Kalman Filtering for Plasma State
Fusing noisy diagnostics over time into a best estimate of the plasma state with quantified uncertainty.
Estimating a hidden state
Controllers need the plasma state, but sensors give noisy, partial, sometimes-dropped measurements of it. A Kalman filter combines a model of how the state evolves with each new measurement to produce a running best estimate and its uncertainty. It answers: given everything seen so far, what is the most likely state now, and how sure are we?
Predict and update
The filter alternates two steps. Predict: use the dynamics model to project the state and its covariance forward one cycle. Update: correct that prediction with the new measurement, weighted by the Kalman gain, which optimally balances trust in the model against trust in the sensor based on their respective uncertainties. The covariance shrinks with good data and grows when data are missing.
Why it helps control
- Smooths sensor noise without adding much lag
- Bridges dropped or late measurements using the model
- Fuses multiple diagnostics into one consistent state
- Provides uncertainty that downstream loops use to set margins
- Rejects outliers that disagree with both model and history
Nonlinear variants
The basic Kalman filter assumes linear dynamics and Gaussian noise. Plasma dynamics are nonlinear, so extended or unscented Kalman filters, which linearize or sample around the current estimate, are used where the nonlinearity matters. These keep the predict-update structure while handling the curvature of the plasma's response.
A note on trust
A Kalman filter is only as good as its models of the dynamics and the noise. Overstated confidence makes it ignore real measurements; understated confidence makes it chase noise. Tuning these covariances honestly - and letting the filter report when its uncertainty grows - is what keeps state estimation trustworthy for control.