مقایسهٔ روش‌ها

	فیلتر ذره سلسله‌مراتبی	فیلتر کالمن
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	2000s–2010s	1960
پدیدآور	Briers, Doucet, and colleagues	Rudolf E. Kalman
نوع	Sequential Monte Carlo / hierarchical state-space inference	recursive Bayesian filter
منبع بنیادین	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.
نام‌های دیگر	nested particle filter, multilevel particle filter, hierarchical SMC, HPF	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
مرتبط	5	5
خلاصه	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.