Linear Estimation

Front Cover
Prentice Hall, 2000 - Mathematics - 854 pages

This original work offers the most comprehensive and up-to-date treatment of the important subject of optimal linear estimation, which is encountered in many areas of engineering such as communications, control, and signal processing, and also in several other fields, e.g., econometrics and statistics. The book not only highlights the most significant contributions to this field during the 20th century, including the works of Wiener and Kalman, but it does so in an original and novel manner that paves the way for further developments. This book contains a large collection of problems that complement it and are an important part of piece, in addition to numerous sections that offer interesting historical accounts and insights. The book also includes several results that appear in print for the first time.

FEATURES/BENEFITS

  • Takes a geometric point of view.
  • Emphasis on the numerically favored array forms of many algorithms.
  • Emphasis on equivalence and duality concepts for the solution of several related problems in adaptive filtering, estimation, and control.
    • These features are generally absent in most prior treatments, ostensibly on the grounds that they are too abstract and complicated. It is the authors' hope that these misconceptions will be dispelled by the presentation herein, and that the fundamental simplicity and power of these ideas will be more widely recognized and exploited. Among other things, these features already yielded new insights and new results for linear and nonlinear problems in areas such as adaptive filtering, quadratic control, and estimation, including the recent Hà theories.

From inside the book

 

83 pages matching stochastic in this book

Where's the rest of this book?

Results 1-3 of 83

Contents

Problems
1
DETERMINISTIC LEASTSQUARES PROBLEMS
40
A On Systems of Linear Equations
74
Copyright

37 other sections not shown

Common terms and phrases

algebraic array algorithm assume assumption backwards causal column computed Consider continuous-time convergence covariance matrix DARE defined denote deterministic diagonal discrete-time displacement structure dual eigenvalues entries equivalent error estimation problem fact formula full rank given Gramian Gramian matrix Hermitian Hermitian matrix initial condition innovations invertible Kailath Kalman filter Kp.i least-squares problem Lemma linear lower triangular Lyapunov equation Moreover nonsingular observations obtain optimal orthogonal P₁ Pi+1 positive-definite positive-semi-definite Prob Proof R₂ random variables Re,i Remark Riccati equation Riccati recursion satisfies scalar Schur Schur complement sequence Show signature matrix solving stabilizable stabilizing solution stable state-space model stationary process stochastic Sy(z Theorem theory time-invariant transformation triangular factorization uncorrelated unique unit circle unitary matrix variance vector verify white-noise Wiener Wiener filtering Xi+1 z-transform zero zero-mean

Bibliographic information

TitleLinear Estimation
Prentice-Hall information and system sciences series
AuthorsThomas Kailath, Ali H. Sayed, Babak Hassibi
Editionillustrated
PublisherPrentice Hall, 2000
Original fromthe University of California
DigitizedApr 6, 2011
ISBN0130224642, 9780130224644
Length854 pages
Subjects ›  › 

Mathematics / Algebra / General
Mathematics / Applied
Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
Technology & Engineering / Electrical
Technology & Engineering / Electronics / General
  
Export CitationBiBTeX EndNote RefMan