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. Kalman filtering also works for modeling the central nervous system's control of movement. Kalman filtering is also one of the main topics of robotic motion planning and control and can be used for trajectory optimization. Furthermore, Kalman filtering is a concept much applied in time series analysis used for topics such as signal processing and econometrics. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Kalman filtering has numerous technological applications. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow. This digital filter is sometimes termed the Stratonovich–Kalman–Bucy filter because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich.
Kálmán, who was one of the primary developers of its theory. x ^ k ∣ k − 1 is the corresponding uncertainty.įor statistics and control theory, Kalman filtering, also known as linear quadratic estimation ( LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The estimate is updated using a state transition model and measurements.
The Kalman filter keeps track of the estimated state of the system and the variance or uncertainty of the estimate.
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