Kalman filter

A recursive algorithm that estimates a changing system’s hidden state from noisy observations and a model of its dynamics. It alternates prediction with uncertainty-weighted correction.

State-space model: A mathematical representation of a system using hidden states, dynamics, and observations. The filter operates on a state-space model of how the system evolves and produces measurements.
Linear algebra: The mathematical study of vectors, matrices, and linear transformations. State transitions and measurement relationships are represented with matrix operations.
Radar tracking: The estimation of an object's position and motion from radar measurements. Kalman filters combine noisy range and velocity observations into smooth trajectories.
Extended Kalman filter: A Kalman-filter variant that linearizes nonlinear dynamics around the current estimate. It extends the classical method to nonlinear models through local approximations.
Rudolf E. Kalman: A Hungarian-American mathematician who developed foundational work on linear filtering and control. His 1960 paper established the recursive estimator that bears his name.
Bayesian filtering: Sequential estimation of hidden states by updating probability distributions as observations arrive. The Kalman filter is a tractable Gaussian case of this broader inference framework.
Gaussian distribution: A continuous probability distribution defined by its mean and covariance. The standard filter summarizes uncertainty with Gaussian state distributions.
Global Positioning System: A satellite navigation system that determines position and time from radio signals. Receivers use filtering to combine satellite measurements with motion and clock models.
Unscented Kalman filter: A nonlinear state estimator that propagates selected sample points to approximate transformed distributions. It handles nonlinear models without the extended filter’s first-order linearization.
Richard S. Bucy: An American mathematician who contributed to continuous-time stochastic filtering theory. His work with Kalman developed the continuous-time counterpart of the discrete filter.

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