## Total Least Squares with mixed and/or weighted disturbances

Version 2.0.0.1 (8.44 KB) by
Generalized Total Least Squares with mixed and/or weighted disturbances
Updated 1 Apr 2021

These functions calculates the solution for the generalized and/or mixed total least squares problem.

The total least squares problem, also known as errors in variables, solves the over-determined set of linear equations (A0+dA)X = (B0+dB), where covariance matrix of the unknown disturbances dA and dB is considered to be diagonal and denoted by E([dA dB]^T[dA dB]) = sigma_d.*I.

The mixed total least squares problem solves the over-determined set of linear equations [A1 A2]X = B, where A1 are the error-free variables, and A2 = A0 + dA2 and B = B0 + dB are the variables with disturbances.

The generalized total least squares problem solves the over-determined set of linear equations (A0 + dA)X = (B0 + dB), where the covariance matrix of the disturbances dA and dB is positive definite and given by sigma_d.*W = E([dA dB]^T[dA dB]).

### Cite As

Ivo Houtzager (2024). Total Least Squares with mixed and/or weighted disturbances (https://github.com/iwoodsawyer/gtls/releases/tag/v2.0.0.1), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2012b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
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##### Acknowledgements

Inspired by: QR/RQ/QL/LQ factorizations

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Version Published Release Notes
2.0.0.1

See release notes for this release on GitHub: https://github.com/iwoodsawyer/gtls/releases/tag/v2.0.0.1

2.0.0.0

- Improved input argument checking
- Fixes in function descriptions
- Add support for under-determined problems
- Fixed estimation with rank deficient problems
- Fixed estimation with full weight matrix W

1.0.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.