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".
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| Robust () |
| | Default Constructor for serialization.
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| Robust (const RobustModel::shared_ptr robust, const NoiseModel::shared_ptr noise) |
| | Constructor.
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| ~Robust () override |
| | Destructor.
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| void | print (const std::string &name) const override |
| bool | equals (const Base &expected, double tol=1e-9) const override |
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const RobustModel::shared_ptr & | robust () const |
| | Return the contained robust error function.
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const NoiseModel::shared_ptr & | noise () const |
| | Return the contained noise model.
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| Vector | whiten (const Vector &v) const override |
| | Whiten an error vector.
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| Matrix | Whiten (const Matrix &A) const override |
| | Whiten a matrix.
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| Vector | unwhiten (const Vector &) const override |
| | Unwhiten an error vector.
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| double | loss (const double squared_distance) const override |
| | Compute loss from the m-estimator using the Mahalanobis distance.
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| double | squaredMahalanobisDistance (const Vector &v) const override |
| | Squared Mahalanobis distance v'*R'*R*v = <R*v,R*v>.
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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.
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| double | weight (const Vector &v) const override |
| | get the weight from the effective loss function on residual vector v
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| | Base (size_t dim=1) |
| | primary constructor
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| virtual bool | isConstrained () const |
| | true if a constrained noise model, saves slow/clumsy dynamic casting
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| virtual bool | isUnit () const |
| | true if a unit noise model, saves slow/clumsy dynamic casting
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size_t | dim () const |
| | Dimensionality.
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| virtual Vector | sigmas () const |
| | Calculate standard deviations.
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virtual double | mahalanobisDistance (const Vector &v) const |
| | Mahalanobis distance.
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| virtual void | whitenInPlace (Vector &v) const |
| | in-place whiten, override if can be done more efficiently
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| virtual void | unwhitenInPlace (Vector &v) const |
| | in-place unwhiten, override if can be done more efficiently
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| virtual void | whitenInPlace (Eigen::Block< Vector > &v) const |
| | in-place whiten, override if can be done more efficiently
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| virtual void | unwhitenInPlace (Eigen::Block< Vector > &v) const |
| | in-place unwhiten, override if can be done more efficiently
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