Differentiating matrix orthogonal transformations (Q901840)

The authors develop two methods for differentiation matrix orthogonal transformations. The article focuses on applications to the Riccati sensitivity equation and the first method uses the matrix square root over its inputs to find the solution to the discrete-time Riccati equation. The second method finds the derivatives of the matrix's entries, solving the discrete-time Riccati equation. Both methods presented are shown to be numerical stable and recommended application fields are Kalman filtering, control systems, and optimization.