An algorithmic approach to the total least-squares problem with linear and quadratic constraints

Burkhard Schaffrin, Yaron A. Felus

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


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.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalStudia Geophysica et Geodaetica
Issue number1
StatePublished - 2009
Externally publishedYes


  • Adjustment with constraints
  • Non-convex optimization
  • Total least-squares


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