Kalman

Kalman commonly refers to the Kalman filter, a recursive algorithm used to estimate the state of a dynamic system from noisy measurements. The term originates from Rudolf E. Kalman, a Hungarian-American mathematician and control theorist who formulated the method in the 1960s.

The Kalman filter presumes a linear dynamic model in discrete time, where the hidden state evolves according to a linear equation and measurements are linear functions of the state plus Gaussian noise. It maintains a probability distribution over the state, represented by a mean vector and a covariance matrix. The algorithm operates in two steps: a prediction step, which projects the current state estimate forward using the system model and accounts for process noise, and an update step, which incorporates the latest measurement to refine the estimate by adjusting the distribution based on measurement noise. When the assumptions hold—linearity and Gaussian noise—the Kalman filter provides the optimal minimum-variance estimate.

Applications span navigation, aerospace, robotics, and sensor fusion, including GPS/ins navigation, radar tracking, and autonomous systems. Numerous extensions address nonlinearity: the Extended Kalman Filter linearizes the model around the current estimate, while the Unscented Kalman Filter uses deterministic sampling to better approximate nonlinear transformations. Kalman smoothing and data assimilation techniques further broaden its use in temporal estimation and forecasting.

Rudolf E. Kalman (1930–2016) made foundational contributions to estimation theory and control. Since its introduction, the Kalman filter has become a standard tool in engineering and scientific disciplines for real-time state estimation under uncertainty. The name Kalman also appears in various contexts as a surname for other individuals.