Square-root information filtering and fixed-interval smoothing with singularities

The square-root information filter and smoother algorithms have been generalized to handle singular state transition matrices and perfect measurements. This has been done to allow 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.