ErrorEquations.hpp File Reference

Error Equations for the local navigation frame. More...

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Functions
Eigen::Matrix3d	NAV::n_F_df_df (const Eigen::Vector3d &beta_a)
	Calculates the matrix 𝐅_𝛿f'_𝛿f.
Eigen::Matrix3d	NAV::n_F_dpsi_dpsi (const Eigen::Vector3d &n_omega_in)
	Calculates the matrix 𝐅_𝜓'_𝜓
Eigen::Matrix3d	NAV::n_F_dpsi_dr (double latitude, double height, const Eigen::Vector3d &n_velocity, double R_N, double R_E)
	Calculates the matrix 𝐅_𝜓'_𝛿r.
Eigen::Matrix3d	NAV::n_F_dpsi_dv (double latitude, double height, double R_N, double R_E)
	Calculates the matrix 𝐅_𝜓'_𝛿v.
Eigen::Matrix3d	NAV::n_F_dpsi_dw (const Eigen::Matrix3d &n_Dcm_b)
	Calculates the matrix 𝐅_𝜓'_𝛿ω
Eigen::Matrix3d	NAV::n_F_dr_dr (const Eigen::Vector3d &n_velocity, double latitude, double height, double R_N, double R_E)
	Calculates the matrix 𝐅_𝛿r'_𝛿r.
Eigen::Matrix3d	NAV::n_F_dr_dv (double latitude, double height, double R_N, double R_E)
	Calculates the matrix 𝐅_𝛿r'_𝛿v.
Eigen::Matrix3d	NAV::n_F_dv_df (const Eigen::Matrix3d &n_Dcm_b)
	Calculates the matrix 𝐅_𝜓'_𝛿f.
Eigen::Matrix3d	NAV::n_F_dv_dpsi (const Eigen::Vector3d &n_force_ib)
	Calculates the matrix 𝐅_𝛿v'_𝜓
Eigen::Matrix3d	NAV::n_F_dv_dr (const Eigen::Vector3d &n_velocity, double latitude, double height, double R_N, double R_E, double g_0, double r_eS_e)
	Calculates the matrix 𝐅_𝛿v'_𝛿r.
Eigen::Matrix3d	NAV::n_F_dv_dv (const Eigen::Vector3d &n_velocity, double latitude, double height, double R_N, double R_E)
	Calculates the matrix 𝐅_𝛿v'_𝛿v.
Eigen::Matrix3d	NAV::n_F_dw_dw (const Eigen::Vector3d &beta_omega)
	Calculates the matrix 𝐅_𝛿ω'_𝛿ω

Detailed Description

Error Equations for the local navigation frame.

Author

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

Date

2022-01-12

Function Documentation

n_F_df_df()

Eigen::Matrix3d NAV::n_F_df_df

(

const Eigen::Vector3d &

beta_a

)

Calculates the matrix 𝐅_𝛿f'_𝛿f.

Parameters

[in]

beta_a

Gauss-Markov constant for the accelerometer 𝛽 = 1 / 𝜏 (𝜏 correlation length)

Returns

3x3 matrix in [1 / s]

Note

See T. Hobiger (2021) Inertialnavigation V06 - equation (6.3)

n_F_dpsi_dpsi()

Eigen::Matrix3d NAV::n_F_dpsi_dpsi

(

const Eigen::Vector3d &

n_omega_in

)

Calculates the matrix 𝐅_𝜓'_𝜓

Parameters

[in]

n_omega_in

Angular rate vector of the n-system with respect to the i-system in [rad / s], resolved in the n-system

Returns

3x3 matrix in [rad / s]

Note

See [17] Groves, ch. 14.2.4, eq. 14.64, p. 587 - 𝐅_11

See T. Hobiger (2021) Inertialnavigation V07 - equation (7.22)

n_F_dpsi_dr()

Eigen::Matrix3d NAV::n_F_dpsi_dr	(	double	latitude,
		double	height,
		const Eigen::Vector3d &	n_velocity,
		double	R_N,
		double	R_E )

Calculates the matrix 𝐅_𝜓'_𝛿r.

Parameters

[in]	latitude	Geodetic latitude of the body in [rad]
[in]	height	Geodetic height of the body in [m]
[in]	n_velocity	Velocity of the body with respect to the e-system in [m / s], resolved in the n-system
[in]	R_N	North/South (meridian) earth radius in [m]
[in]	R_E	East/West (prime vertical) earth radius in [m]

Returns

3x3 matrix in [rad / s] for latitude and [1 / (m · s)] for height

Note

See [17] Groves, ch. 14.2.4, eq. 14.66, p. 587 - 𝐅_13

See T. Hobiger (2021) Inertialnavigation V07 - equation (7.21)

n_F_dpsi_dv()

Eigen::Matrix3d NAV::n_F_dpsi_dv	(	double	latitude,
		double	height,
		double	R_N,
		double	R_E )

Calculates the matrix 𝐅_𝜓'_𝛿v.

Parameters

[in]	latitude	Geodetic latitude of the body in [rad]
[in]	height	Geodetic height of the body in [m]
[in]	R_N	North/South (meridian) earth radius in [m]
[in]	R_E	East/West (prime vertical) earth radius in [m]

Returns

3x3 matrix in [1 / m]

Note

See [17] Groves, ch. 14.2.4, eq. 14.65, p. 587 - 𝐅_12

See T. Hobiger (2021) Inertialnavigation V07 - equation (7.21)

n_F_dpsi_dw()

Eigen::Matrix3d NAV::n_F_dpsi_dw

(

const Eigen::Matrix3d &

n_Dcm_b

)

Calculates the matrix 𝐅_𝜓'_𝛿ω

Parameters

[in]

n_Dcm_b

DCM from body to navigation frame

Returns

3x3 matrix in [-]

Note

See [17] Groves, ch. 14.2.4, eq. 14.63, p. 587 - 𝐅_15

n_F_dr_dr()

Eigen::Matrix3d NAV::n_F_dr_dr	(	const Eigen::Vector3d &	n_velocity,
		double	latitude,
		double	height,
		double	R_N,
		double	R_E )

Calculates the matrix 𝐅_𝛿r'_𝛿r.

Parameters

[in]	n_velocity	Velocity of the body with respect to the e-system in [m / s], resolved in the n-system
[in]	latitude	Geodetic latitude of the body in [rad]
[in]	height	Geodetic height of the body in [m]
[in]	R_N	North/South (meridian) earth radius in [m]
[in]	R_E	East/West (prime vertical) earth radius in [m]

Returns

3x3 matrix in [1 / s] for latitude and [1 / (m · s)] for height

Note

See [17] Groves, ch. 14.2.4, eq. 14.71, p. 588 - 𝐅_33

See T. Hobiger (2021) Inertialnavigation V07 - equation (7.5)

n_F_dr_dv()

Eigen::Matrix3d NAV::n_F_dr_dv	(	double	latitude,
		double	height,
		double	R_N,
		double	R_E )

Calculates the matrix 𝐅_𝛿r'_𝛿v.

Parameters

[in]	latitude	Geodetic latitude of the body in [rad]
[in]	height	Geodetic height of the body in [m]
[in]	R_N	North/South (meridian) earth radius in [m]
[in]	R_E	East/West (prime vertical) earth radius in [m]

Returns

3x3 matrix in [1 / m] for latitude and longitude and [-] for height

Note

See [17] Groves, ch. 14.2.4, eq. 14.70, p. 588 - 𝐅_32

See T. Hobiger (2021) Inertialnavigation V07 - equation (7.5)

n_F_dv_df()

Eigen::Matrix3d NAV::n_F_dv_df

(

const Eigen::Matrix3d &

n_Dcm_b

)

Calculates the matrix 𝐅_𝜓'_𝛿f.

Parameters

[in]

n_Dcm_b

DCM from body to navigation frame

Returns

3x3 matrix in [-]

Note

See [17] Groves, ch. 14.2.4, eq. 14.63, p. 587 - 𝐅_24

n_F_dv_dpsi()

Eigen::Matrix3d NAV::n_F_dv_dpsi

(

const Eigen::Vector3d &

n_force_ib

)

Calculates the matrix 𝐅_𝛿v'_𝜓

Parameters

[in]

n_force_ib

Specific force of the body with respect to inertial frame in [m / s^2], resolved in local navigation frame coordinates

Returns

3x3 matrix in [m / s^2]

Note

See [17] Groves, ch. 14.2.4, eq. 14.67, p. 587 - 𝐅_21

See T. Hobiger (2021) Inertialnavigation V08 - equation (8.4)

n_F_dv_dr()

Eigen::Matrix3d NAV::n_F_dv_dr	(	const Eigen::Vector3d &	n_velocity,
		double	latitude,
		double	height,
		double	R_N,
		double	R_E,
		double	g_0,
		double	r_eS_e )

Calculates the matrix 𝐅_𝛿v'_𝛿r.

Parameters

[in]	n_velocity	Velocity of the body with respect to the e-system in [m / s], resolved in the n-system
[in]	latitude	Geodetic latitude of the body in [rad]
[in]	height	Geodetic height of the body in [m]
[in]	R_N	North/South (meridian) earth radius in [m]
[in]	R_E	East/West (prime vertical) earth radius in [m]
[in]	g_0	Magnitude of the gravity vector in [m/s^2] (see [17] Groves, ch. 2.4.7, eq. 2.135, p. 70)
[in]	r_eS_e	Geocentric radius. The distance of a point on the Earth's surface from the center of the Earth in [m]

Returns

3x3 matrix in [m / s^2] for latitude and [1 / s^2] for height

Note

See [17] Groves, ch. 14.2.4, eq. 14.69, p. 588 - 𝐅_23

See T. Hobiger (2021) Inertialnavigation V08 - equation (8.14, 8.16)

n_F_dv_dv()

Eigen::Matrix3d NAV::n_F_dv_dv	(	const Eigen::Vector3d &	n_velocity,
		double	latitude,
		double	height,
		double	R_N,
		double	R_E )

Calculates the matrix 𝐅_𝛿v'_𝛿v.

Parameters

[in]	n_velocity	Velocity of the body with respect to the e-system in [m / s], resolved in the n-system
[in]	latitude	Geodetic latitude of the body in [rad]
[in]	height	Geodetic height of the body in [m]
[in]	R_N	North/South (meridian) earth radius in [m]
[in]	R_E	East/West (prime vertical) earth radius in [m]

Returns

3x3 matrix in [1 / s]

Note

See [17] Groves, ch. 14.2.4, eq. 14.68, p. 587 - 𝐅_22

See T. Hobiger (2021) Inertialnavigation V08 - equation (8.6, 8.15)

n_F_dw_dw()

Eigen::Matrix3d NAV::n_F_dw_dw

(

const Eigen::Vector3d &

beta_omega

)

Calculates the matrix 𝐅_𝛿ω'_𝛿ω

Parameters

[in]

beta_omega

Gauss-Markov constant for the gyroscope 𝛽 = 1 / 𝜏 (𝜏 correlation length)

Returns

3x3 matrix in [1 / s]

Note

See T. Hobiger (2021) Inertialnavigation V06 - equation (6.3)