Kalman Filter
Definition
The Kalman filter estimates the hidden state of a linear dynamic system from noisy measurements.
It combines a process model with new measurements and weights both according to their uncertainty. The classical filter assumes linear dynamics and certain noise assumptions.
Simply explained
Like a running estimate that sensibly mixes prediction and new measurement repeatedly.
Why it matters in practice
Relevant for sensor fusion, tracking, and state estimation in technical systems.
Example from business
A system combines noisy position and velocity measurements into a more stable state estimate.
Limits and pitfalls
- Do not check model and noise assumptions; use filter unchanged for strongly nonlinear systems; set covariances arbitrarily.
Origin & history
Rudolf E. Kalman published the fundamental recursive solution for linear filtering problems in 1960.
Use in mid-sized companies
- Possible applications: sensor fusion, condition monitoring, tracking, and technical forecasting.
Frequently asked questions
Is the classical Kalman filter intended for nonlinear systems?
No; there are extensions like EKF or UKF for that. Does it need uncertainty models? Yes.
Sources
- A New Approach to Linear Filtering and Prediction Problems · Kalman (1960), A New Approach to Linear Filtering and Prediction Problems
- zugängliche Hochschulkopie · Kalman (1960), zugängliche Hochschulkopie
Sources checked: 10./11.10.2026.
Editorially reviewed on: