DocumentCode :
1233389
Title :
Recovering the poles from third-order cumulants of system output
Author :
Tugnait, Jitendra K.
Author_Institution :
Exxon Production Res. Co., Houston, TX, USA
Volume :
34
Issue :
10
fYear :
1989
fDate :
10/1/1989 12:00:00 AM
Firstpage :
1085
Lastpage :
1089
Abstract :
The problem of identifying the poles of single-input/single-output (SISO) linear stochastic systems from the higher-order statistics of noisy observations is considered. It is assumed that the system is driven by an independent and identically distributed non-Gaussian process with nonzero third-order cumulant function at zero lag. There is no other restriction of the probability distribution of the driving noise. The system is assumed to be of known order, causal, and exponentially stable, but is not required to be minimum phase. The system output is observed in additive, possibly non-Gaussian, noise. It is shown that if there are no pole-zero cancellations in the transfer function of the given system, then it is necessary and sufficient for a block Hankel matrix to have rank equal to the system order where the matrix is constructed from a partial set of third-order cumulants of the noisy output sequence. This fundamental result then leads to a linear solution to the problem of estimating the coefficients of the system characteristic polynomial from which the system poles can be found via root-finding
Keywords :
linear systems; matrix algebra; poles and zeros; stochastic systems; transfer functions; SISO systems; block Hankel matrix; characteristic polynomial; driving noise; higher-order statistics; linear systems; noisy observations; poles identification; probability distribution; root-finding; stochastic systems; third-order cumulants; transfer function; Adaptive control; Additive noise; Automatic control; Autoregressive processes; Higher order statistics; Noise cancellation; Parameter estimation; Programmable control; System identification; Transfer functions;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/9.35282
Filename :
35282
Link To Document :
بازگشت