Kalman filter implementation clarification

[maximilian.gold@…]

What is the exact kalman filter implementation used in BNC? I was not able to find this exact square root filter implementation anywhere in the literature or understand it properly. The Cholesky decomposition used in combination with a QRZ Decomposition used on an Augmentation Matrix including weights, the square root of the filter covariances and a combination of the the square root of the filter covariances and Design Matrix seems unusual. A clarification would be appreciated a lot.