Ah. Sayed et al., GENERALIZED CHANDRASEKHAR RECURSIONS FROM THE GENERALIZED SCHUR-ALGORITHM, IEEE transactions on automatic control, 39(11), 1994, pp. 2265-2269
Citations number
26
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control","Engineering, Eletrical & Electronic
We present a new approach to the Chandrasekhar recursions and some gen
eralizations thereof. The derivation uses the generalized Schur recurs
ions, which are O(N-2) recursions for the triangular factorization of
NxN matrices having a certain Toeplitz-like displacement structure. It
is shown that when the extra structure provided by an underlying stat
e-space model is properly incorporated into the generalized Schur algo
rithm, it reduces to the Chandrasekhar recursions, which are O(Nn(2))
recursions for estimating the n-dimensional state of a time-invariant
(or constant-parameter) system from N measured outputs. It is further
noted that the generalized Schur algorithm factors more general struct
ured matrices, and this fact is readily used to extend the Chandrasekh
ar recursions to a class of time-variant state-space models, special c
ases of which often arise in adaptive filtering.