Predictor

Definition · applies to state estimation

High school

Consider a quantity that changes over time, and the data about it available now. A predictor estimates a future value of the quantity from that data.

Undergraduate

Consider a system with state $x(t)$, measured up to time $t$, and a time $\tau > 0$ into the future. A predictor estimates the future state $x(t + \tau)$ from the measurements up to time $t$.

Examples

Examples

• A weather forecast for tomorrow High school
  A weather forecast is a predictor because it estimates a future state.

Non-examples

Things that may be mistaken for examples.

• A least-squares estimate of a constant parameter from data High school
  A least-squares estimate of a constant parameter from data is not predictor, because it estimates a constant parameter, not a changing state.
• A low-pass filter on a sensor signal High school
  A low-pass filter on a sensor signal is not a predictor, because it does not estimate the future state of a system.
• A Kalman filter (definition) Undergraduate
  A Kalman filter is not a predictor, because it estimates the present state, not a future one.
• A Luenberger observer (definition) Undergraduate
  A Luenberger observer is not a predictor, because it estimates the present, not the future.
• A particle filter (definition) Undergraduate
  A particle filter is not a predictor, because it estimates the present.
• An extended Kalman filter (definition) Undergraduate
  An extended Kalman filter is not a predictor, because it estimates the present state, not a future one.
• An unscented Kalman filter (definition) Graduate
  An unscented Kalman filter is not a predictor, because it estimates the present state, not a future one.

Notes

Distinctions involving this term

• Types of estimators: When the state of a system is not measured directly, it can be estimated in several ways. An estimator is any rule for estimating an unknown quantity. An observer is a dynamical system whose state estimate converges to the true state. A filter estimates the current state from noisy measurements, and a predictor estimates a future state.

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