A system has a state: the collection of quantities that describe its condition at a particular time. A vehicle's state might include its position and velocity. Some state variables are not measured directly, so they are hidden or latent.
Sensors provide measurements related to the state, but measurements are usually imperfect. GPS positions can jump around, for example, while wheel-based dead reckoning can be smooth but gradually drift. A Kalman filter combines information from the system's expected behavior and the measurements to estimate the hidden state.
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Process noise
Unpredictable changes or model imperfections that affect how a system evolves.
Measurement noise
Uncertainty or error in sensor observations of a system's state.
Innovation
The difference between a new observation and the observation predicted by the current state estimate.
Kalman gain
A matrix that determines how strongly the innovation changes the predicted state estimate.
Smoother
An estimator that uses later observations to refine estimates of past states.
Quiz questions
Which equation represents the standard discrete-time linear state-transition model with control input?Answer: xk=Fkxk−1+Bkuk+wk
In a Kalman filter, what is the innovation?Answer: The new observation minus the observation predicted from the prior state estimate.
With known means and covariances, what can the standard linear Kalman filter remain when the noise is non-Gaussian?Answer: The best linear estimator in the minimum mean-square-error sense.
How do the extended and unscented Kalman filters handle nonlinear relationships differently?Answer: The extended filter uses local linearization; the unscented filter propagates representative points.
How does a smoother differ from a filter when estimating a past state?Answer: A smoother can use observations received after that past state occurred.
Based on the Wikipedia article Kalman filter, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.