Detailed Description

Base class for robust error models The robust M-estimators above simply tell us how to re-weight the residual, and are isotropic kernels, in that they do not allow for correlated noise.

They also have no way to scale the residual values, e.g., dividing by a single standard deviation. Hence, the actual robust noise model below does this scaling/whitening in sequence, by passing both a standard noise model and a robust estimator.

Taking as an example noise = Isotropic::Create(d, sigma), we first divide the residuals uw = |Ax-b| by sigma by "whitening" the system (A,b), obtaining r = |Ax-b|/sigma, and then we pass the now whitened residual 'r' through the robust M-estimator. This is currently done by multiplying with sqrt(w), because the residuals will be squared again in error, yielding 0.5 \sum w(r)*r^2.

In other words, while sigma is expressed in the native residual units, a parameter like k in the Huber norm is expressed in whitened units, i.e., "nr of sigmas".

Inheritance diagram for gtsam::noiseModel::Robust:

Public Member Functions
	Robust ()
	Default Constructor for serialization.

	Robust (const RobustModel::shared_ptr robust, const NoiseModel::shared_ptr noise)
	Constructor.

	~Robust () override
	Destructor.

void	print (const std::string &name) const override

bool	equals (const Base &expected, double tol=1e-9) const override

const RobustModel::shared_ptr &	robust () const
	Return the contained robust error function.

const NoiseModel::shared_ptr &	noise () const
	Return the contained noise model.

Vector	whiten (const Vector &v) const override
	Whiten an error vector. More...

Matrix	Whiten (const Matrix &A) const override
	Whiten a matrix. More...

Vector	unwhiten (const Vector &) const override
	Unwhiten an error vector. More...

double	loss (const double squared_distance) const override
	Compute loss from the m-estimator using the Mahalanobis distance. More...

virtual void	WhitenSystem (Vector &b) const

void	WhitenSystem (std::vector< Matrix > &A, Vector &b) const override

void	WhitenSystem (Matrix &A, Vector &b) const override

void	WhitenSystem (Matrix &A1, Matrix &A2, Vector &b) const override

void	WhitenSystem (Matrix &A1, Matrix &A2, Matrix &A3, Vector &b) const override

Vector	unweightedWhiten (const Vector &v) const override
	Useful function for robust noise models to get the unweighted but whitened error. More...

double	weight (const Vector &v) const override
	get the weight from the effective loss function on residual vector v More...

Public Member Functions inherited from gtsam::noiseModel::Base
	Base (size_t dim=1)
	primary constructor More...

virtual bool	isConstrained () const
	true if a constrained noise model, saves slow/clumsy dynamic casting More...

virtual bool	isUnit () const
	true if a unit noise model, saves slow/clumsy dynamic casting More...

size_t	dim () const
	Dimensionality.

virtual void	print (const std::string &name="") const =0

virtual bool	equals (const Base &expected, double tol=1e-9) const =0

virtual Vector	sigmas () const
	Calculate standard deviations. More...

virtual Vector	whiten (const Vector &v) const =0
	Whiten an error vector. More...

virtual Matrix	Whiten (const Matrix &H) const =0
	Whiten a matrix. More...

virtual Vector	unwhiten (const Vector &v) const =0
	Unwhiten an error vector. More...

virtual double	squaredMahalanobisDistance (const Vector &v) const
	Squared Mahalanobis distance v'R'Rv = <Rv,R*v> More...

virtual double	mahalanobisDistance (const Vector &v) const
	Mahalanobis distance.

virtual double	loss (const double squared_distance) const
	loss function, input is Mahalanobis distance More...

virtual void	WhitenSystem (std::vector< Matrix > &A, Vector &b) const =0

virtual void	WhitenSystem (Matrix &A, Vector &b) const =0

virtual void	WhitenSystem (Matrix &A1, Matrix &A2, Vector &b) const =0

virtual void	WhitenSystem (Matrix &A1, Matrix &A2, Matrix &A3, Vector &b) const =0

virtual void	whitenInPlace (Vector &v) const
	in-place whiten, override if can be done more efficiently More...

virtual void	unwhitenInPlace (Vector &v) const
	in-place unwhiten, override if can be done more efficiently More...

virtual void	whitenInPlace (Eigen::Block< Vector > &v) const
	in-place whiten, override if can be done more efficiently More...

virtual void	unwhitenInPlace (Eigen::Block< Vector > &v) const
	in-place unwhiten, override if can be done more efficiently More...

virtual Vector	unweightedWhiten (const Vector &v) const
	Useful function for robust noise models to get the unweighted but whitened error. More...

virtual double	weight (const Vector &v) const
	get the weight from the effective loss function on residual vector v More...

Static Public Member Functions
static shared_ptr	Create (const RobustModel::shared_ptr &robust, const NoiseModel::shared_ptr noise)

Public Types
typedef boost::shared_ptr< Robust >	shared_ptr

Public Types inherited from gtsam::noiseModel::Base
typedef boost::shared_ptr< Base >	shared_ptr

Protected Types
typedef mEstimator::Base	RobustModel

typedef noiseModel::Base	NoiseModel

Protected Attributes
const RobustModel::shared_ptr	robust_
	robust error function used

const NoiseModel::shared_ptr	noise_
	noise model used

Protected Attributes inherited from gtsam::noiseModel::Base
size_t	dim_