#### Title

STATE-SPACE APPROACH FOR OBTAINING SPECTRAL MODELS FROM NONPOSITIVE COVARIANCE MODELS.

#### Document Type

Conference Proceeding

#### Date of Original Version

12-1-1987

#### Abstract

The problem considered is the following: given a state-space model for a symmetric sequence r//j which is not positive, (i. e. , its Fourier transform takes on negative values), find a model for a positive sequence r//j which gives a good approximation to r//j. The positive covariance model can then be used to define a spectrum, if desired. This problem arises, for example, when the original covariance model comes from an estimated covariance sequence which is not positive. A solution to the positivity problem is given which uses state-space models and a scaled algebraic Riccati equation. The procedure leaves the poles of the original model and the value of r//0 unchanged. A simulation example is given to compare the proposed method with a different approach based on an ARMA (autoregressive moving-average) parameterization of the spectrum. In this example, the squared error between the given sequence and the sequence obtained by the proposed method is within 5% of the optimal value.

#### Publication Title

Proceedings of the IEEE Conference on Decision and Control

#### Citation/Publisher Attribution

Vaccaro, Richard J., and Fu Li.
"STATE-SPACE APPROACH FOR OBTAINING SPECTRAL MODELS FROM NONPOSITIVE COVARIANCE MODELS.."
*Proceedings of the IEEE Conference on Decision and Control*
,
(1987): 1050-1055.
https://digitalcommons.uri.edu/ele_facpubs/1194