Lessons in Estimation Theory for Signal Processing, Commu-
D. Subbaram Naidu, Manor Mendel, I. J. Shynk · 1996
Each lesson begins with a short summary (similar to a paper abstract) and an introduction, followed by several detailed sec- tions that include derivations of the estimators, discussions of their properties, related theorems and proofs, and examples of the key concepts and techniques. It concludes with a set of summary questions that review the lesson as well as several problems designed as homework exercises. Some of the lessons also include a discussion of computational issues which is a new feature of this edition. In an appendix, all of the major results are briefly listed either by theorem, corollary, or equation number for ease of reference. After the basic discrete-time measurement model is defined in the second lesson, least-squares (LS) estimators (for both batch and recursive processing) are presented in the next several lessons. These sections introduce and utilize the matrix inversion lemma (Sher- man-Morrison-Woodbury formula) to derive the recursive updates and discuss how singular value decomposition can be used to compute least-squares estimates. (Unfortunately, the QR factorization, which is often used to solve least-squares problems numerically, is not mentioned in this section.) They are followed by a general discussion of small-sample and large-sample (asymptotic) properties of estima- tors such as unbiasedness, efficiency (the Cramer-Rao lower bound and the Fisher information matrix), consistency, and asymptotic normality. The best linear unbiased estimator (BLUE) is then derived