ShonanAveragingParameters

Created by Codex.

Configure the relaxation, gauge handling, anchoring, robustness, and certification used by Shonan averaging.

Authors: Frank Dellaert, et al. (see THANKS for the full author list)

See LICENSE for the license information

Mathematical idea¶

At each staircase level, the optimizer searches on $\mathrm{SO}(p)$ and evaluates a certificate matrix $S$ . A nonnegative minimum eigenvalue,

\lambda_{\min}(S)\ge 0,

(1)

certifies the relaxed optimum under the Shonan construction; a negative eigenvector supplies an escape direction to the next level. The embedded Levenberg–Marquardt (LM) parameters control each nonlinear solve.

try:
    import google.colab
    %pip install --quiet gtsam-develop
except ImportError:
    pass

import gtsam
import numpy as np

from gtsam import symbol_shorthand

C = symbol_shorthand.C
K = symbol_shorthand.K
P = symbol_shorthand.P
S = symbol_shorthand.S
X = symbol_shorthand.X

Python variants¶

Use ShonanAveragingParameters2 with planar rotations and ShonanAveragingParameters3 with spatial rotations. Both wrap a LevenbergMarquardtParams object and add Shonan-specific controls.

lm = gtsam.LevenbergMarquardtParams()
lm.setMaxIterations(100)

parameters = gtsam.ShonanAveragingParameters3(lm)
parameters.setAnchor(0, gtsam.Rot3())
parameters.setAnchorWeight(1e3)
parameters.setUseHuber(True)
parameters.setCertifyOptimality(True)
parameters.setOptimalityThreshold(1e-4)

print("anchor:", parameters.getAnchor()[0])
print("Huber enabled:", parameters.getUseHuber())
print("certification enabled:", parameters.getCertifyOptimality())

anchor: 0
Huber enabled: True
certification enabled: True

Tuning guidance¶

Start from defaults. Set an anchor when a particular world frame matters; otherwise the algorithm handles the global rotation gauge. Huber loss helps with moderate outliers, but severely corrupted rotation graphs may need explicit outlier rejection before averaging. Certification costs extra eigenvalue work and is valuable when a global-optimality statement matters.

Source¶

ShonanAveraging.h