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	線形二次ガウス (Linear Quadratic Gaussian)	カルマンフィルター
分野	制御理論	ベイズ
系統	Machine learning	Bayesian methods
提唱年	1960	1960
提唱者	Rudolf Kalman	Rudolf E. Kalman
種類	algorithm	recursive Bayesian filter
原典	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
別名	LQG, LQR with Kalman Filter	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
関連	3	5
概要	The Linear Quadratic Gaussian (LQG) controller combines the Linear Quadratic Regulator (LQR) with a Kalman Filter to handle stochastic systems with measurement noise and process noise. Developed by Kalman and later formalized by Athans and others, LQG is the natural stochastic extension of LQR and remains the gold standard for optimal linear control under noise, with applications spanning spacecraft, aircraft autopilot, and industrial process control.	The Kalman filter is an optimal recursive algorithm for estimating the hidden state of a linear dynamical system from noisy measurements. At each time step it alternates between a prediction step — projecting the state forward using the system model — and an update step that corrects the prediction with the new observation, producing minimum-variance state estimates and their uncertainty in real time.