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	Symulacja cyfrowego bliźniaka	Filtr Kalmana
Dziedzina	Symulacja	Statystyka bayesowska
Rodzina	Process / pipeline	Bayesian methods
Rok powstania	2002 (concept); 2014 (white paper formalization)	1960
Twórca	Michael Grieves (University of Michigan, 2002; white paper 2014)	Rudolf E. Kalman
Typ	Hybrid physics-based + machine-learning simulation	recursive Bayesian filter
Źródło pierwotne	Grieves, M. (2014). Digital Twin: Manufacturing Excellence through Virtual Factory Replication. White Paper, University of Michigan.	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
Inne nazwy	Dijital İkiz Simülasyonu (Digital Twin), digital twin, digital shadow, cyber-physical twin	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
Pokrewne	4	5
Podsumowanie	Digital Twin Simulation, first conceptualised by Michael Grieves at the University of Michigan around 2002 and formally described in his 2014 white paper, creates a continuously updated virtual copy of a physical system by fusing real-time sensor data with a mechanistic (physics-based) model and machine-learning components. The twin mirrors the physical asset's current state and projects its future behaviour, enabling fault detection, predictive maintenance, and operational optimisation without disrupting the real system.	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.