"Derivation and proof" of SVD's most small squares

0.SLAM in SVD The application of least squares

In slam applications, the least squares are used when calculating the homography matrix,fundamental Matrix, as well as for triangulation (triangulation).

1. Background

Least squares fitting of a pile of observed noisy data

2. Theoretical Models

3. Optimize your goals

4. Optimization Process

5. Engineering Implementation

6. Proof of the least squares optimal solution using SVD for the homogeneous equation (thanks to the derivation of the @ Liu Yi )

7. method of least squares for other non-homogeneous equations

8. discussion of different least squares methods

9. The theoretical provenance of this article

The above deduction is not complicated, but if you want to understand the ins and outs of least squares optimization, it is recommended that you see the Appendix 5:least-squares minimization in multiple View Geometry in computer Vision)

Thank you.

Thank you @ Liu Yi the derivation of the SVD of the homogeneous equation Group is the proof of the least squares.

Thank you for the introduction of the matrix condition number, and some related proof derivation.

Thanks for the intense discussion of the other members of the @ Bubble robot .

"Derivation and proof" of SVD's most small squares