Mistake in Attitude From Tilt documentation

[adrian-soch]

In the Attitude From Tilt, the documentation assigns roll=θ, and pitch=φ. However, in calculation of ψ the roll and pitch symbols have been swapped. This makes sense, since the original NXP documentation assigns the symbols this way - and was likely an error when translating the equation.

The code is still correct, however the documentation should be updated to match.

ahrs/ahrs/filters/tilt.py

Lines 47 to 78 in 48ed893

	.. math::
	\\begin{array}{cl}
	\\mathbf{b} &=
	R_y(-\\theta)R_x(-\\phi)\\mathbf{m} = R_y(\\theta)^TR_x(\\phi)^T\\mathbf{m} \\\\
	&=
	\\begin{bmatrix}
	\\cos\\theta & \\sin\\theta\\sin\\phi & \\sin\\theta\\cos\\phi \\\\
	0 & \\cos\\phi & -\\sin\\phi \\\\
	-\\sin\\theta & \\cos\\theta\\sin\\phi & \\cos\\theta\\cos\\phi
	\\end{bmatrix}
	\\begin{bmatrix}m_x \\\\ m_y \\\\ m_z\\end{bmatrix} \\\\
	\\begin{bmatrix}b_x \\\\ b_y \\\\ b_z\\end{bmatrix} &=
	\\begin{bmatrix}
	m_x\\cos\\theta + m_y\\sin\\theta\\sin\\phi + m_z\\sin\\theta\\cos\\phi \\\\
	m_y\\cos\\phi - m_z\\sin\\phi \\\\
	-m_x\\sin\\theta + m_y\\cos\\theta\\sin\\phi + m_z\\cos\\theta\\cos\\phi
	\\end{bmatrix}
	\\end{array}
	Where :math:`\\mathbf{m}=\\begin{bmatrix}m_x & m_y & m_z\\end{bmatrix}^T` is
	the *normalized* vector of the measured magnetic field, which means
	:math:`\\|\\mathbf{m}\\|=1`.
	The yaw angle :math:`\\psi` is the tilt-compensated heading angle relative to
	magnetic North, computed as [FS-AN4248]_:
	.. math::
	\\begin{array}{ll}
	\\psi &= \\mathrm{arctan2}(-b_y, b_x) \\\\
	&= \\mathrm{arctan2}\\big(m_z\\sin\\phi - m_y\\cos\\phi, \\; m_x\\cos\\theta + \\sin\\theta(m_y\\sin\\phi + m_z\\cos\\phi)\\big)
	\\end{array}