TY - GEN
T1 - Geometric aspects of the covariance partial realization problem
AU - Chang, Chin
AU - Georgiou, Tryphon T.
PY - 1993
Y1 - 1993
N2 - In this paper, both Euclidean geometric and non-Euclidean geometric descriptions for the regions of the solution set to the covariance partial realization problem are discussed. In particular, it is shown that all the solution functions are located inside a Euclidean disk - the Weyl disk, and a non-Euclidean disk - the Apollonian disk. The radius of each disk depends on the norm of the parameterizing Schur functions. Moreover, it is pointed out that the well known maximum entropy solution is exactly the hyperbolic center of the Apollonian disk; while, the associated power spectral density function is the geometric mean center of the real region where the Wyel disk is projected to along the imaginary axis. Sensitivity analysis of the Weyl disk radius and Apollonian disk center due to the perturbation of the given finite covariance data is presented.
AB - In this paper, both Euclidean geometric and non-Euclidean geometric descriptions for the regions of the solution set to the covariance partial realization problem are discussed. In particular, it is shown that all the solution functions are located inside a Euclidean disk - the Weyl disk, and a non-Euclidean disk - the Apollonian disk. The radius of each disk depends on the norm of the parameterizing Schur functions. Moreover, it is pointed out that the well known maximum entropy solution is exactly the hyperbolic center of the Apollonian disk; while, the associated power spectral density function is the geometric mean center of the real region where the Wyel disk is projected to along the imaginary axis. Sensitivity analysis of the Weyl disk radius and Apollonian disk center due to the perturbation of the given finite covariance data is presented.
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U2 - 10.23919/acc.1993.4792934
DO - 10.23919/acc.1993.4792934
M3 - Conference contribution
AN - SCOPUS:0027802072
SN - 0780308611
SN - 9780780308619
T3 - American Control Conference
SP - 627
EP - 632
BT - American Control Conference
PB - Publ by IEEE
T2 - Proceedings of the 1993 American Control Conference Part 3 (of 3)
Y2 - 2 June 1993 through 4 June 1993
ER -