Classes
class	Data

class	Direction

class	EqF

class	G

class	Input

class	Measurement

class	State

Functions
np.ndarray	blockDiag (np.ndarray A, np.ndarray B)

def	checkNorm (np.ndarray x, float tol=1e-3)

np.ndarray	lift (State xi, Input u)

np.ndarray	local_coords (State e)

"State"	local_coords_inv (np.ndarray eps)

np.ndarray	numericalDifferential (f, x)

np.ndarray	outputAction (G X, Direction y, int idx=-1)

np.ndarray	repBlock (np.ndarray A, int n)

State	stateAction (G X, State xi)

np.ndarray	stateActionDiff (State xi)

Input	velocityAction (G X, Input u)

Variables
string	coordinate = "EXPONENTIAL"

Detailed Description

Implementation of Attitude-Bias-Calibration EqF form:
"Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation with Online Calibration"
https://ieeexplore.ieee.org/document/9905914

This module is Alessandro Fornasier's equivariant filter code (https://github.com/aau-cns/ABC-EqF) 
converted to use GTSAM's libraries.

Authors: Jennifer Oum & Darshan Rajasekaran

Function Documentation

◆ blockDiag()

np.ndarray gtsam.examples.EqF.blockDiag	(	np.ndarray	A,
		np.ndarray	B
	)

Create a lock diagonal matrix from blocks A and B

:param A: numpy array
:param B: numpy array
:return: numpy array representing a block diagonal matrix composed of blocks A and B

Definition at line 302 of file EqF.py.

◆ checkNorm()

def gtsam.examples.EqF.checkNorm	(	np.ndarray	x,
		float	tol = `1e-3`
	)

Check norm of a vector being 1 or nan

:param x: A numpy array
:param tol: tollerance, default 1e-3
:return: Boolean true if norm is 1 or nan

Definition at line 21 of file EqF.py.

◆ lift()

np.ndarray gtsam.examples.EqF.lift	(	State	xi,
		Input	u
	)

The Lift of the system (Theorem 3.8, Equation 7)

:param xi: A element of the State
:param u: A element of the Input space
:return: A numpy array representing the Lift

Definition at line 354 of file EqF.py.

◆ local_coords()

np.ndarray gtsam.examples.EqF.local_coords ( State e )

Local coordinates assuming __xi_0 = identity (Equation 9)

:param e: A element of the State representing the equivariant error
:return: Local coordinates assuming __xi_0 = identity

Definition at line 428 of file EqF.py.

◆ local_coords_inv()

"State" gtsam.examples.EqF.local_coords_inv ( np.ndarray eps )

Local coordinates inverse assuming __xi_0 = identity

:param eps: A numpy array representing the equivariant error in local coordinates
:return: Local coordinates inverse assuming __xi_0 = identity

Definition at line 456 of file EqF.py.

◆ numericalDifferential()

np.ndarray gtsam.examples.EqF.numericalDifferential	(	f,
		x
	)

Compute the numerical derivative via central difference

Definition at line 337 of file EqF.py.

◆ outputAction()

np.ndarray gtsam.examples.EqF.outputAction	(	G	X,
		Direction	y,
		int	idx = `-1`
	)

Action of the symmetry group on the output space, return rho(X, y) (Equation 6)

:param X: A element of the group G
:param y: A direction measurement
:param idx: indicate the index of the B element in the list, -1 in case no B element exist
:return: A numpy array given by the action of rho of G in the Output space

Definition at line 413 of file EqF.py.

◆ repBlock()

np.ndarray gtsam.examples.EqF.repBlock	(	np.ndarray	A,
		int	n
	)

Create a block diagonal matrix repeating the A block n times

:param A: numpy array representing the block A
:param n: number of times to repeat A
:return: numpy array representing a block diagonal matrix composed of n-times the blocks A

Definition at line 323 of file EqF.py.

◆ stateAction()

State gtsam.examples.EqF.stateAction	(	G	X,
		State	xi
	)

Action of the symmetry group on the state space, return phi(X, xi) (Equation 4)

:param X: A element of the group G
:param xi: A element of the State
:return: A new element of the state given by the action of phi of G in the State space

Definition at line 382 of file EqF.py.

◆ stateActionDiff()

np.ndarray gtsam.examples.EqF.stateActionDiff ( State xi )

Differential of the phi action phi(xi, E) at E = Id in local coordinates (can be found within equation 23)

:param xi: A element of the State
:return: (Dtheta) * (Dphi(xi, E) at E = Id)

Definition at line 475 of file EqF.py.

◆ velocityAction()

Input gtsam.examples.EqF.velocityAction	(	G	X,
		Input	u
	)

Action of the symmetry group on the input space, return psi(X, u) (Equation 5)

:param X: A element of the group G
:param u: A element of the Input
:return: A new element of the Input given by the action of psi of G in the Input space

Definition at line 402 of file EqF.py.

Variable Documentation

◆ coordinate

string gtsam.examples.EqF.coordinate = "EXPONENTIAL"

Definition at line 18 of file EqF.py.

Classes

Functions

Variables