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gtsam::noiseModel::mEstimator Namespace Reference

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 | 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...

## 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.