gtsam::noiseModel::mEstimator Namespace Reference

Classes
class	Base
class	Cauchy
class	DCS
class	Fair
	Fair implements the "Fair" robust error model (Zhang97ivc) More...
class	GemanMcClure
class	Huber
	Huber implements the "Huber" robust error model (Zhang97ivc) More...
class	L2WithDeadZone
class	Null
	Null class should behave as Gaussian. More...
class	Tukey
	Tukey implements the "Tukey" robust error model (Zhang97ivc) More...
class	Welsch
	Welsch implements the "Welsch" robust error model (Zhang97ivc) More...

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 (r_i), where 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 (x) 0.5*x^2 |x| 0.5*x^2 if |x|<k, 0.5*k^2 + k|x-k| otherwise Derivative (x) x sgn(x) x if |x|<k, k sgn(x) otherwise Weight w(x)=(x)/x 1 1/|x| 1 if |x|<k, k/|x| otherwise

With these definitions, D((x), p) = (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 w(r_i) (r_i)

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