Kalmanfiltrering

Kalman filtering is a recursive algorithm used for estimating the state of a linear dynamic system from a series of noisy measurements. It was developed by Rudolf E. Kálmán in 1960 and is widely used in various fields such as navigation, control systems, and signal processing. The algorithm combines predictions from a model with measurements to produce an optimal estimate of the system's state.

The Kalman filter operates in two main steps: prediction and update. In the prediction step, the filter uses the system's model to predict the next state and the associated uncertainty. In the update step, it incorporates the new measurement to refine the prediction and reduce the uncertainty. This process is repeated for each new measurement, allowing the filter to track the system's state over time.

The key advantage of the Kalman filter is its ability to handle noisy data and provide a more accurate estimate of the system's state than using measurements alone. It is particularly useful in applications where the system's state cannot be directly measured, and the measurements are subject to significant noise.

The standard Kalman filter assumes that the system is linear and that the noise is Gaussian. However, there are extensions of the Kalman filter, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which can handle nonlinear systems and non-Gaussian noise. These extensions have further expanded the applicability of Kalman filtering in various fields.