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	階層カルマンフィルタ（Hierarchical Kalman Filter, HKF）	カルマンフィルター
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1994	1960
提唱者	Chou, Willsky & Benveniste	Rudolf E. Kalman
種類	recursive Bayesian state estimator	recursive Bayesian filter
原典	Chou, K. C., Willsky, A. S., & Benveniste, A. (1994). Multiscale recursive estimation, data fusion, and regularization. IEEE Transactions on Automatic Control, 39(3), 464–478.	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
別名	multi-scale Kalman filter, multilevel Kalman filter, hierarchical state-space filter, HKF	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
関連	4	5
概要	The Hierarchical Kalman Filter (HKF) extends the classic Kalman filter to systems with multiple levels or scales of state representation. It applies Kalman recursions at each level of a hierarchy — from coarse to fine resolution or from global to local subsystems — and passes information across levels via upward and downward sweeps, producing optimal linear state estimates throughout a structured state-space.	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.