gtsam::noiseModel::mEstimator Namespace Reference

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

Classes
class	Base
class	Cauchy
	Cauchy implements the "Cauchy" robust error model (Lee2013IROS). More...
class	DCS
	DCS implements the Dynamic Covariance Scaling robust error model from the paper Robust Map Optimization (Agarwal13icra). More...
class	Fair
	Fair implements the "Fair" robust error model (Zhang97ivc) More...
class	GemanMcClure
	GemanMcClure implements the "Geman-McClure" robust error model (Zhang97ivc). More...
class	Huber
	Huber implements the "Huber" robust error model (Zhang97ivc) More...
class	L2WithDeadZone
	L2WithDeadZone implements a standard L2 penalty, but with a dead zone of width 2*k, centered at the origin. More...
class	Null
	Null class is not robust so is a Gaussian ? More...
class	Tukey
	Tukey implements the "Tukey" robust error model (Zhang97ivc) More...
class	Welsh
	Welsh implements the "Welsh" robust error model (Zhang97ivc) More...

Detailed Description

The mEstimator name space contains all robust error functions.

It mirrors the exposition at http://research.microsoft.com/en-us/um/people/zhang/INRIA/Publis/Tutorial-Estim/node24.html which talks about minimizing \sum \rho(r_i), where \rho is a residual 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 Residual \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.