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Due to the time delay between issuing motor commands and receiving sensory feedback, usage of the Kalman filter supports the realistic model for making estimates of the current state of the motor system and issuing updated commands. In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties.

Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. It can run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.

This allows for a representation of linear relationships between different state variables (such as position, velocity, and acceleration) in any of the transition models or covariances.

As an example application, consider the problem of determining the precise location of a truck.

Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems.

The underlying model is a Bayesian model similar to a hidden Markov model except that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions.

and Peter Swerling developed a similar algorithm earlier. Bucy of the University of Southern California contributed to the theory, leading to it often being called the Kalman–Bucy filter. Schmidt is generally credited with developing the first implementation of a Kalman filter.

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. It is also used in the guidance and navigation systems of reusable launch vehicles and the attitude control and navigation systems of spacecraft which dock at the International Space Station.

The Kalman filter has numerous applications in technology.This process is repeated at every time step, with the new estimate and its covariance informing the prediction used in the following iteration.This means that the Kalman filter works recursively and requires only the last "best guess", rather than the entire history, of a system's state to calculate a new a library implementing an Extended Kalman Filter in C . Subclassing allows to define different matrix contents for the filter to work with.Kalman filters are used for some time now, in aeronautics, robot vision and robotics in general.At the extremes, a high gain close to one will result in a more jumpy estimated trajectory, while low gain close to zero will smooth out noise but decrease the responsiveness.