IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 46, NO. 11, NOVEMBER 1998 3123 where it was found that the introduction of the delay in MMSE filter design significantly improved the separation performance at the expense of increased computational complexity. REFERENCES [1] C. Jutten and J. Herault, “Blind separation of sources, Part I: An adaptive algorithm based on neuromorphic architecture,” Signal Process., vol. 24, pp. 1–10, 1991. [2] J. L. Lacoume and P. Ruiz, “Separation of independent sources from cor- related inputs,” IEEE Trans. Signal Processing, vol. 40, pp. 3074–3078, Dec. 1992. [3] D. Yellin and E. Weinstein, “Criteria for multichannel signal separation,” IEEE Trans. Signal Processing, vol. 42, pp. 2158–2168, Aug. 1994. [4] A. Swami, G. B. Giannakis, and S. Shamsunder, “Multichannel ARMA processes,” IEEE Trans. Signal Processing, vol. 42, pp. 898–914, Apr. 1994. [5] J. K. 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Grimble Abstract— The solution of the optimal weighted minimum-variance estimation problem is considered using a polynomial matrix description for the continuous-time linear system description, which allows for the possible presence of transport delays on the measurements. The filter or predictor is given by the solution of two diophantine equations and is equivalent (in the delay-free case) to the state equation form of the steady- state Kalman filter or the transfer-function matrix form of the Wiener filter. The pole-zero properties of the optimal filter are more obvious in the polynomial representation, and useful insights into the disturbance rejection properties of the filter are obtained. Allowance is made for both control and disturbance input subsystems and white and colored measurement noise (or an output disturbance subsystem). The model structure was determined by the needs of filtering and prediction problems in the metal processing industries, where, for example, there are delays between the X-ray gauge and the roll gap of the mill. I. INTRODUCTION Linear filtering and prediction problems are considered for continuous-time systems where signals are to be estimated from delayed noisy measurements and given plant and noise descriptions. In real applications, measurements are often delayed, and hence, the system model allows for pure transport delays ( terms) in the measurement channel. This causes considerable additional difficulty compared with the delay-free case [1] since the calculation of the causal components of the transforms requires the time shifted impulse responses to be considered. Although the control problem for continuous systems with delays has been explored [2], using a frequency domain approach, the estimation problems have not previously been considered. The use of polynomial estimation methods in real signal processing applications has been described in [3]. II. SIGNAL MODEL AND OUTPUT ESTIMATOR Since both control and signal processing problems are of interest, the system model shown in Fig. 1 can represent either an industrial plant or a message generating process [9]. The system is assumed to be linear and time invariant, and the noise sources are stationary. These white noise signals are mutually inde- pendent with zero means, and the respective covariances are defined as cov cov and cov , respectively. Here, denotes the unit impulse response function, and the assumption is normally made that The system is assumed to be in the steady state, that is, the initial time The various subsystems are necessarily taken to be free of unstable hidden modes and are defined as Plant (1) Signal (2) Manuscript received September 17, 1996; revised March 4, 1998. This work was supported by the Engineering and Physical Sciences Research Council on Flight Control project GR/K/56 216. The associate editor coordinating the review of this paper and approving it for publication was Prof. Pierre Comon. The author is with the Industrial Control Centre, University of Strathclyde, Glasgow, U.K. Publisher Item Identifier S 1053-587X(98)07823-4. 1053–587X/98$10.00  1998 IEEE