Data Science - (Kalman Filtering|Linear quadratic estimation (LQE))

Thomas Bayes


Kalman Filtering or Linear quadratic estimation (LQE) is an algorithm that uses a series of measurements observed over time

Because of the algorithm's recursive nature, 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.


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.


  • guidance, navigation and control of vehicles, particularly aircraft and spacecraft.
  • time series analysis used in fields such as signal processing and econometrics.
  • robotic motion planning and control,
  • trajectory optimization.

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