SUKF

SUKF stands for the Square-root Unscented Kalman Filter, a numerically robust variant of the Unscented Kalman Filter (UKF) used for nonlinear state estimation. Like the UKF, the SUKF approximates the state distribution with a set of sigma points that are propagated through nonlinear dynamics and measurements, but it represents the state covariance in square-root form rather than as a full covariance matrix.

In operation, the current state estimate and its square-root covariance are used to generate sigma points from the square-root factor, which are then propagated through the nonlinear process and measurement models. The predicted state and the associated cross-covariances are computed, and the square-root factors are updated using linear algebra techniques such as QR or Cholesky decompositions. This square-root formulation avoids explicit construction of the full covariance matrix, which improves numerical stability and reduces sensitivity to round-off errors, especially in high-dimensional or ill-conditioned problems.

SUKF is used in areas where nonlinear estimation is important and numerical reliability matters, including robotics, navigation, aerospace, and signal processing. It is a variant of the UKF that retains the same core idea of sigma-point propagation but emphasizes maintaining covariance information in a square-root representation. While both UKF and SUKF aim to capture the effects of nonlinearity on mean and uncertainty, SUKF offers enhanced numerical robustness and can be advantageous in resource-constrained or precision-sensitive applications.