It was during a visit by Kálmán to the NASA Ames Research Center that Schmidt saw the applicability of Kálmán's ideas to the nonlinear problem of trajectory estimation for the Apollo program resulting in its incorporation in the Apollo navigation computer. He realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements. Schmidt is generally credited with developing the first implementation of a Kalman filter. Bucy of the Johns Hopkins Applied Physics Laboratory contributed to the theory, causing it to be known sometimes as Kalman–Bucy filtering. Kálmán, although Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. The filtering method is named for Hungarian émigré Rudolf E. Kalman filtering has been used successfully in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filtering. The basis is a hidden Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Įxtensions and generalizations of the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The primary sources are assumed to be independent gaussian random processes with zero mean the dynamic systems will be linear." Though regardless of Gaussianity, if the process and measurement covariances are known, the Kalman filter is the best possible linear estimator in the minimum mean-square-error sense. Kálmán: "In summary, the following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. Optimality of Kalman filtering assumes that errors have a normal (Gaussian) distribution. It can operate in real time, using only the present input measurements and the state calculated previously and its uncertainty matrix no additional past information is required. Once the outcome of the next measurement (necessarily corrupted with some error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with greater certainty. For the prediction phase, the Kalman filter produces estimates of the current state variables, along with their uncertainties. The algorithm works by a two-phase process. 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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