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Total least squares with linear constraints
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992Numerically stable closed form expressions for the solution of the total least squares (TLS) problem with linear equality constraints (LCTLS) are derived. A constrained subspace linear predictive frequency estimation technique called LCTLS-linear predictive (LCTLS-LP) is proposed.
Eric M. Dowling +2 more
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2010
In atmospheric remote sensing, near real-time software processors frequently use approximations of the Jacobian matrix in order to speed up the calculation. If the forward model F(x) depends on the state vector x through some model parameters bk, F(x) = F(b1 (x),..., bN (x)),
Adrian Doicu +2 more
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In atmospheric remote sensing, near real-time software processors frequently use approximations of the Jacobian matrix in order to speed up the calculation. If the forward model F(x) depends on the state vector x through some model parameters bk, F(x) = F(b1 (x),..., bN (x)),
Adrian Doicu +2 more
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An Analysis of the Total Least Squares Problem
SIAM Journal on Numerical Analysis, 1980Totla least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector $b (mxl)$ and in the data matrix $A (mxn)$. The technique has been discussed by several authors and amounts to fitting a "best" subspace to the points $(a^{T}_{i},b_{i}), i=1,\ldots,m,$ where $a^{T}_{i}$ is the $i$-th row of $A$. In
Golub, Gene H., Van Loan, Charles F.
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Total least mean squares algorithm
IEEE Transactions on Signal Processing, 1998Widrow (1971) proposed the least mean squares (LMS) algorithm, which has been extensively applied in adaptive signal processing and adaptive control. The LMS algorithm is based on the minimum mean squares error. On the basis of the total least mean squares error or the minimum Raleigh quotient, we propose the total least mean squares (TLMS) algorithm ...
Da-Zheng Feng +2 more
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Total least squares in robot calibration
2005The role of input noise is seldom considered in robot calibration. The methodology of total least squares may be applied to handle both input and output noise in robot calibration. Experimentally, we apply this method towards joint torque sensor calibration, and towards kinematic calibration of a redundant parallel-drive spherical joint in a variant ...
John M. Hollerbach, Ali Nahvi
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2018
The chapter treats total least squares (TLS), which in statistics corresponds to orthogonal regression. Some different extensions are discussed, including ways to show how uncertainties in different matrix elements may be related or correlated. The application of TLS to identification of dynamic systems is also treated.
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The chapter treats total least squares (TLS), which in statistics corresponds to orthogonal regression. Some different extensions are discussed, including ways to show how uncertainties in different matrix elements may be related or correlated. The application of TLS to identification of dynamic systems is also treated.
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The Total Least Squares Technique
1995Abstract Notice that AXo = (AA+)B and, as AA+ is just the orthogonal projector onto Im A, Xo is the minimum norm solution of the consistent system AX = (AA+)B obtained by projecting Im B onto Im A. Thus, in this process, the subspace Im A plays the pivotal role and the “right-hand side” matrix B is “adjusted” to produce a solvable ...
Peter Lancaster, Leiba Rodman
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Structured Total Least Squares
2002In this paper an overview is given of the Structured Total Least Squares (STLS) approach and its recent extensions. The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be imposed.
Philippe Lemmerling, Sabine Van Huffel
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On the Significance of Nongeneric Total Least Squares Problems
SIAM Journal on Matrix Analysis and Applications, 1992Consider an overdetermined system \(AX=B\), where \(A\in\mathbb{R}^{m\times n}\), \(B\in\mathbb{R}^{m\times d}\). Any \(X\in\mathbb{R}^{n\times d}\) is called a total least squares solution of this system, provided \(X\) solves \(\widehat A X=\widehat B\), where \([\widehat A,\widehat B]\in\mathbb{R}^{m\times(n+d)}\) minimizes \(\| [A,B]-[\widehat A ...
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