unscented Kalman filter
The unscented Kalman filter, or UKF, is another way to make a Kalman filter cope with a curvy, nonlinear world — but instead of flattening the curve with math, like the extended Kalman filter does, it samples the curve. The idea is that it is often easier and more accurate to push a few carefully chosen points through the true equations than to approximate the equations with a straight line. If you want to know where a thrown ball lands under wind, you learn more by tossing a handful of test balls than by drawing a straight line tangent to the ball's path.
Here is how it works. The filter's current uncertainty is shaped like a fuzzy cloud around its best guess. The UKF picks a small, clever set of representative points from that cloud — called sigma points — typically one at the center and a couple spread out along each direction of uncertainty. It then runs every one of those points through the robot's real, unmodified motion and sensor equations, curves and all. Looking at where the points land, it measures the new center (the mean) and the new spread (the covariance), and from those it rebuilds the updated cloud — no slope-taking, no Jacobians required.
Because it feeds the genuine nonlinear equations rather than a flattened stand-in, the UKF usually tracks sharp curves more faithfully than an EKF, with comparable computing cost and no hand-derived derivatives. That accuracy and convenience make it a popular choice for tricky systems like spacecraft attitude or aggressive drone maneuvers. The name is a bit of an in-joke from its inventor and carries no deep meaning; what matters is the sigma-point trick at its heart.
To track a tumbling satellite's orientation, a UKF spreads, say, a dozen sigma points around its current guess, spins each one forward through the true rotation equations, then reads off the new average orientation and how uncertain it is.
The UKF learns the curve's effect by sending real test points through it, rather than approximating the curve with a tangent line.
Sigma points are a fixed, small handful chosen by formula — not random samples — so the UKF stays fast and predictable, unlike the particle filter, which scatters many random samples.