Functions concerning the ellipsoid model. More...

Functions
template<std::floating_point Scalar>
Scalar	NAV::calcEarthRadius_E (const Scalar &latitude, const Scalar &a=InsConst::WGS84::a, const Scalar &e_squared=InsConst::WGS84::e_squared)
	Calculates the East/West (prime vertical) earth radius.

template<std::floating_point Scalar>
Scalar	NAV::calcEarthRadius_N (const Scalar &latitude, const Scalar &a=InsConst::WGS84::a, const Scalar &e_squared=InsConst::WGS84::e_squared)
	Calculates the North/South (meridian) earth radius.

template<std::floating_point Scalar>
Scalar	NAV::calcGeocentricRadius (const Scalar &latitude, const Scalar &R_E, const Scalar &e_squared=InsConst::WGS84::e_squared)
	r_eS^e The distance of a point on the Earth's surface from the center of the Earth

template<std::floating_point Scalar>
Scalar	NAV::calcGeographicalDistance (Scalar lat1, Scalar lon1, Scalar lat2, Scalar lon2)
	Measure the distance between two points over an ellipsoidal-surface.

template<std::floating_point Scalar>
Scalar	NAV::calcGreatCircleDistance (Scalar lat1, Scalar lon1, Scalar lat2, Scalar lon2)
	Measure the distance between two points on a sphere.

template<typename Derived >
Eigen::Matrix3< typename Derived::Scalar >	NAV::conversionMatrixCartesianCurvilinear (const Eigen::MatrixBase< Derived > &lla_position, const typename Derived::Scalar &R_N, const typename Derived::Scalar &R_E)
	Conversion matrix between cartesian and curvilinear perturbations to the position.

Detailed Description

Functions concerning the ellipsoid model.

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

Date: 2021-11-28

Function Documentation

◆ calcEarthRadius_E()

template<std::floating_point Scalar>

Scalar NAV::calcEarthRadius_E	(	const Scalar &	latitude,
		const Scalar &	a = InsConst::WGS84::a,
		const Scalar &	e_squared = InsConst::WGS84::e_squared )

nodiscard

Calculates the East/West (prime vertical) earth radius.

Parameters

[in]	latitude	𝜙 Latitude in [rad]
[in]	a	Semi-major axis
[in]	e_squared	Square of the first eccentricity of the ellipsoid

Returns: East/West (prime vertical) earth radius [m]

Note: See [17] Groves, ch. 2.4.2, eq. 2.106, p. 59; See [47] Titterton, ch. 3.7.2, eq. 3.84, p. 49

◆ calcEarthRadius_N()

template<std::floating_point Scalar>

Scalar NAV::calcEarthRadius_N	(	const Scalar &	latitude,
		const Scalar &	a = InsConst::WGS84::a,
		const Scalar &	e_squared = InsConst::WGS84::e_squared )

nodiscard

Calculates the North/South (meridian) earth radius.

Parameters

[in]	latitude	𝜙 Latitude in [rad]
[in]	a	Semi-major axis
[in]	e_squared	Square of the first eccentricity of the ellipsoid

Returns: North/South (meridian) earth radius [m]

Note: See [17] Groves, ch. 2.4.2, eq. 2.105, p. 59; See [47] Titterton, ch. 3.7.2, eq. 3.83, p. 49

◆ calcGeocentricRadius()

template<std::floating_point Scalar>

Scalar NAV::calcGeocentricRadius	(	const Scalar &	latitude,
		const Scalar &	R_E,
		const Scalar &	e_squared = InsConst::WGS84::e_squared )

nodiscard

r_eS^e The distance of a point on the Earth's surface from the center of the Earth

Parameters

[in]	latitude	𝜙 Latitude in [rad]
[in]	R_E	Prime vertical radius of curvature (East/West) in [m]
[in]	e_squared	Square of the first eccentricity of the ellipsoid

Returns: Geocentric Radius in [m]

Note: [17] Groves, ch. 2.4.7, eq. 2.137, p. 71

◆ calcGeographicalDistance()

template<std::floating_point Scalar>

Scalar NAV::calcGeographicalDistance	(	Scalar	lat1,
		Scalar	lon1,
		Scalar	lat2,
		Scalar	lon2 )

nodiscard

Measure the distance between two points over an ellipsoidal-surface.

Parameters

[in]	lat1	Latitude of first point in [rad]
[in]	lon1	Longitude of first point in [rad]
[in]	lat2	Latitude of second point in [rad]
[in]	lon2	Longitude of second point in [rad]

Returns: The distance in [m]

Note: See Lambert's formula for long lines (https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines)

◆ calcGreatCircleDistance()

template<std::floating_point Scalar>

Scalar NAV::calcGreatCircleDistance	(	Scalar	lat1,
		Scalar	lon1,
		Scalar	lat2,
		Scalar	lon2 )

nodiscard

Measure the distance between two points on a sphere.

Parameters

[in]	lat1	Latitude of first point in [rad]
[in]	lon1	Longitude of first point in [rad]
[in]	lat2	Latitude of second point in [rad]
[in]	lon2	Longitude of second point in [rad]

Returns: The distance in [m]

Note: See Haversine Formula (https://www.movable-type.co.uk/scripts/latlong.html)

◆ conversionMatrixCartesianCurvilinear()

template<typename Derived >

Eigen::Matrix3< typename Derived::Scalar > NAV::conversionMatrixCartesianCurvilinear	(	const Eigen::MatrixBase< Derived > &	lla_position,
		const typename Derived::Scalar &	R_N,
		const typename Derived::Scalar &	R_E )

nodiscard

Conversion matrix between cartesian and curvilinear perturbations to the position.

Parameters

[in]	lla_position	Position as Lat Lon Alt in [rad rad m]
[in]	R_N	Meridian radius of curvature in [m]
[in]	R_E	Prime vertical radius of curvature (East/West) [m]

Returns: T_rn_p A 3x3 matrix

Note: See [17] Groves, ch. 2.4.3, eq. 2.119, p. 63