数字信号处理chapter-12-5数字信号处理chapter7-12-5数字信号处理chapter7-12-5数字信号处理chapter7-12-5.ppt

Statistical and Adaptive Signal ProcessingChapter 7 Ju Liu juliu@sdu.edu.cn Chapter 7 Fundaments of Order-recursive Algorithms In this chapter, we present different algorithms for the solution of the normal equations, the computation of the minimum mean square error (MMSE), and the implementation of the optimum filter. We start in Section 7.1 with a discussion of some results from matrix algebra that are useful for the development of order-recursive algorithms and introduce an algorithm for the order-recursive computation of the LDLH decomposition, the MMSE, and the optimum estimate in the general case. In Section 7.2, we present some interesting interpretations for the various introduced algorithmic quantities and procedures that provide additional insight into the optimum filtering problem. Chapter 7 Fundaments of Order-recursive Algorithms Chapter 7 Fundaments of Order-recursive Algorithms Section 7.5 provides a derivation of the lattice-ladder structures foroptimum filtering and prediction, their structural and statistical properties, and algorithms for transformations between the various sets of parameters. Section 7.7 deals with efficient,order-recursive algorithms for the triangularization and inversion of Toeplitz matrices. The chapter concludes with Section 7.8 which provides a concise introduction to the Kalman filtering algorithm. The Kalman filter provides a recursive solution to the minimum MSE filtering problem when the input stochastic process is described by a known state space model. This is possible because the state space model leads to a recursive formula for the updating of the required second-order moments. Clearly, if we know the vector , we can determine , using (7.1.32); however,its practical utility depends on how easily we can obtain the vector . In general, requires the solution of an m×m line