State Space Models / Kalman Filter

Best for: Dynamic systems

How it works

Represents the system as latent dynamics $x_t=F_t x_{t-1}+w_t$ and an observation equation $y_t=H_t x_t+v_t$ with Gaussian process/measurement noise. The Kalman filter alternates a predict step, $\hat x_{t|t-1}=F_t\hat x_{t-1|t-1}$ with covariance $P_{t|t-1}=F_tP_{t-1|t-1}F_t^\top+Q$, and an update step that folds in the new observation via the Kalman gain $K_t=P_{t|t-1}H_t^\top(H_tP_{t|t-1}H_t^\top+R)^{-1}$. This yields the minimum-variance linear estimate of the latent state and is optimal when the model is linear-Gaussian.

Common fields

Robotics · navigation · economics