Sequential Importance Resampling

Sequential Importance Resampling (SIR) is a method used to estimate the state of a system that changes over time, especially when measurements are uncertain. It works by generating many possible scenarios (particles) with different states, assigning each a weight based on how well it matches observed data. Over time, less accurate scenarios are discarded and replaced by duplicating better-fitting ones, maintaining a diverse set of plausible states. This process allows for more accurate tracking of the system's true state, even with noisy or incomplete information, and is widely used in areas like robotics, navigation, and signal processing.