Classes
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.



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autogenerated on Sat May 8 2021 02:58:53