Math & Kinematics

Covariance Matrix

A covariance matrix is a symmetric positive semi-definite matrix whose entries are the pairwise covariances of a random vector's components, characterizing the spread and correlation of uncertainty around the mean. In robotics it represents state uncertainty in Kalman filters and SLAM, sensor noise models, and pose estimation confidence, with its eigenstructure describing uncertainty ellipsoids. Propagating covariance through motion and measurement models is the core computation of Gaussian state estimation.

Why it matters for physical AI

Calibrated uncertainty lets robots know what they do not know, informing when to re-observe, slow down, or defer to a human, which is fundamental to safe autonomy under imperfect perception.