Rudolf E. Kálmán in the context of National Medal of Science

In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán.

Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion planning and control, and can be used for trajectory optimization. Kalman filtering also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, the use of Kalman filters provides a realistic model for making estimates of the current state of a motor system and issuing updated commands.

Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs.In control theory, the observability and controllability of a linear system are mathematical duals.

The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer for that system, such as Kalman filters.