Real Time Estimation and Prediction Using Optimistic Simulation and Control Theory Techniques

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Real Time Estimation and Prediction Using
Optimistic Simulation and Control Theory
Techniques

• Jeffrey S. Steinman, Ph.D.
• WarpIV Technologies, Inc.
• www.warpiv.com
• Timothy Busch, Ph.D.
• Air Force Research Labs, Rome Labs

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Topics

• Paper reflects ongoing RD implemented in the
  WarpIV Kernel
• Conceptual Overview of the Paper
• Description of Problem
• Control Theory and Kalman Filters
• Techniques of Optimistic Simulation
• Conceptual Operation
• Multiple Hypothesis Branching
• Statistical Algebra
• Measures of Effectiveness
• Summary Conclusions
• Please refer to paper 06S-SIW-017 for more
  details

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Description of Problem

• A wide variety of applications would benefit from
  being able to continually estimate their current
  state based on live data and to be able to
  predict future outcomes in real time
• Examples Air traffic control (FAA), Road
  Congestion (DOT), Energy Grid (DOE), Battle
  Management (DOD), Economic Forecasts (DOTT), etc.
• Optimistic simulation combined with control
  theory can support estimation and prediction of
  complex systems
• The simulation can always rollback to update the
  current state with live data
• Simulation is always forecasting the future state
  of the system
• Benefits to this approach
• Eliminates redundant computations
• Supports scalable parallel and distributed
  processing
• Accurate handling of measurement noise and system
  uncertainty

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Estimation and Prediction

• An estimate of the state vector, X, is computed
  by optimally combining noisy measurements
  obtained in real time with the previous
  prediction
• Then a new prediction is made using the current
  estimate of the state vector and the represented
  model of the system

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Kalman Filters

• True state equation
• Kalman Filter equation (see paper for full
  derivation)

Unknown Inputs
Transition Matrix
Aiding Terms
State Vector
Kalman Gain
Measurement Residual
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Kalman Filters (Cont.)

• Kalman Filter Terms
• State Vector is the representation of the modeled
  system through the collection of attributes that
  change over time
• Transition matrix allows the state of the system
  to be transformed from one time to another time
• Aiding terms represent accurately known inputs
  that are fed into the modeled system
• System noise represents unknown factors in the
  model such as opponent plans and maneuvering
  tactics
• Measurements are collected over time and have a
  degree of noise or uncertainty
• Kalman Gains balance measurement noise with
  system noise to obtain the best estimate of the
  state vector

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Techniques of Optimistic Simulation

• Primarily used to synchronize parallel and
  distributed discrete event simulations
• Events are processed aggressively on each node
  without regard for synchronization
• Straggler messages rollback events that were
  processed out of order
• Rollbacks undo two things
• Undo changes that were made to state variables
• Retract scheduled events
• Only events affected by the straggler are rolled
  back, not the entire node
• Antimessages retract events that were scheduled
  for other compute nodes
• Cascading rollbacks and antimessages can occur
• Flow control is necessary to help stabilize
  rollbacks and minimize cascading antimessage
  overheads
• Rollback and rollforward techniques allow the
  simulation to freely move forward and backward in
  time

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Conceptual Operation

• The simulation is always executing and
  forecasting the future within a moving time
  window
• This provides the operator with forecasts of the
  system state along with relevant measures of
  effectiveness to indicate the anticipated
  operation of the system
• Live data is continually injected into the
  simulation potentially causing affected models to
  be rolled back
• Accurately known data are like the aiding terms
  in Kalman Filters
• Noisy sensor data are like measurements in Kalman
  Filters and must be carefully weighed with
  earlier predictions to obtain the best estimate
  of the current state
• Multiple hypothesis branching might occur in the
  simulation
• Example A combat aircraft is shot at by enemy
  fire
• Three possible outcomes Destroyed, missed, or
  impaired
• Managing multiple branches is difficult to
  support efficiently, but it must be handled as
  part of the overall solution

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Multiple Hypothesis Branching

• Current approaches
• Monte Carlo approach executes many simulation
  replications to obtain a statistical distribution
  of possible outcomes
• Simulation Spawning launches new simulation
  replications at decision points
• Cloning Objects duplicates entire objects at
  decision points
• A new approach is to manage event processing and
  attribute values for different replication sets
• All events maintain the full replication set at
  startup
• Events are split into multiple replication sets
  at key decision points
• Events may join other events to consolidate
  replication sets
• State variables maintain an array of values for
  all replications
• Special bitfield masks identify state values with
  corresponding replication sets
• Operator overloading hides details to simplify
  models

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Replicated Attributes
Value
Replication Mask
Array of Replication Values

• Each bit that is set in the Replication Mask
  represents the array index for other Values that
  are identical to my Value
• Access and assignment operators are overloaded to
  efficiently maintain replication masks and event
  replication subsets

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Multiple Hypothesis Branching (Cont.)

• Please refer to the paper for more details on
  Multiple Hypothesis Branching
• Data structures
• Algorithms
• Event management
• Parallel processing
• Hardware acceleration

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Statistical Algebra

• Random number generation must be avoided to
  minimize the number of replication branches
• Statistical Algebra represents state values as
  distributions and not as single-valued quantities
• Operator overloading automates operations on
  statistical values
• Convolutions are automatically provided during
  algebraic operations
• Capabilities currently provided by the WarpIV
  Kernel
• Support for standard distributions and
  user-defined distributions
• Full set of transcendental functions are
  supported
• Curve fitting for various distributions
• Smoothing, rebinning, printing, computing mean
  and standard deviation, etc.
• For more details, see the paper

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Statistical Algebra Example
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Measures of Effectiveness

• Measures of effectiveness must be provided
• Provides feedback to operators indicating the
  effectiveness of the plan
• Required for decision-making optimization
• Raw Effectiveness (see paper for details)
• Normalized quantity ranging from 0 to 1
  indicating overall status of assets
• 1 means all red assets destroyed and no blue
  assets destroyed
• 0 means all blue assets destroyed and no blue
  assets destroyed
• Relative Effectiveness (see paper for details)
• Normalized quantity ranging from 0 to 1
  indicating how well the plan is being carried out
• Example, broken play in football
• 1 means that the plan is being followed perfectly
• 0 means that the plan is not being followed at all

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Summary Conclusions

• Current estimation and prediction approaches can
  be wasteful because they replicate computations
• Running predictions periodically from scratch
• Running large numbers of replications with
  redundant computations
• Optimistic simulation supports estimation and
  prediction in a manner that constantly calibrates
  the estimate of the current state with live data
  while maintaining forecasts of the future
• Multiple hypothesis branch management can be
  handled by using special attribute
  representations and event processing
• Statistical algebra is required to eliminate
  throwing random numbers
• Measures of raw and relative effectiveness must
  be computed to provide feedback to the operator
  and to optimize decision making

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WarpIV Simulation Kernel

• Implementation of a proposed Open Standard
  Layered Architecture for Modeling and Simulation
  (OSLAMS)
• Open Source freely available
• 250,000 lines of C code
• Supports UNIX-based operating systems
• Virtually all compilers supported
• Limited documentation (hoping to remedy this)