niosus / notebooks

Just a bunch of iPython notebooks for future references.

IPython3 Notebooks

Just a bunch of iPython notebooks for future references.

List of notebooks

Matrix Decomposition: Eigenvalue decomposition vs SVD

ICP: SVD vs Least Squares

Non-Linear Least Squares

We start with a typical least squares formulation and go through most useful methods for solving this type of minimization problems, such as Steepest Gradient Descent and the Gauss-Newton method. We derive everything from the way the problem looks like and use its Taylor expansion.

notebooks's Issues

Question Regarding Covariance/Information Matrix

Greetings,

I had a question about estimating the Covariance/Information matrix of the resulting transform in order to use the ICP algorithm as a front end for graph SLAM. I noticed the value being computed in the prepare_system function. However that is a scalar value and I believe that I am looking for a 3x3 information matrix for graph SLAM in SE(2) (x and y positions along with heading angle theta).

I have come across a few methods suggesting that computing the Hessian of the error function should be able to provide me with the matrix I am looking for, but I wanted to check and see whether that is the appropriate method and whether the provided icp.ipynb notebook already computes it somewhere I am not seeing.

Thank you for your time!

Possible Issue with Jacobian Function

Greetings,

The Jacobian function in the icp.ipynb file on line "In [14]" uses the derivative of the rotation matrix at a constant angle of zero rather than the derivative of the rotation matrix at the current angle. Because of this, I suspect that the Jacobian may be approximating about the wrong point.

Should my math be correct, I would recommend replacing the zero with the variable "theta".

Update step in Newton's method

Dear @niosus ,

thanks for the informative least-squares notebook.
I have a simple clarification question.
Should the formula for finding the parameter $h$ be $Hh = -F'(x)$. It occurs right after the formula (8).

Thanks!

Can the ICP iteration be stopped once convergence is achieved?

Hi,

Since the convergence of data is reached before 5 iteration, can it be stopped to improved to computational time since the data had already been converge. If so, how do you suggest in doing this?