Function navtk::inertial::calc_rot_rate(const Matrix3&, double, double, double, double, double, const Vector3&, double, double, const Vector3&, double)
Defined in File inertial_functions.hpp
Function Documentation
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Vector3 navtk::inertial::calc_rot_rate(const Matrix3 &C_s_to_n0, double r_e, double r_n, double alt0, double cos_l, double dt, const Vector3 &dth, double sin_l, double tan_l, const Vector3 &v_ned0, double omega = navutils::ROTATION_RATE)
Converts a measured delta rotation vector (sensor with respect to inertial frame) to a rotation rate vector with respect to the navigation (NED) frame by removing the net effects of the earths rotation with respect to the inertial frame \( \omega^{n}_{ie} \)eq and the rotation of the navigation frame with respect to the earth \( \omega^{n}_{en} \).
That is
\( \omega^{s}_{ns} = \omega^{s}_{is} - C^{s}_{n}[\omega^n_{ie} + \omega^n_{en}] \) (eq 3.29)
where
\( \omega^n_{ie} = \begin{bmatrix} \Omega \cos{lat} & 0 & -\Omega\sin{lat} \end{bmatrix} \) (eq 3.72)
and \( \omega^n_{en} = \begin{bmatrix} \frac{v_e}{R_e + h} & \frac{-v_n}{R_n + h} & \frac{-v_e\tan{lat}}{R_e + h} \end{bmatrix}\) (eq 3.87, with correction on the last term)
Equation numbers reference Titterton and Weston, 2nd ed.
- Parameters
C_s_to_n0 – Current inertial sensor-to-nav DCM.
r_e – See return value of navtk::navutils::transverse_radius.
r_n – See return value of navtk::navutils::meridian_radius.
alt0 – The inertial’s current ellipsoidal altitude, m.
cos_l – Cosine of inertial latitude.
dt – Delta time that
dthwas measured over.dth – Vector3 of delta rotations over dt in the inertial sensor frame, \( \Theta^{s}_{is} \) rad.
sin_l – Sine of inertial latitude.
tan_l – Tangent of inertial latitude.
v_ned0 – Vector3 of inertial velocity at the start of integration in the NED frame, m/s.
omega – Earth rotation rate, rad/s. Defaults to navtk::navutils::ROTATION_RATE.
- Returns
Inertial sensor rotation rate with respect to the navigation frame coordinatized in the sensor frame, \( \omega^{s}_{ns}\).