ProcessNoise.hpp File Reference

General process Noise definitions. More...

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Functions
template<typename KeyType, typename T>
KeyedMatrixX< T, KeyType, KeyType >	NAV::e_noiseInput_G (const Eigen::Quaterniond &b_quat_p, const Eigen::Quaternion< T > &e_quat_b, bool accelBiases, bool gyroBiases, bool accelScaleFactor, bool gyroScaleFactor, bool accelMisalignment, bool gyroMisalignment)
	Calculate the noise input matrix in Earth frame coordinates.
template<typename KeyType, typename T>
KeyedMatrixX< T, KeyType, KeyType >	NAV::e_noiseScale_W (const Eigen::Vector3d &sigma2_ra, const Eigen::Vector3d &sigma2_rg, const Eigen::Vector3d &sigma2_bad, const Eigen::Vector3d &sigma2_bgd, const Eigen::Vector3d &sigma2_sad, const Eigen::Vector3d &sigma2_sgd, bool accelBiases, bool gyroBiases, bool accelScaleFactor, bool gyroScaleFactor)
	Calculate the noise scale matrix in Earth frame coordinates.
Eigen::Matrix3d	NAV::G_GaussMarkov1 (const Eigen::Vector3d &sigma2, const Eigen::Vector3d &beta)
	Submatrix 𝐆_a of the noise input matrix 𝐆
Eigen::Matrix3d	NAV::G_RandomWalk (const Eigen::Vector3d &sigma2)
	Random walk noise input matrix 𝐆
Eigen::Matrix3d	NAV::ie_Q_dr_df (const Eigen::Vector3d &S_bad, const Eigen::Matrix3d &ie_Dcm_b, const double &tau_s)
	Submatrix 𝐐_34 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ie_Q_dr_domega (const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ie_F_21, const Eigen::Matrix3d &ie_Dcm_b, const double &tau_s)
	Submatrix 𝐐_35 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ie_Q_dr_dr (const Eigen::Vector3d &S_ra, const Eigen::Vector3d &S_bad, const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ie_F_21, const double &tau_s)
	Submatrix 𝐐_33 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ie_Q_dr_dv (const Eigen::Vector3d &S_ra, const Eigen::Vector3d &S_bad, const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ie_F_21, const double &tau_s)
	Submatrix 𝐐_32 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ie_Q_dr_psi (const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ie_F_21, const double &tau_s)
	Submatrix 𝐐_31 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ien_Q_dv_domega (const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ien_F_21, const Eigen::Matrix3d &ien_Dcm_b, const double &tau_s)
	Submatrix 𝐐_25 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ien_Q_dv_dv (const Eigen::Vector3d &S_ra, const Eigen::Vector3d &S_bad, const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ien_F_21, const double &tau_s)
	Submatrix 𝐐_22 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::ien_Q_dv_psi (const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &ien_F_21, const double &tau_s)
	Submatrix 𝐐_21 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::n_Q_dr_df (const Eigen::Vector3d &S_bad, const Eigen::Matrix3d &T_rn_p, const Eigen::Matrix3d &n_Dcm_b, const double &tau_s)
	Submatrix 𝐐_34 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::n_Q_dr_domega (const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &n_F_21, const Eigen::Matrix3d &T_rn_p, const Eigen::Matrix3d &n_Dcm_b, const double &tau_s)
	Submatrix 𝐐_35 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::n_Q_dr_dr (const Eigen::Vector3d &S_ra, const Eigen::Vector3d &S_bad, const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &n_F_21, const Eigen::Matrix3d &T_rn_p, const double &tau_s)
	Submatrix 𝐐_33 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::n_Q_dr_dv (const Eigen::Vector3d &S_ra, const Eigen::Vector3d &S_bad, const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &n_F_21, const Eigen::Matrix3d &T_rn_p, const double &tau_s)
	Submatrix 𝐐_32 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::n_Q_dr_psi (const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &n_F_21, const Eigen::Matrix3d &T_rn_p, const double &tau_s)
	Submatrix 𝐐_31 of the system noise covariance matrix 𝐐
Eigen::Vector3d	NAV::psd2BiasGaussMarkov (const Eigen::Vector3d &sigma2_bd, const Eigen::Vector3d &tau_bd)
	u_bias^2 Power Spectral Density of the bias for a Gauss-Markov random process
Eigen::Matrix3d	NAV::Q_df_df (const Eigen::Vector3d &S_bad, const double &tau_s)
	Submatrix 𝐐_44 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::Q_df_dv (const Eigen::Vector3d &S_bad, const Eigen::Matrix3d &b_Dcm_ien, const double &tau_s)
	Submatrix 𝐐_42 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::Q_domega_domega (const Eigen::Vector3d &S_bgd, const double &tau_s)
	Submatrix 𝐐_55 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::Q_domega_psi (const Eigen::Vector3d &S_bgd, const Eigen::Matrix3d &b_Dcm_ien, const double &tau_s)
	Submatrix 𝐐_51 of the system noise covariance matrix 𝐐
Eigen::Matrix2d	NAV::Q_gnss (const double &S_cPhi, const double &S_cf, const double &tau_s)
	Submatrix 𝐐_66 of the system noise covariance matrix 𝐐
Eigen::Matrix3d	NAV::Q_psi_psi (const Eigen::Vector3d &S_rg, const Eigen::Vector3d &S_bgd, const double &tau_s)
	Submatrix 𝐐_11 of the system noise covariance matrix 𝐐

Detailed Description

General process Noise definitions.

Author

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

Date

2022-01-31

Function Documentation

e_noiseInput_G()

template<typename KeyType, typename T>

KeyedMatrixX< T, KeyType, KeyType > NAV::e_noiseInput_G ( const Eigen::Quaterniond & b_quat_p, const Eigen::Quaternion< T > & e_quat_b, bool accelBiases, bool gyroBiases, bool accelScaleFactor, bool gyroScaleFactor, bool accelMisalignment, bool gyroMisalignment )

nodiscard

Calculate the noise input matrix in Earth frame coordinates.

Parameters

b_quat_p	Quaternion from IMU platform frame to body frame
e_quat_b	Quaternion from body to Earth frame
accelBiases	Flag wether to calculate the rows and columns for the acceleration bias
gyroBiases	Flag wether to calculate the rows and columns for the angular rate bias
accelScaleFactor	Flag wether to calculate the rows and columns for the acceleration scale factor
gyroScaleFactor	Flag wether to calculate the rows and columns for the angular rate scale factor
accelMisalignment	Flag wether to calculate the rows and columns for the accelerometer misalignment
gyroMisalignment	Flag wether to calculate the rows and columns for the gyroscope misalignment

e_noiseScale_W()

template<typename KeyType, typename T>

KeyedMatrixX< T, KeyType, KeyType > NAV::e_noiseScale_W ( const Eigen::Vector3d & sigma2_ra, const Eigen::Vector3d & sigma2_rg, const Eigen::Vector3d & sigma2_bad, const Eigen::Vector3d & sigma2_bgd, const Eigen::Vector3d & sigma2_sad, const Eigen::Vector3d & sigma2_sgd, bool accelBiases, bool gyroBiases, bool accelScaleFactor, bool gyroScaleFactor )

nodiscard

Calculate the noise scale matrix in Earth frame coordinates.

Parameters

sigma2_ra	𝜎²_ra Variance of the noise on the accelerometer specific-force measurements [m^2 / s^4 / Hz]
sigma2_rg	𝜎²_rg Variance of the noise on the gyro angular-rate measurements [rad^2 / s^2 /Hz]
sigma2_bad	𝜎²_bad Variance of the accelerometer dynamic bias [m^2 / s^4]
sigma2_bgd	𝜎²_bgd Variance of the gyro dynamic bias [rad^2/s^2]
sigma2_sad	𝜎²_sad Variance of the accelerometer dynamic scale factor [-]
sigma2_sgd	𝜎²_sgd Variance of the gyro dynamic scale factor [-]
accelBiases	Flag wether to calculate the rows and columns for the acceleration bias
gyroBiases	Flag wether to calculate the rows and columns for the angular rate bias
accelScaleFactor	Flag wether to calculate the rows and columns for the acceleration scale factor
gyroScaleFactor	Flag wether to calculate the rows and columns for the angular rate scale factor

G_GaussMarkov1()

Eigen::Matrix3d NAV::G_GaussMarkov1	(	const Eigen::Vector3d &	sigma2,
		const Eigen::Vector3d &	beta )

Submatrix 𝐆_a of the noise input matrix 𝐆

Parameters

[in]	sigma2	Variance of the noise on the measurements
[in]	beta	Gauss-Markov constant 𝛽 = 1 / 𝜏 (𝜏 correlation length)

Note

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

G_RandomWalk()

Eigen::Matrix3d NAV::G_RandomWalk

(

const Eigen::Vector3d &

sigma2

)

Random walk noise input matrix 𝐆

Parameters

[in]

sigma2

Variance of the noise on the measurements

Note

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

ie_Q_dr_df()

Eigen::Matrix3d NAV::ie_Q_dr_df ( const Eigen::Vector3d & S_bad, const Eigen::Matrix3d & ie_Dcm_b, const double & tau_s )

nodiscard

Submatrix 𝐐_34 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	ie_Dcm_b	Direction Cosine Matrix from body to {i,e} coordinates
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_34

Note

See Groves (2013) equation (14.81)

ie_Q_dr_domega()

Eigen::Matrix3d NAV::ie_Q_dr_domega ( const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ie_F_21, const Eigen::Matrix3d & ie_Dcm_b, const double & tau_s )

nodiscard

Submatrix 𝐐_35 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ie_F_21	Submatrix 𝐅_21 of the system matrix 𝐅
[in]	ie_Dcm_b	Direction Cosine Matrix from body to {i,e} coordinates
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_35

Note

See Groves (2013) equation (14.81)

ie_Q_dr_dr()

Eigen::Matrix3d NAV::ie_Q_dr_dr ( const Eigen::Vector3d & S_ra, const Eigen::Vector3d & S_bad, const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ie_F_21, const double & tau_s )

nodiscard

Submatrix 𝐐_33 of the system noise covariance matrix 𝐐

Parameters

[in]	S_ra	Power Spectral Density of the accelerometer random noise
[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ie_F_21	Submatrix 𝐅_21 of the system matrix 𝐅 in {i,e} frame
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_33

Note

See Groves (2013) equation (14.81)

ie_Q_dr_dv()

Eigen::Matrix3d NAV::ie_Q_dr_dv ( const Eigen::Vector3d & S_ra, const Eigen::Vector3d & S_bad, const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ie_F_21, const double & tau_s )

nodiscard

Submatrix 𝐐_32 of the system noise covariance matrix 𝐐

Parameters

[in]	S_ra	Power Spectral Density of the accelerometer random noise
[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ie_F_21	Submatrix 𝐅_21 of the system matrix 𝐅 in {i,e} frame
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_32

Note

See Groves (2013) equation (14.81)

ie_Q_dr_psi()

Eigen::Matrix3d NAV::ie_Q_dr_psi ( const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ie_F_21, const double & tau_s )

nodiscard

Submatrix 𝐐_31 of the system noise covariance matrix 𝐐

Parameters

[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ie_F_21	Submatrix 𝐅_21 of the system matrix 𝐅 in {i,e} frame
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_31

Note

See Groves (2013) equation (14.81)

ien_Q_dv_domega()

Eigen::Matrix3d NAV::ien_Q_dv_domega ( const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ien_F_21, const Eigen::Matrix3d & ien_Dcm_b, const double & tau_s )

nodiscard

Submatrix 𝐐_25 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ien_F_21	Submatrix 𝐅_21 of the system matrix 𝐅
[in]	ien_Dcm_b	Direction Cosine Matrix from body to {i,e,n} frame
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_25

Note

See Groves (2013) equation (14.80)

ien_Q_dv_dv()

Eigen::Matrix3d NAV::ien_Q_dv_dv ( const Eigen::Vector3d & S_ra, const Eigen::Vector3d & S_bad, const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ien_F_21, const double & tau_s )

nodiscard

Submatrix 𝐐_22 of the system noise covariance matrix 𝐐

Parameters

[in]	S_ra	Power Spectral Density of the accelerometer random noise
[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ien_F_21	Submatrix 𝐅_21 of the system matrix 𝐅 in {i,e,n} frame
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_22

Note

See Groves (2013) equation (14.81)

ien_Q_dv_psi()

Eigen::Matrix3d NAV::ien_Q_dv_psi ( const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & ien_F_21, const double & tau_s )

nodiscard

Submatrix 𝐐_21 of the system noise covariance matrix 𝐐

Parameters

[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	ien_F_21	Submatrix 𝐅_21 of the system matrix 𝐅 in {i,e,n} frame
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_21

Note

See Groves (2013) equation (14.81)

n_Q_dr_df()

Eigen::Matrix3d NAV::n_Q_dr_df ( const Eigen::Vector3d & S_bad, const Eigen::Matrix3d & T_rn_p, const Eigen::Matrix3d & n_Dcm_b, const double & tau_s )

nodiscard

Submatrix 𝐐_34 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	T_rn_p	Conversion matrix between cartesian and curvilinear perturbations to the position
[in]	n_Dcm_b	Direction Cosine Matrix from body to navigation coordinates
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_34

Note

See Groves (2013) equation (14.81)

n_Q_dr_domega()

Eigen::Matrix3d NAV::n_Q_dr_domega ( const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & n_F_21, const Eigen::Matrix3d & T_rn_p, const Eigen::Matrix3d & n_Dcm_b, const double & tau_s )

nodiscard

Submatrix 𝐐_35 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	n_F_21	Submatrix 𝐅_21 of the system matrix 𝐅
[in]	T_rn_p	Conversion matrix between cartesian and curvilinear perturbations to the position
[in]	n_Dcm_b	Direction Cosine Matrix from body to navigation coordinates
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_35

Note

See Groves (2013) equation (14.81)

n_Q_dr_dr()

Eigen::Matrix3d NAV::n_Q_dr_dr ( const Eigen::Vector3d & S_ra, const Eigen::Vector3d & S_bad, const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & n_F_21, const Eigen::Matrix3d & T_rn_p, const double & tau_s )

nodiscard

Submatrix 𝐐_33 of the system noise covariance matrix 𝐐

Parameters

[in]	S_ra	Power Spectral Density of the accelerometer random noise
[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	n_F_21	Submatrix 𝐅_21 of the system matrix 𝐅
[in]	T_rn_p	Conversion matrix between cartesian and curvilinear perturbations to the position
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_33

Note

See Groves (2013) equation (14.81)

n_Q_dr_dv()

Eigen::Matrix3d NAV::n_Q_dr_dv ( const Eigen::Vector3d & S_ra, const Eigen::Vector3d & S_bad, const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & n_F_21, const Eigen::Matrix3d & T_rn_p, const double & tau_s )

nodiscard

Submatrix 𝐐_32 of the system noise covariance matrix 𝐐

Parameters

[in]	S_ra	Power Spectral Density of the accelerometer random noise
[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	n_F_21	Submatrix 𝐅_21 of the system matrix 𝐅
[in]	T_rn_p	Conversion matrix between cartesian and curvilinear perturbations to the position
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_32

Note

See Groves (2013) equation (14.81)

n_Q_dr_psi()

Eigen::Matrix3d NAV::n_Q_dr_psi ( const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & n_F_21, const Eigen::Matrix3d & T_rn_p, const double & tau_s )

nodiscard

Submatrix 𝐐_31 of the system noise covariance matrix 𝐐

Parameters

[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	n_F_21	Submatrix 𝐅_21 of the system matrix 𝐅
[in]	T_rn_p	Conversion matrix between cartesian and curvilinear perturbations to the position
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_31

Note

See Groves (2013) equation (14.81)

psd2BiasGaussMarkov()

Eigen::Vector3d NAV::psd2BiasGaussMarkov ( const Eigen::Vector3d & sigma2_bd, const Eigen::Vector3d & tau_bd )

nodiscard

u_bias^2 Power Spectral Density of the bias for a Gauss-Markov random process

Parameters

[in]	sigma2_bd	𝜎²_bd standard deviation of the bias noise
[in]	tau_bd	𝜏 Correlation length in [s]

Note

See Brown & Hwang (2011) - Introduction to Random Signals and Applied Kalman Filtering (example 9.6)

Q_df_df()

Eigen::Matrix3d NAV::Q_df_df ( const Eigen::Vector3d & S_bad, const double & tau_s )

nodiscard

Submatrix 𝐐_44 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_44

Note

See Groves (2013) equation (14.80)

Q_df_dv()

Eigen::Matrix3d NAV::Q_df_dv ( const Eigen::Vector3d & S_bad, const Eigen::Matrix3d & b_Dcm_ien, const double & tau_s )

nodiscard

Submatrix 𝐐_42 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bad	Power Spectral Density of the accelerometer bias variation
[in]	b_Dcm_ien	Direction Cosine Matrix from {i,e,n} to body coordinates
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_42

Note

See Groves (2013) equation (14.80)

Q_domega_domega()

Eigen::Matrix3d NAV::Q_domega_domega ( const Eigen::Vector3d & S_bgd, const double & tau_s )

nodiscard

Submatrix 𝐐_55 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_55

Note

See Groves (2013) equation (14.80)

Q_domega_psi()

Eigen::Matrix3d NAV::Q_domega_psi ( const Eigen::Vector3d & S_bgd, const Eigen::Matrix3d & b_Dcm_ien, const double & tau_s )

nodiscard

Submatrix 𝐐_51 of the system noise covariance matrix 𝐐

Parameters

[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	b_Dcm_ien	Direction Cosine Matrix from {i,e,n} to body coordinates
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_51

Note

See Groves (2013) equation (14.80)

Q_gnss()

Eigen::Matrix2d NAV::Q_gnss ( const double & S_cPhi, const double & S_cf, const double & tau_s )

nodiscard

Submatrix 𝐐_66 of the system noise covariance matrix 𝐐

Parameters

[in]	S_cPhi	Power Spectral Density of the receiver clock phase drift in [m^2 s^-1]
[in]	S_cf	Power Spectral Density of the receiver clock frequency-drift [m^2 s^-3]
[in]	tau_s	Time interval in [s]

Returns

See Groves (2013) equation (9.152)

Q_psi_psi()

Eigen::Matrix3d NAV::Q_psi_psi ( const Eigen::Vector3d & S_rg, const Eigen::Vector3d & S_bgd, const double & tau_s )

nodiscard

Submatrix 𝐐_11 of the system noise covariance matrix 𝐐

Parameters

[in]	S_rg	Power Spectral Density of the gyroscope random noise
[in]	S_bgd	Power Spectral Density of the gyroscope bias variation
[in]	tau_s	Time interval in [s]

Returns

The 3x3 matrix 𝐐_11

Note

See Groves (2013) equation (14.81)