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	階層型粒子フィルタ	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	2000s–2010s	1960
提唱者	Briers, Doucet, and colleagues	Rudolf E. Kalman
種類	Sequential Monte Carlo / hierarchical state-space inference	recursive Bayesian filter
原典	Briers, M., Doucet, A. & Maskell, S. (2010). Smoothing algorithms for state-space models. Annals of the Institute of Statistical Mathematics, 62(1), 61-89.	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
別名	nested particle filter, multilevel particle filter, hierarchical SMC, HPF	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
関連	5	5
概要	A hierarchical particle filter extends Sequential Monte Carlo to state-space models with multiple levels of latent variables. Particles are propagated at each level of the hierarchy, allowing the method to track both fine-grained state dynamics and slower-varying hyperparameters simultaneously, yielding calibrated posterior distributions across all levels of the model.	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.