Inertial Navigation Mechanization Functions in ECEF frame. More...

Functions
template<typename DerivedA, typename DerivedB>
Eigen::Vector4< typename DerivedA::Scalar >	NAV::calcTimeDerivativeFor_e_Quat_b (const Eigen::MatrixBase< DerivedA > &b_omega_eb, const Eigen::MatrixBase< DerivedB > &e_Quat_b_coeffs)
	Calculates the time derivative of the quaternion e_Quat_b.

template<typename T>
Eigen::Vector< T, 10 >	NAV::e_calcPosVelAttDerivative (const Eigen::Vector< T, 10 > &y, const Eigen::Vector< T, 6 > &z, const PosVelAttDerivativeConstants &c, double=0.0)
	Calculates the derivative of the quaternion, velocity and position in ECEF coordinates.

template<typename Derived>
Eigen::Vector3< typename Derived::Scalar >	NAV::e_calcTimeDerivativeForPosition (const Eigen::MatrixBase< Derived > &e_velocity)
	Calculates the time derivative of the ECEF position.

template<typename DerivedA, typename DerivedB, typename DerivedC, typename DerivedD>
Eigen::Vector3< typename DerivedA::Scalar >	NAV::e_calcTimeDerivativeForVelocity (const Eigen::MatrixBase< DerivedA > &e_measuredForce, const Eigen::MatrixBase< DerivedB > &e_coriolisAcceleration, const Eigen::MatrixBase< DerivedC > &e_gravitation, const Eigen::MatrixBase< DerivedD > &e_centrifugalAcceleration)
	Calculates the time derivative of the velocity in ECEF frame coordinates.

Detailed Description

Inertial Navigation Mechanization Functions in ECEF frame.

Author: T. Topp (topp@.nosp@m.ins..nosp@m.uni-s.nosp@m.tutt.nosp@m.gart..nosp@m.de)

Date: 2022-06-12

Function Documentation

◆ calcTimeDerivativeFor_e_Quat_b()

template<typename DerivedA, typename DerivedB>

Eigen::Vector4< typename DerivedA::Scalar > NAV::calcTimeDerivativeFor_e_Quat_b	(	const Eigen::MatrixBase< DerivedA > &	b_omega_eb,
		const Eigen::MatrixBase< DerivedB > &	e_Quat_b_coeffs )

Calculates the time derivative of the quaternion e_Quat_b.

$\begin{equation} \label{eq:eq-INS-Mechanization-e_Quat_b-dot} \mathbf{\dot{q}}_b^e = \begin{bmatrix} \dot{x} \\ \dot{y} \\ \dot{z} \\ \dot{w} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 0 & \omega_{eb,z}^b & -\omega_{eb,y}^b & \omega_{eb,x}^b \\ -\omega_{eb,z}^b & 0 & \omega_{eb,x}^b & \omega_{eb,y}^b \\ \omega_{eb,y}^b & -\omega_{eb,x}^b & 0 & \omega_{eb,z}^b \\ -\omega_{eb,x}^b & -\omega_{eb,y}^b & -\omega_{eb,z}^b & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \\ w \end{bmatrix} \end{equation}$

Parameters

[in]	b_omega_eb	ω_eb_b Body rate with respect to the ECEF frame, expressed in the body frame
[in]	e_Quat_b_coeffs	Coefficients of the quaternion e_Quat_b in order x, y, z, w (q = w + ix + jy + kz)

Returns: The time derivative of the coefficients of the quaternion e_Quat_b in order x, y, z, w (q = w + ix + jy + kz)

Note: See Propagation of quaternion with time equation $\eqref{eq:eq-ImuIntegrator-Mechanization-e-Attitude-Quaternion-matrix}$

◆ e_calcPosVelAttDerivative()

template<typename T>

Eigen::Vector< T, 10 > NAV::e_calcPosVelAttDerivative	(	const Eigen::Vector< T, 10 > &	y,
		const Eigen::Vector< T, 6 > &	z,
		const PosVelAttDerivativeConstants &	c,
		double	= 0.0 )

Calculates the derivative of the quaternion, velocity and position in ECEF coordinates.

Parameters

[in]	y	[x, y, z, v_x, v_y, v_z, e_q_bx, e_q_by, e_q_bz, e_q_bw]^T
[in]	z	[fx, fy, fz, ωx, ωy, ωz]^T
[in]	c	Constant values needed to calculate the derivatives

Returns: The derivative ∂/∂t [x, y, z, v_x, v_y, v_z, e_q_bx, e_q_by, e_q_bz, e_q_bw]^T

◆ e_calcTimeDerivativeForPosition()

template<typename Derived>

Eigen::Vector3< typename Derived::Scalar > NAV::e_calcTimeDerivativeForPosition ( const Eigen::MatrixBase< Derived > & e_velocity )

Calculates the time derivative of the ECEF position.

$\begin{equation} \label{eq:eq-INS-Mechanization-x_e-dot} \boldsymbol{\dot{x}}^e = \boldsymbol{v}^e \end{equation}$

Parameters

[in] e_velocity Velocity with respect to the Earth in ECEF frame coordinates [m/s]

Returns: The time derivative of the ECEF position

Note: See Position equation $\eqref{eq:eq-ImuIntegrator-Mechanization-e-Position}$

◆ e_calcTimeDerivativeForVelocity()

template<typename DerivedA, typename DerivedB, typename DerivedC, typename DerivedD>

Eigen::Vector3< typename DerivedA::Scalar > NAV::e_calcTimeDerivativeForVelocity	(	const Eigen::MatrixBase< DerivedA > &	e_measuredForce,
		const Eigen::MatrixBase< DerivedB > &	e_coriolisAcceleration,
		const Eigen::MatrixBase< DerivedC > &	e_gravitation,
		const Eigen::MatrixBase< DerivedD > &	e_centrifugalAcceleration )

Calculates the time derivative of the velocity in ECEF frame coordinates.

$\begin{equation} \label{eq:eq-INS-Mechanization-v_e-dot} \boldsymbol{\dot{v}}^e = \overbrace{\boldsymbol{f}^e}^{\hidewidth\text{measured}\hidewidth} -\ \underbrace{2 \boldsymbol{\omega}_{ie}^e \times \boldsymbol{v}^e}_{\text{coriolis acceleration}} +\ \overbrace{\mathbf{g}^e}^{\hidewidth\text{gravitation}\hidewidth} -\ \underbrace{\left(\boldsymbol{\omega}_{ie}^e \times [ \boldsymbol{\omega}_{ie}^e \times \mathbf{x}^e ] \right)}_{\text{centrifugal acceleration}} \end{equation}$

Parameters

[in]	e_measuredForce	f_e Specific force vector as measured by a triad of accelerometers and resolved into ECEF frame coordinates
[in]	e_coriolisAcceleration	Coriolis acceleration in ECEF coordinates in [m/s^2]
[in]	e_gravitation	Local gravitation vector (caused by effects of mass attraction) in ECEF frame coordinates [m/s^2]
[in]	e_centrifugalAcceleration	Centrifugal acceleration in ECEF coordinates in [m/s^2]

Returns: The time derivative of the velocity in ECEF frame coordinates

Note: See Velocity equation $\eqref{eq:eq-ImuIntegrator-Mechanization-e-Velocity}$