噪声自协方差估计.pdfVIP

2 TWMCC Texas-Wisconsin Modeling and Control Consortium 1 Technical report number 2003-04 A New Autocovariance Least-Squares Method for Estimating Noise Covariances ∗ Brian J. Odelson, Murali R. Rajamani and James B. Rawlings Department of Chemical Engineering University of Wisconsin-Madison Madison, WI 53706 September 1, 2003 revised: August 18, 2004 re-revised: April 4, 2005 Abstract Industrial implementation of model-based control methods, such as model predictive control, is often complicated by the lack of knowledge about the disturbances entering the system. In this pa- per, we present a new method (ALS) to estimate the variances of the disturbances entering the process using routine operating data. A variety of methods have been proposed to solve this problem. Of note, we compare ALS to the classic approach presented in [12]. This classic method, and those based on it, use a three-step pro- cedure to compute the covariances. The method presented in this paper is a one-step procedure, which yields covariance estimates with lower variance on all examples tested. Furthermore, the for- mulation used in this paper provides necessary and sufficient con- ditions for uniqueness of the estimated covariances, previously not available in the literature. We show that the estimated covariances are unbiased and converge to the true values with increasing sam- ple size. We also use semidefinite programming to add posit