Gauss Newton Method for Accelerometer calibration

Question

I am following the code obtained in matlab file exchange for the paper

http://ieeexplore.ieee.org/document/4655611/

He calculates the Hessian matrix as follows using Jacobian Matrix J,

**H = inv(J'*J); % Hessian matrix,** 

How is this relation true.

And also the g value used is 1 to construct the COST function to be minimized using LEAST SQUARES , but should'nt it be the local gravity value at the particular place you are carrying out the calibration??

Link to the code :

MATLAB Code

Please throw some light on this. Thank You.

Answer 1

$J^T \times J$ is an approximation to the Hessian which comes from the Levenberg Marquardt Algorithm. It is a least-squares approach, and seems to be used frequently in a variety of optimization problems (such as training artificial neural networks). See equations 6 and 7 of Appendix A from this paper http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=4593&context=etd for a derivation.