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	空間カルマンフィルター	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	1960 (base); spatial extensions 1990s–2000s	1960
提唱者	R. E. Kalman (base filter, 1960); extended to spatial settings by Cressie, Wikle and colleagues	Rudolf E. Kalman
種類	Bayesian state-space model	recursive Bayesian filter
原典	Cressie, N. & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley. ISBN: 978-0-471-69274-4	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
別名	spatial state-space filter, spatio-temporal Kalman filter, SKF, spatial dynamic linear model	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
関連	6	5
概要	The spatial Kalman filter applies classical Kalman filtering to spatio-temporal state-space models, treating a spatially distributed latent field as the hidden state that evolves over time. At each time step, the filter recursively predicts the spatial field forward and then updates the prediction with new spatial observations, producing optimal linear estimates of the field and its uncertainty across all locations.	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.