four proposed
  notions possibility, necessity, plausibility,
  and credibility distributions .
• Geometric Methods, e.g. using uncertainty
  ellipsoids. Parametrical identification if we
  know model, we can estimate parameters

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Level 2,3,4 fusion
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• Belief Propagation Nets
• Markov Random Fields
• Factor Graphs
• Game theory

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New research direction
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• New tracking filters may be FISST, may be new
  one
• Increased interest in image fusion methods -
  improvement of existing, search for new ones.
• Increased interest on higher level fusion not
  only theoretical but engineering approach
• Decision level methods for fusion like Dezert
  Smarandache Theory or new ones.

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