# Kalman Filter

The Kalman filter, also known as linear quadratic estimation (LQE), is an algorithm which uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those that would be based on a single measurement alone. More formally, the Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state. The filter is named for Rudolf (Rudy) E. Kálmán, one of the primary developers of its theory.

The Kalman filter has numerous applications in technology. A common application is for guidance, navigation and control of vehicles, particularly aircraft and spacecraft. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics.

The algorithm works in a two-step process: 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. Because of the algorithm's recursive nature, it can run in real time using only the present input measurements and the previously calculated state; no additional past information is required.

From a theoretical standpoint, the main assumption of the Kalman filter is that the underlying system is a linear dynamical system and that all error terms and measurements have a Gaussian distribution (often a multivariate Gaussian distribution). 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 but where the state space of the latent variables is continuous and where all latent and observed variables have Gaussian distributions.

### Other articles related to "kalman filter, filter, kalman filters, filters":

State Of Charge - Determining SOC - Kalman Filtering
... and the Current integration method, a Kalman filter can be used ... Subsequently the Kalman filter will then predict the over-voltage, due to the current, and in combination with coulomb counting, make an accurate estimation of the state of charge ... The strength of a Kalman filter is that it is able to adjust its trust of the battery voltage and coulomb counting in real time ...
Stanley F. Schmidt
... NASA Ames Research Center, where he discovered the utility of the Kalman filter as applied to data processing for the nonlinear navigation equations of ... There he applied filter theory and model identification techniques and developed digital computer programs for processing tracking data and giving postflight evaluation of launch vehicle guidance ... He also developed a formulation of the Kalman filter which was named the Schmidt–Kalman filter in his honor ...
Alpha Beta Filter - Relationship To Kalman Filters
... A Kalman filter estimates the values of state variables and corrects them in a manner similar to an alpha beta filter or a state observer ... However, a Kalman filter does this in a much more formal and rigorous manner ... The principal differences between Kalman filters and alpha beta filters are the following ...