The Kalman Filter is an algorithm that provides estimates of unknown variables by using a series of measurements observed over time, which may contain noise and inaccuracies. Named after Rudolf Kalman, who introduced it in the 1960s, this filter is widely used in various fields such as robotics, navigation, and economics to predict the state of a system and to refine these predictions as new data becomes available.
The Kalman Filter operates in two phases: the prediction phase and the update phase. In the prediction phase, it uses the current state estimate and a mathematical model of the system to predict the next state. In the update phase, it incorporates new measurements to correct the predicted state, yielding a more accurate estimate. This process effectively reduces uncertainty by weighing the predictions against the observed data.
Mathematically, the Kalman Filter is based on a linear dynamic system model, expressed in state-space form. It assumes that both the process noise and the measurement noise are Gaussian distributed, which allows for optimal estimation under these conditions. The filter provides not only the best estimate of the state but also an estimation of the uncertainty associated with that estimate.
Due to its efficiency and relatively low computational requirements, the Kalman Filter has become a fundamental tool in the fields of control theory, signal processing, and artificial intelligence, particularly in applications that involve real-time data processing and sensor fusion.