Square-Root Quadrature Kalman Filtering

The quadrature Kalman filter (QKF) is a recursive, nonlinear filtering algorithm developed in the Kalman filtering framework. It computes the mean and covariance of all conditional densities using the Gauss–Hermite quadrature rule. In this correspondence, we develop a square-root extension of the quadrature Kalman filter using matrix triangularizations. The square-root quadrature Kalman filter (SQKF) propagates the mean and the square root of the covariance. Although equivalent to the QKF algebraically, the SQKF exhibits excellent numerical characteristics, but at the expense of increased computational complexity. We also present possible refinements of the generic SQKF.