diff --git a/environment_v2_linux_cpuonly.yml b/environment_v2_linux_cpuonly.yml
new file mode 100644
index 000000000..2e1e18020
--- /dev/null
+++ b/environment_v2_linux_cpuonly.yml
@@ -0,0 +1,56 @@
+name: gtsfm-v2
+channels:
+  # for priority order, we prefer pytorch as the highest priority as it supplies
+  # latest stable packages for numerous deep learning based methods. conda-forge
+  # supplies higher versions of packages like opencv compared to the defaults
+  # channel.
+  - pytorch
+  - conda-forge
+dependencies:
+  # python essentials
+  - python
+  - pip
+  # formatting and dev environment
+  - black
+  - coverage
+  - mypy
+  - pylint
+  - pytest
+  - flake8
+  - isort
+  # dask and related
+  - dask # same as dask[complete] pip distribution
+  - asyncssh
+  - python-graphviz
+  # core functionality and APIs
+  - matplotlib
+  - networkx
+  - numpy
+  - nodejs
+  - pandas
+  - pillow
+  - scikit-learn
+  - seaborn
+  - scipy
+  - hydra-core
+  - gtsam
+  # 3rd party algorithms for different modules
+  - cpuonly # replacement of cudatoolkit for cpu only machines
+  - pytorch
+  - torchvision
+  - kornia
+  - pycolmap
+  - opencv
+  # io
+  - h5py
+  - plotly
+  - tabulate
+  - simplejson
+  - open3d
+  - colour
+  - pydot
+  - trimesh
+  # testing
+  - parameterized
+  # - pip:
+      # - pydegensac
diff --git a/gtsfm/averaging/rotation/shonan.py b/gtsfm/averaging/rotation/shonan.py
index ad8643a43..12288c1ce 100644
--- a/gtsfm/averaging/rotation/shonan.py
+++ b/gtsfm/averaging/rotation/shonan.py
@@ -11,6 +11,7 @@
 Authors: Jing Wu, Ayush Baid, John Lambert
 """
 
+import math
 from typing import Dict, List, Optional, Set, Tuple
 
 import gtsam
@@ -79,7 +80,9 @@ def __measurements_from_2view_relative_rotations(
                 continue
             if self._weight_by_inliers and num_correspondences_dict[(i1, i2)] > 0:
                 # ignore translation during rotation averaging
-                noise_model = gtsam.noiseModel.Isotropic.Sigma(ROT3_DOF, 1 / num_correspondences_dict[(i1, i2)])
+                noise_model = gtsam.noiseModel.Isotropic.Sigma(
+                    ROT3_DOF, 1 / math.sqrt(num_correspondences_dict[(i1, i2)])
+                )
 
             measurements.append(gtsam.BinaryMeasurementRot3(i2, i1, i2Ri1, noise_model))