Part 6b : Kalman Filters

• Common problem : try to estimate the state of a physical system from noisy, incomplete observations over time

  -> could be formulated as a state-observation model :

  • transition model
  • observation model
• When a transition model and observation model become continuous conditional distributions --> HMMS cannot deal witht his and are not applicable
• Discretisation :

  • split the domain of a variable into a fixed number of intervals :reprsenteach continuous value by the label of its interval
  • + all of our representatation and reasoning machinery is directly applicable.

  -

  • loss of information
  • complexity
• Work with continuous variables and CPDs

  • permit conditinous random variables X with Val(X) in R
  • model CPDs as continuous density functions p(X) and p(X| pa(X))
• Work with continuous variables and cpds,

  General approach :

  • use a parameterisable familiy of density functions to model distributions
  • design a general rule that uniquely computes the paramters of condition distribution as a function of the specific parent value x
• Linear Gaussian Models

  A) linear function of

  B) is independant of

  C) mean

  D) variance

  
• Kalman Filter

  A) state-observation

  B) all state and observations

  C) Gaussians

  D) linear Gaussian models

  E) linear

  F) linear

  G) noise

  H) real-time

  
• Models

  A) transition

  B) observation

  
• Kalman filter formal specification :

  A) state-observation

  B) hidden

  C) observation

  D) prior state

  E) matrix

  F) covariance

  
• Tracking with the kalman filter :

  1. State Propagation
  2. Conditioning on new observations
• The Gaussian Familiy of Distributions remains closed un the update operations.
• Forward Algorithm for Kalman Filtering

  A) transition

  B) observation

  C) Predict

  D) likely

  E) prediction

  F) update

  
• Kalmal filter limitations :

  • The gaussian, linear dependency and fixed variance assumptions are rather severe restrictions.
  • may be satisfied in some processes and applications and not in toher