Square-Root Sigma-Point Information Filtering

The sigma-point information filters employ a number of deterministic sigma-points to calculate the mean and covariance of a random variable which undergoes a nonlinear transformation. These sigma-points can be generated by the unscented transform or Stirling´s interpolation, which corresponds to the unscented information filter (UIF) and the central difference information filter (CDIF) respectively. In this technical note, we develop the square-root extensions of UIF and CDIF, which have better numerical properties than the original versions, e.g., improved numerical accuracy, double order precision and preservation of symmetry. We also show that the square-root unscented information filter (SRUIF) might lose the positive-definiteness due to the negative Cholesky update, whereas the square-root central difference information filter (SRCDIF) has only positive Cholesky update. Therefore, the SRCDIF is preferable to the SRUIF concerning the numerical stability.