SLIDE 1
Outline
- Mathematical formulation
- Belanger's method
- A modified version of Belanger's method
- Numerical results
- Future work
An Adaptive Covariance Estimation Method Yicun Zhen (joined work - - PowerPoint PPT Presentation
An Adaptive Covariance Estimation Method Yicun Zhen (joined work - - PowerPoint PPT Presentation
An Adaptive Covariance Estimation Method Yicun Zhen (joined work with John Harlim) Group Meeting Dec 11-12, 2014 Outline Mathematical formulation Belanger's method A modified version of Belanger's method Numerical results
SLIDE 2
SLIDE 3
Mathematical formulation
- True model:
State variable Deterministic model
- perator
System noise (random variable)
SLIDE 4
Mathematical formulation
- Observational model:
- bservation
Observation
- perator
Observation noise
SLIDE 5
Mathematical formulation
- Goal: find out the variance of and ,
which are denoted by Q and R.
- This is different from the model error
problem.
SLIDE 6
Belanger's method
- Construct a new set of “observations” for Q
and R from the existing observations:
Observation at time t_n Observation at time t_{n-l}
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Belanger's method
This newly constructed observations satisfy:
- 1,
- 2, can be computed
recursively.
linear
SLIDE 8
Belanger's method
Process: 1, primary filter (Kalman filter) 2, secondary filter: implement Kalman filter on the
- bservation model:
to estimate Q and R.
SLIDE 9
A modified version of Belanger's method
- Starting from the relation:
- consider
- and solve it directly using least-square
method.
SLIDE 10
A modified version of Belanger's method
- Without computing the variance of the
newly constructed observations, it is computationally cheaper than the original Belanger's method.
SLIDE 11
Numerical results
- Results with Lorenz96 model:
- 20 observation, R=I, Q=0.5dt
SLIDE 12
Numerical results
SLIDE 13
Future work
- First Implement this with Sequential