The mEstimator name space contains all robust error functions. More...

Classes
class	Base
	Pure virtual class for all robust error function classes. More...
class	Null
	"Null" robust loss function, equivalent to a Gaussian pdf noise model, or plain least-squares (non-robust). More...
class	Fair
	Implementation of the "Fair" robust error model (Zhang97ivc). More...
class	Huber
	The "Huber" robust error model (Zhang97ivc). More...
class	Cauchy
	Implementation of the "Cauchy" robust error model (Lee2013IROS). More...
class	Tukey
	Implementation of the "Tukey" robust error model (Zhang97ivc). More...
class	Welsch
	Implementation of the "Welsch" robust error model (Zhang97ivc). More...
class	GemanMcClure
	Implementation of the "Geman-McClure" robust error model (Zhang97ivc). More...
class	TruncatedLeastSquares
	Truncated Least Squares (TLS) robust error model. More...
class	DCS
	DCS implements the Dynamic Covariance Scaling robust error model from the paper Robust Map Optimization (Agarwal13icra). More...
class	L2WithDeadZone
	L2WithDeadZone implements a standard L2 penalty, but with a dead zone of width 2*k, centered at the origin. More...
class	AsymmetricTukey
	Implementation of the "AsymmetricTukey" robust error model. More...
class	AsymmetricCauchy
	Implementation of the "AsymmetricCauchy" robust error model. More...
class	Custom
	Implementation of the "Custom" robust error model. More...

Typedefs
using	CustomLossFunction = std::function<double(double)>
using	CustomWeightFunction = std::function<double(double)>
using	CustomGraduatedLossFunction
using	CustomGraduatedWeightFunction

Detailed Description

The mEstimator name space contains all robust error functions.

It mirrors the exposition at https://members.loria.fr/MOBerger/Enseignement/Master2/Documents/ZhangIVC-97-01.pdf which talks about minimizing \sum \rho(r_i), where \rho is a loss function of choice.

To illustrate, let's consider the least-squares (L2), L1, and Huber estimators as examples:

Name Symbol Least-Squares L1-norm Huber Loss \rho(x) 0.5*x^2 |x| 0.5*x^2 if |x|<k, 0.5*k^2 + k|x-k| otherwise Derivative \phi(x) x sgn(x) x if |x|<k, k sgn(x) otherwise Weight w(x)=\phi(x)/x 1 1/|x| 1 if |x|<k, k/|x| otherwise

With these definitions, D(\rho(x), p) = \phi(x) D(x,p) = w(x) x D(x,p) = w(x) D(L2(x), p), and hence we can solve the equivalent weighted least squares problem \sum w(r_i) \rho(r_i)

Each M-estimator in the mEstimator name space simply implements the above functions.

Each M-estimator additionally implements "graduated" versions of these functions. Name Symbol Graduated Loss \rho(x,\mu) Graduated Weight \w(x,\mu) The control parameter \mu in [0, 1] transitions the loss from convex (\mu=0) to its original robust form (\mu=1). This is used by continuation-style algorithms (GNC, riSAM) to modify the underlying problem structure.

GTSAM convention for graduated robust losses: \mu in [0, 1] \mu = 0: most convex / least-squares-like initialization \mu = 1: final target robust loss Increasing \mu always increases non-convexity, and both endpoints are exact rather than approached asymptotically.

Typedef Documentation

◆ CustomGraduatedLossFunction

using gtsam::noiseModel::mEstimator::CustomGraduatedLossFunction

Initial value:

std::optional<std::function<double(double, double)>>

◆ CustomGraduatedWeightFunction

using gtsam::noiseModel::mEstimator::CustomGraduatedWeightFunction