Unscented Kalman Filter

A Kalman filter for nonlinear systems that propagates a small set of sample points instead of taking derivatives.

The Unscented Kalman Filter is one nonlinear variant of the Kalman filter, proposed by Julier and Uhlmann in the mid-to-late 1990s. The Extended Kalman Filter (EKF) handles nonlinearity by linearizing around the current estimate using a Jacobian matrix, which introduces large errors when the nonlinearity is strong and requires deriving that Jacobian by hand. The UKF takes a different approach: it picks a small, deterministic set of sample points (sigma points) based on the current mean and covariance, passes each one directly through the true motion or observation model, and recomputes the mean and covariance from the transformed points — a step called the unscented transform. It needs no Jacobian, and is usually more accurate than the EKF under strong nonlinearity, at the cost of more computation. In robotics it is used to fuse IMU, wheel speed, and GPS for state estimation; ROS’s robot_localization package provides both EKF and UKF nodes.

ExampleUsing robot_localization’s ukf_localization_node to fuse wheel odometry with IMU data gives a mobile base a smooth, continuous pose estimate.

Also called

UKF, Sigma-Point Kalman Filter

Related

Kalman Filter · Extended Kalman Filter · Particle Filter · State Estimation · Multi-Sensor Fusion · Error-State Kalman Filter

Sources

Unscented transform - Wikipedia
robot_localization: State Estimation Nodes