Methoden vergleichen

	Räumlicher Kalman-Filter	Partikelfilter (Sequentieller Monte-Carlo-Algorithmus)
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1960 (base); spatial extensions 1990s–2000s	1993
Urheber	R. E. Kalman (base filter, 1960); extended to spatial settings by Cressie, Wikle and colleagues	Gordon, Salmond & Smith
Typ	Bayesian state-space model	Sequential Monte Carlo estimator
Wegweisende Quelle	Cressie, N. & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley. ISBN: 978-0-471-69274-4	Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F (Radar and Signal Processing), 140(2), 107–113.
Aliasnamen	spatial state-space filter, spatio-temporal Kalman filter, SKF, spatial dynamic linear model	SMC, sequential Monte Carlo, bootstrap filter, condensation algorithm
Verwandt	6	4
Zusammenfassung	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 particle filter, introduced by Gordon, Salmond, and Smith in 1993, is a sequential Monte Carlo algorithm that approximates the Bayesian filtering distribution for nonlinear and non-Gaussian state-space models. Rather than tracking a single best estimate, it maintains a cloud of N weighted random samples — particles — that collectively represent the full posterior distribution of a hidden state at each point in time as new observations arrive.