Covariance is the formal statement of how uncertain a satellite's estimated position and velocity are — a matrix that draws an "error ellipsoid" around the predicted state. It is the raw material of collision-risk maths: without realistic covariance, a probability of collision cannot be computed honestly.
Understanding Covariance
Why the ellipsoid points along the track
Orbital dynamics converts energy errors into timing errors. Estimate a satellite's semi-major axis a few metres high and you have its period wrong by milliseconds; within hours those milliseconds compound into a position error of kilometres — all of it along the direction of flight. Radial and cross-track errors, by contrast, oscillate rather than accumulate. The result is the signature cigar-shaped ellipsoid, often tens of times longer along-track than across it. Close-approach geometry inherits this shape: a conjunction that looks alarming in raw miss distance may carry most of its separation across the narrow axes of both ellipsoids, or vice versa, which is precisely what the probability-of-collision integral untangles.
Covariance realism — the hard part
A covariance is itself an estimate, and making it truthful is notoriously difficult. Filters produce formal covariances that reflect only the errors they model; unmodelled effects — atmospheric density surprises during a geomagnetic storm, unannounced manoeuvres, sensor biases — leave the formal number too optimistic. Operators therefore validate covariance empirically, comparing predictions against later truth and inflating the matrix until it matches observed error statistics. During strong solar activity, LEO covariances can balloon within hours as drag forecasts degrade, temporarily blinding screening systems at exactly the moment risk rises.