# GraphSlam Matrix Subtraction doubt

I am trying to implement GraphSlam from this paper. I have some doubt regarding the algorithm described in this paper at table2: Algorithm GraphSLAM_linearize.

I have a doubt in line 7. As per my knowledge, Gt is a 3*3 matrix. How could I subtract 1 from a 3*3 matrix? As per matrix subtraction rule both matrices should be in same dimension.

That is not $[1 - G_t]$, it's $[1 \qquad -G_t]$ (exaggerating the space between the two elements. For all intents and purposes, consider $1$ to be the equivalent identity matrix, and $G_t$ is just a submatrix in this. Intuitively, in this case, $1$ would be $I_{3\times3}$.

In equation 7, the multiplication follows this order:

$(6 \times 3) * (3 \times 3) * (3 \times 6)$

Remember that the information matrix is not $(3\times3)$. It's a big, sparse matrix with non-zero submatrices along its diagonal, so adding a $(6\times6)$ matrix to that would mean you need to decompose the resulting matrix from equation 7 into submatrices that correspond to $\Omega$ at $x_t$ and $x_{t-1}$, etc.

• Thank you. Now it's clear to me. What is the dimension of Omega Matrix? Is that depend upon the how many odometer data I have and how many measurement data I have? I am using UTIAS Multi robot Co-operative Localization and Mapping Dataset. Robot 1 have near about 1lakh odometer data and 8000 measurement data. So in respect to original Omega dimension is it 1lakh8000*1lakh8000 Matrix? – Encipher Jul 7 '18 at 7:14
• robotics.stackexchange.com/questions/16026/… please take look in this question. – Encipher Jul 13 '18 at 17:45
• What is the need of augmented a identity matrix with Gt? – Encipher Jul 19 '18 at 18:06