Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications

Front Matter....Pages i-x
Introduction to Total Least Squares and Errors-In-Variables Modeling....Pages 1-11
Front Matter....Pages 13-13
TLS and Its Improvements by Semiparametric Approach....Pages 15-24
Unifying Least Squares, Total Least Squares and Data Least Squares....Pages 25-34
Bounds for the Least Squares Residual Using Scaled Total Least Squares....Pages 35-44
Front Matter....Pages 45-45
Recent Developments in Rank Revealing and Lanczos Methods for TLS-Related Problems....Pages 47-56
A Regularized Total Least Squares Algorithm....Pages 57-66
The Parametric Quadratic Form Method for Solving TLS Problems with Elementwise Weighting....Pages 67-76
Front Matter....Pages 77-77
Structured Total Least Squares....Pages 79-91
Fast Structured Total Least Squares Algorithms via Exploitation of the Displacement Structure....Pages 93-106
The Extended STLS Algorithm for Minimizing the Extended LS Criterion....Pages 107-117
Front Matter....Pages 119-119
Bayesian Smoothing for Measurement Error Problems....Pages 121-130
On the Polynomial Measurement Error Model....Pages 131-143
On Consistent Estimators in Nonlinear Functional Errors-In-Variables Models....Pages 145-154
On Consistent Estimators in Linear and Bilinear Multivariate Errors-In-Variables Models....Pages 155-164
Identification of Semi-Linear Models within an Errors-In-Variables Framework....Pages 165-177
Cox’s Proportional Hazards Model under Covariate Measurement Error....Pages 179-188
Front Matter....Pages 189-189
State-Space Estimation with Uncertain Models....Pages 191-202
Models for Robust Estimation and Identification....Pages 203-212
Robust Solutions to Linear Approximation Problems under Ellipsoidal Uncertainty....Pages 213-222
Front Matter....Pages 223-223
QR Factorization of the Jacobian in Some Structured Nonlinear Least Squares Problems....Pages 225-234
Front Matter....Pages 223-223
Neural Minor Component Analysis and TLS....Pages 235-250
On the Structural Line Segment Model....Pages 251-260
Model Fitting for Multiple Variables by Minimising the Geometric Mean Deviation....Pages 261-267
Front Matter....Pages 269-269
Perspectives on Errors-In-Variables Estimation for Dynamic Systems....Pages 271-280
Errors-In-Variables Filtering in Behavioural and State-Space Contexts....Pages 281-291
Weighted Total Least Squares, Rank Deficiency and Linear Matrix Structures....Pages 293-304
Frequency-Domain TLS and GTLS Algorithms for Modal Analysis Applications....Pages 305-318
Front Matter....Pages 319-319
A New Decimative Spectral Estimation Method with Unconstrained Model Order and Decimation Factor....Pages 321-330
Modeling Audio with Damped Sinusoids Using Total Least Squares Algorithms....Pages 331-340
Real-Time TLS Algorithms in Gaussian and Impulse Noise Environments....Pages 341-350
Front Matter....Pages 351-351
Efficient Computation of the Riemannian SVD in Total Least Squares Problems in Information Retrieval....Pages 353-364
Constrained Total Least Squares for Color Image Reconstruction....Pages 365-374
Total Least Squares in Astronomy....Pages 375-384
TLS and Constrained TLS Neural Networks for Computer Vision....Pages 385-395
Back Matter....Pages 397-397