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| Spatial Kalman Filter× | Partikelfilter (sekventiell Monte Carlo)× | |
|---|---|---|
| Ämnesområde | Bayesiansk statistik | Bayesiansk statistik |
| Familj | Bayesian methods | Bayesian methods |
| Ursprungsår≠ | 1960 (base); spatial extensions 1990s–2000s | 1993 |
| Upphovsperson≠ | 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 |
| Ursprungskälla≠ | 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. DOI ↗ |
| Alias≠ | spatial state-space filter, spatio-temporal Kalman filter, SKF, spatial dynamic linear model | SMC, sequential Monte Carlo, bootstrap filter, condensation algorithm |
| Närliggande≠ | 6 | 4 |
| Sammanfattning≠ | 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. |
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