Kalman Filter
A recursive state estimator that combines model prediction with noisy measurements while explicitly tracking estimation uncertainty.
Predict and Update
At each step, a Kalman filter first predicts the next system state from a model and then corrects that prediction when a measurement arrives.
The classical filter provides a closed-form solution for linear models with Gaussian noise assumptions.
Covariance Matters
The filter tracks not only the estimated state but also uncertainty through covariance. A noisy sensor should influence the update differently from a highly trusted measurement.
System Boundary
Incorrect process or measurement-noise assumptions can produce a visually smooth estimate without making it accurate. Bias and model error need separate consideration.