Abstract The square-root information filter algorithm and the related covariance smoother algorithm have been generalized to handle singular state-transition matrices and perfect measurements. This allows the use of SRIF techniques for problems with delays and state constraints. The generalized algorithms use complete QR factorization to isolate deterministically known parts of the state and nonsingular parts of the state transition and disturbance influence matrices. These factorizations and the corresponding changes of coordinates are used to solve the recursive least-squares problems that are basic to the SRIF technique. Numerical stability, computation time, and storage requirements are comparable to the traditional SRIF algorithms.