Smoothing versus Filtering

Filtering estimates the state now from data up to now; smoothing improves past estimates using data that arrived later.

Two questions about time

Estimation comes in two flavors distinguished by which data they use. Filtering estimates the current state using all observations up to the present, the right tool for real-time operation and control. Smoothing revisits a past state using observations from both before and after it, producing a better estimate in hindsight. Both matter to a twin, for different purposes.

Why smoothing is more accurate

Kronos motion — pid vs model

An estimate of a past moment can be sharpened by data that came after it, because later measurements constrain what the earlier state must have been to lead to them. Smoothing uses this future information, so its estimates of past states are less uncertain than the filtered estimates were at the time. The cost is that it is not causal: it cannot be done in real time, only after the fact.

Uses of each

Filtering: real-time state estimation, control, live anomaly detection
Smoothing: post-pulse and post-campaign reanalysis, calibration, training-data generation
Prediction: rolling the filtered state forward, used for forecasts and what-if studies

Fixed-lag smoothing

A middle ground, fixed-lag smoothing, produces improved estimates a short, fixed time behind real time, accepting a small delay to gain accuracy. This suits functions that can tolerate a brief lag, giving better estimates than pure filtering without waiting for a whole campaign to finish.

In a fusion twin

A Kronos twin filters in real time to drive control of the Hyperion breeder and the burner, but smooths after each pulse or campaign to produce the most accurate reconstruction for physics study, calibration, and life accounting. The smoothed history is also the cleanest training data for surrogates and the best record for governance. Both are built on the same models exercised on simulated data today, with real application after the machines operate. See calibration and variational assimilation.