State estimation

State estimation infers an unobserved dynamical state from noisy observations and a model of its evolution.

The Kalman filter recursively computes the conditional mean and covariance of the state in a linear system with Gaussian initial state and Gaussian noise.

Suppose $x\mid \mathcal{F}\sim N(\hat{x},V)$ and the new observation is $y=x+\eta$, where $\eta \sim N(0,R)$ is independent. ThenThe coefficient $V/(V+R)$ is the scalar Kalman gain.