Kalman-Glättung ist eine fortgeschrittene statistische Methode used primarily in Zeitreihenanalyse and Schätzungstheorie. It builds upon the Kalman-Filter, which is used for estimating the state of a linear dynamic system from a series of noisy measurements. While the Kalman filter provides estimates at each time step, Kalman smoothing enhances these estimates by utilizing all available data points, both past and future, to produce a more accurate estimate of the system’s state.
The process involves two main steps: the forward pass, which generates the initial estimates using the Kalman filter, and the Rückwärtsdurchlauf, where these estimates are refined by considering subsequent observations. This dual approach allows for the incorporation of future information, which can lead to improved accuracy in predictions and state estimations. Kalman smoothing is particularly valuable in applications where data points are collected sequentially over time, such as in robotics, finance, and various engineering disciplines.
Mathematically, Kalman smoothing operates by optimizing the estimates of the system’s state, minimizing the mittlerer quadratischer Fehler of the estimations. The result is a set of smoothed estimates that reflect a more accurate depiction of the underlying process, removing much of the noise inherent in the measurements. This technique is especially useful in scenarios with high levels of uncertainty and variability in the data.