Inertial Navigation Helper Functions. More...

Functions
template<typename Derived>
Derived::Scalar	NAV::calcPitchFromStaticAcceleration (const Eigen::MatrixBase< Derived > &b_accel)
	Calculates the pitch angle from a static acceleration measurement.

template<typename Derived>
Derived::Scalar	NAV::calcPitchFromVelocity (const Eigen::MatrixBase< Derived > &n_velocity)
	Calculates the Pitch angle from the trajectory defined by the given velocity.

template<typename Derived>
Derived::Scalar	NAV::calcRollFromStaticAcceleration (const Eigen::MatrixBase< Derived > &b_accel)
	Calculates the roll angle from a static acceleration measurement.

template<typename Derived>
Derived::Scalar	NAV::calcYawFromVelocity (const Eigen::MatrixBase< Derived > &n_velocity)
	Calculates the Yaw angle from the trajectory defined by the given velocity.

template<typename DerivedA, typename DerivedB = DerivedA>
Eigen::Vector3< typename DerivedA::Scalar >	NAV::e_calcCentrifugalAcceleration (const Eigen::MatrixBase< DerivedA > &e_position, const Eigen::MatrixBase< DerivedB > &e_omega_ie=InsConst::e_omega_ie)
	Calculates the centrifugal acceleration in [m/s^2] (acceleration that makes a body follow a curved path)

template<typename DerivedA, typename DerivedB>
Eigen::Vector3< typename DerivedB::Scalar >	NAV::e_calcCoriolisAcceleration (const Eigen::MatrixBase< DerivedA > &e_omega_ie, const Eigen::MatrixBase< DerivedB > &e_velocity)
	Calculates the coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)

template<typename DerivedA, typename DerivedB, typename DerivedC>
Eigen::Vector3< typename DerivedA::Scalar >	NAV::n_calcCoriolisAcceleration (const Eigen::MatrixBase< DerivedA > &n_omega_ie, const Eigen::MatrixBase< DerivedB > &n_omega_en, const Eigen::MatrixBase< DerivedC > &n_velocity)
	Calculates the coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)

template<typename DerivedA, typename DerivedB>
Eigen::Vector3< typename DerivedA::Scalar >	NAV::n_calcTransportRate (const Eigen::MatrixBase< DerivedA > &lla_position, const Eigen::MatrixBase< DerivedB > &n_velocity, const auto &R_N, const auto &R_E)
	Calculates the transport rate ω_en_n (rotation rate of the Earth frame relative to the navigation frame)

Detailed Description

Inertial Navigation Helper Functions.

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

Date: 2020-09-02

Function Documentation

◆ calcPitchFromStaticAcceleration()

template<typename Derived>

Derived::Scalar NAV::calcPitchFromStaticAcceleration ( const Eigen::MatrixBase< Derived > & b_accel )

nodiscard

Calculates the pitch angle from a static acceleration measurement.

Parameters

[in] b_accel Acceleration measurement in static condition in [m/s^2]

Returns: The pitch angle in [rad]

Note: See E.-H. Shin (2005) - Estimation Techniques for Low-Cost Inertial Navigation (Chapter 2.6)

◆ calcPitchFromVelocity()

template<typename Derived>

Derived::Scalar NAV::calcPitchFromVelocity ( const Eigen::MatrixBase< Derived > & n_velocity )

nodiscard

Calculates the Pitch angle from the trajectory defined by the given velocity.

$\begin{equation} \label{eq:eq-INS-Mechanization-Pitch} P = \tan^{-1}\left(\frac{-v_D}{\sqrt{v_N^2 + v_E^2}}\right) \end{equation}$

Parameters

[in] n_velocity Velocity in [m/s] in local-navigation frame coordinates

Returns: Pitch angle in [rad]

Note: See [17] Groves, ch. 6.1.4, eq. 6.17, p. 225

◆ calcRollFromStaticAcceleration()

template<typename Derived>

Derived::Scalar NAV::calcRollFromStaticAcceleration ( const Eigen::MatrixBase< Derived > & b_accel )

nodiscard

Calculates the roll angle from a static acceleration measurement.

Parameters

[in] b_accel Acceleration measurement in static condition in [m/s^2]

Returns: The roll angle in [rad]

Note: See E.-H. Shin (2005) - Estimation Techniques for Low-Cost Inertial Navigation (Chapter 2.6)

◆ calcYawFromVelocity()

template<typename Derived>

Derived::Scalar NAV::calcYawFromVelocity ( const Eigen::MatrixBase< Derived > & n_velocity )

nodiscard

Calculates the Yaw angle from the trajectory defined by the given velocity.

$\begin{equation} \label{eq:eq-INS-Mechanization-Yaw} Y = \tan^{-1}\left(\frac{v_E}{v_N}\right) \end{equation}$

Parameters

[in] n_velocity Velocity in [m/s] in local-navigation frame coordinates

Returns: Yaw angle in [rad]

Note: See [17] Groves, ch. 6.1.4, eq. 6.14, p. 225

◆ e_calcCentrifugalAcceleration()

template<typename DerivedA, typename DerivedB = DerivedA>

Eigen::Vector3< typename DerivedA::Scalar > NAV::e_calcCentrifugalAcceleration	(	const Eigen::MatrixBase< DerivedA > &	e_position,
		const Eigen::MatrixBase< DerivedB > &	e_omega_ie = InsConst::e_omega_ie )

nodiscard

Calculates the centrifugal acceleration in [m/s^2] (acceleration that makes a body follow a curved path)

$\begin{equation} \label{eq:eq-INS-Mechanization-CentrifugalAcceleration} \boldsymbol{\omega}_{ie}^e \times [ \boldsymbol{\omega}_{ie}^e \times \mathbf{x}^e ] \end{equation}$

Parameters

[in]	e_position	Position in coordinates in [m]
[in]	e_omega_ie	Angular rate of the Earth rotation in [rad/s] in the Earth coordinate frame

Returns: Centrifugal acceleration in the Earth coordinate frame in [m/s^2]

◆ e_calcCoriolisAcceleration()

template<typename DerivedA, typename DerivedB>

Eigen::Vector3< typename DerivedB::Scalar > NAV::e_calcCoriolisAcceleration	(	const Eigen::MatrixBase< DerivedA > &	e_omega_ie,
		const Eigen::MatrixBase< DerivedB > &	e_velocity )

nodiscard

Calculates the coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)

$\begin{equation} \label{eq:eq-INS-Mechanization-CoriolisAcceleration-e} 2 \boldsymbol{\omega}_{ie}^e \times \boldsymbol{v}^e \end{equation}$

Parameters

[in]	e_omega_ie	ω_ie_e Angular rate of the Earth rotation in [rad/s] in ECEF coordinates
[in]	e_velocity	Velocity in ECEF frame coordinates in [m/s^2]

Returns: Coriolis acceleration in ECEF coordinates in [m/s^2]

◆ n_calcCoriolisAcceleration()

template<typename DerivedA, typename DerivedB, typename DerivedC>

Eigen::Vector3< typename DerivedA::Scalar > NAV::n_calcCoriolisAcceleration	(	const Eigen::MatrixBase< DerivedA > &	n_omega_ie,
		const Eigen::MatrixBase< DerivedB > &	n_omega_en,
		const Eigen::MatrixBase< DerivedC > &	n_velocity )

nodiscard

Calculates the coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)

$\begin{equation} \label{eq:eq-INS-Mechanization-CoriolisAcceleration} (2 \boldsymbol{\omega}_{ie}^n + \boldsymbol{\omega}_{en}^n) \times \boldsymbol{v}^n \end{equation}$

Parameters

[in]	n_omega_ie	ω_ie_n Angular rate of the Earth rotation in [rad/s] in local-navigation coordinates
[in]	n_omega_en	ω_en_n Transport rate in [rad/s] in local-navigation coordinates
[in]	n_velocity	Velocity in local-navigation frame coordinates in [m/s^2]

Returns: Coriolis acceleration in local-navigation coordinates in [m/s^2]

◆ n_calcTransportRate()

template<typename DerivedA, typename DerivedB>

Eigen::Vector3< typename DerivedA::Scalar > NAV::n_calcTransportRate	(	const Eigen::MatrixBase< DerivedA > &	lla_position,
		const Eigen::MatrixBase< DerivedB > &	n_velocity,
		const auto &	R_N,
		const auto &	R_E )

nodiscard

Calculates the transport rate ω_en_n (rotation rate of the Earth frame relative to the navigation frame)

$\begin{equation} \label{eq:eq-INS-Mechanization-TransportRate} \boldsymbol{\omega}_{en}^n = \begin{bmatrix} \dfrac{v_E}{R_E + h} & \dfrac{-v_N}{R_N + h} & \dfrac{-v_E \tan{\phi}}{R_E + h} \end{bmatrix}^T \end{equation}$

Parameters

[in]	lla_position	[𝜙, λ, h] Latitude, Longitude and altitude in [rad, rad, m]
[in]	n_velocity	Velocity in [m/s], in navigation coordinate
[in]	R_N	North/South (meridian) earth radius [m]
[in]	R_E	East/West (prime vertical) earth radius [m]

Returns: ω_en_n Transport Rate in local-navigation coordinates in [rad/s]

Note: See [17] Groves, ch. 5.4.1, eq. 5.44, p. 177; See [14] Gleason, ch. 6.2.3.2, eq. 6.15, p. 155; See [47] Titterton, ch. 3.7.2, eq. 3.87, p. 50 (mistake in denominator 3rd term)