SPECTRAL FACTORIZATION OF LINEAR PERIODIC-SYSTEMS WITH APPLICATION TO THE OPTIMAL PREDICTION OF PERIODIC ARMA MODELS

被引:11
作者
BITTANTI, S [1 ]
DENICOLAO, G [1 ]
机构
[1] POLITECN MILAN,DIPARTIMENTO ELETTRON,CNR,CTR TEORIA SISTEMI,I-20133 MILAN,ITALY
关键词
DISCRETE-TIME SYSTEMS; TIME-VARYING SYSTEMS; SPECTRAL FACTORIZATION; ZEROS; PREDICTION THEORY; KALMAN FILTERS; ARMA MODELS; PERIODIC SYSTEMS; CYCLOSTATIONARY PROCESSES;
D O I
10.1016/0005-1098(93)90149-N
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A cyclostationary process is a stochastic process whose statistical parameters, such as mean and autocorrelation, exhibit suitable periodicity. In this paper, we consider the cyclospectral factorization problem which consists of finding a Markovian (state-space) realization of a given cyclostationary process. It is shown that a significant class of periodic state-space representations is in a one-to-one correspondence with the periodic solutions of a difference periodic Riccati equation. This result is applied to the solution of the prediction problem for ARMA models with periodically varying coefficients. If the periodic ARMA model is minimum-phase, the optimal predictor is given a simple input-output expression that generalizes the well-known one for time-invariant ARMAs. Otherwise, the computation of the optimal predictor calls for the solution of a cyclospectral factorization problem.
引用
收藏
页码:517 / 522
页数:6
相关论文
共 25 条
[1]   SPECTRAL FACTORIZATION OF TIME-VARYING COVARIANCE FUNCTIONS [J].
ANDERSON, BD ;
MOORE, JB ;
LOO, SG .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1969, 15 (05) :550-+
[2]   SPECTRAL FACTORIZATION OF A FINITE-DIMENSIONAL NONSTATIONARY MATRIX COVARIANCE [J].
ANDERSON, BD ;
MOYLAN, PJ .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1974, AC19 (06) :680-692
[3]  
[Anonymous], 1979, OPTIMAL FILTERING
[4]   DISCRETE-TIME LINEAR PERIODIC-SYSTEMS - GRAMIAN AND MODAL CRITERIA FOR REACHABILITY AND CONTROLLABILITY [J].
BITTANTI, S ;
BOLZERN, P .
INTERNATIONAL JOURNAL OF CONTROL, 1985, 41 (04) :909-928
[5]   THE DIFFERENCE PERIODIC RICCATI EQUATION FOR THE PERIODIC PREDICTION-PROBLEM [J].
BITTANTI, S ;
COLANERI, P ;
DENICOLAO, G .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1988, 33 (08) :706-712
[6]   DISCRETE-TIME LINEAR PERIODIC-SYSTEMS - A NOTE ON THE REACHABILITY AND CONTROLLABILITY INTERVAL LENGTH [J].
BITTANTI, S ;
COLANERI, P ;
DENICOLAO, G .
SYSTEMS & CONTROL LETTERS, 1986, 8 (01) :75-78
[7]   AN ALGEBRAIC RICCATI EQUATION FOR THE DISCRETE-TIME PERIODIC PREDICTION-PROBLEM [J].
BITTANTI, S ;
COLANERI, P ;
DENICOLAO, G .
SYSTEMS & CONTROL LETTERS, 1990, 14 (01) :71-78
[8]  
BITTANTI S, 1990, 11TH IFAC WORLD C TA, V6, P200
[9]  
BITTANTI S, 1988, 1986 P C LIN ALG SIG, P315
[10]  
BITTANTI S, 1991, RICCATI EQUATION, P127