CISL

1
Stochastic FIR filter
Structure

• Basic Concept
• uses the finite measurements and inputs on the
  most recent interval
  called the horizon or window
• requires the information about the horizon
  initial state

CISL
Seoul Natl Univ.
2
Stochastic FIR filter
Structure

• Basic Concept

FIR Structure
CISL
Seoul Natl Univ.
3
Stochastic FIR filter
Previous works

• Various existing stochastic FIR filters
• Limited Memory Filter Jazwinski 68
• Finite Memory Filter Schweppe 73
• Fixed Memory Recursive Filter Buxbaum74
• Fixed Memory Least Square Filter Bierman75
• Recursive Limited Memory Filter Bruckstein85
• Optimal FIR Filter Kwon 89,94

CISL
Seoul Natl Univ.
4
Stochastic FIR filter
Previous works

• For state space model without input and system
  noise
• Limited Memory Filter Jazwinski 68
• Finite Memory Filter Schweppe 73
• Fixed Memory Recursive Filter Buxbaum74
• Fixed Memory Least Square Filter Bierman75

• may be sensitive for system noise

CISL
Seoul Natl Univ.
5
Stochastic FIR filter
Previous works

• For state space model without input
• Recursive Limited Memory Filter Bruckstein85
• Optimal FIR Filter Kwon 89,94

• might find it hard to understand the derivation
  of
• complicated filtering algorithm
• could not be utilized in feedback control
  problems

CISL
Seoul Natl Univ.
6
Stochastic FIR filter
Previous works

• Kalman filter RH strategy Kwon, IEEE TAC 1999
• derived for generalized state space model with
  system and measurement noises, and control inputs

CISL
Seoul Natl Univ.