手法を比較

	カルマンフィルター	パーティクルフィルタ（逐次モンテカルロ法）
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1960	1993
提唱者	Rudolf E. Kalman	Gordon, Salmond & Smith
種類	recursive Bayesian filter	Sequential Monte Carlo estimator
原典	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.	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.
別名	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter	SMC, sequential Monte Carlo, bootstrap filter, condensation algorithm
関連	5	4
概要	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.	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.