Estimator
High school
Consider an unknown quantity and some data related to it. An estimator is a rule for guessing the unknown quantity from the data.
Undergraduate
Consider an unknown quantity, such as a state or a parameter, and the data available about it. An estimator is any rule for computing an estimate of the quantity from the data.
Examples
Examples
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A least-squares estimate of a constant parameter from data
High school
A least-squares estimate is an estimator because it estimates a quantity from data.
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A Kalman filter
(definition)
Undergraduate
A Kalman filter is an estimator, because it estimates the state from noisy measurements.
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A Luenberger observer
(definition)
Undergraduate
A Luenberger observer is an observer, and so an estimator, because it estimates the current state of a deterministic system from its inputs and outputs.
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A particle filter
(definition)
Undergraduate
A particle filter is a filter, and so an estimator, because it estimates the current state from noisy measurements, by approximating the state’s distribution with weighted samples.
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An extended Kalman filter
(definition)
Undergraduate
An extended Kalman filter is a filter, and so an estimator, because it estimates the current state of a nonlinear system from noisy measurements, by applying the Kalman filter to a linearization of the system.
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An unscented Kalman filter
(definition)
Graduate
An unscented Kalman filter is a filter, and so an estimator, because it estimates the current state of a nonlinear system from noisy measurements, by passing sample points through the system’s model.
Properties
- Observers, filters, and predictors are all estimators of a state.
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.