Kalmansuotimet

Kalmansuotimet, also known as 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 the 1960s and is widely used in various fields such as navigation, control systems, and signal processing. The algorithm operates in two main steps: prediction and update. In the prediction step, the algorithm estimates the current state based on the previous state and the system's model. In the update step, it incorporates the new measurement to refine the estimate. Kalman filtering is particularly useful when the system's state cannot be directly observed, and the measurements are noisy. It provides an optimal estimate of the state in the sense that it minimizes the mean squared error. The algorithm assumes that the system and the measurements are linear and that the noise is Gaussian. For non-linear systems, extensions such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) have been developed. Kalman filtering has become a fundamental tool in modern engineering and science, enabling accurate state estimation in the presence of uncertainty.