A sequence of vectors x(t) with dimension N is given, such that x(t+1) is obtained from x(t) by introducing p new elements, deleting p old ones, and shifting the others in some fashion. The sequence of vectors $ is sought. This paper presents a method of calculating these vectors with proportional-to-Np operations and memory locations, in contrast to the conventional way which requires proportional-to-N2 operations and memory locations. A non-symmetric case is also treated.

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Persistent URL dx.doi.org/10.1080/00207177808922343
Journal International Journal of Control
Ljung, L. (Lennart), Morf, M. (Martin), & Falconer, D.D. (1978). Fast calculation of gain matrices for recursive estimation schemes. International Journal of Control, 27(1), 1–19. doi:10.1080/00207177808922343