Kalman Filtering is a mathematical algorithm that provides estimates of unknown variables by processing a series of measurements observed over time. It effectively combines noisy sensor data with a system’s dynamic model to produce more accurate and reliable state estimates.
Key Features:
- State Estimation: Kalman filters predict the state of a system at a future time based on current and past measurements, accounting for uncertainties in both the system model and the measurements.
- Recursive Processing: The algorithm updates estimates recursively, making it efficient for real-time applications where new data is continuously available.
- Optimality: Under certain conditions, Kalman filters provide the best possible estimate in the least-squares sense, minimizing the estimation error covariance.
Applications:
- Navigation Systems: Kalman filters are widely used in GPS and inertial navigation systems to provide accurate position and velocity estimates.
- Robotics: They assist robots in localizing themselves within an environment and mapping their surroundings.
- Economics: Kalman filters are employed to estimate unobserved economic variables, such as potential output or natural interest rates.