An algorithmic approach to the total least-squares problem with linear and quadratic constraints |
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Authors: | Burkhard Schaffrin Yaron A Felus |
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Institution: | (1) School of Earth Sciences, The Ohio State University, Columbus, OH, USA;(2) Surveying Engineering Department, Ferris State University, Big Rapids, MI, USA |
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Abstract: | Proper incorporation of linear and quadratic constraints is critical in estimating parameters from a system of equations.
These constraints may be used to avoid a trivial solution, to mitigate biases, to guarantee the stability of the estimation,
to impose a certain “natural” structure on the system involved, and to incorporate prior knowledge about the system. The Total
Least-Squares (TLS) approach as applied to the Errors-In-Variables (EIV) model is the proper method to treat problems where
all the data are affected by random errors. A set of efficient algorithms has been developed previously to solve the TLS problem,
and a few procedures have been proposed to treat TLS problems with linear constraints and TLS problems with a quadratic constraint.
In this contribution, a new algorithm is presented to solve TLS problems with both linear and quadratic constraints. The new
algorithm is developed using the Euler-Lagrange theorem while following an optimization process that minimizes a target function.
Two numerical examples are employed to demonstrate the use of the new approach in a geodetic setting. |
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Keywords: | total least-squares non-convex optimization adjustment with constraints |
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