Namespaces
namespace	internal

Functions
template<typename DerivedA, typename DerivedQ, typename DerivedL, typename DerivedD>
double	calcChi2 (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedQ > &Q, const Eigen::MatrixBase< DerivedL > &L_LTDL_Q, const Eigen::MatrixBase< DerivedD > &D_LTDL_Q, const Eigen::Index &ncand=2, double factor=1.5)
	Calculates $\chi^2$ , the size of the ellipsoidal region.
double	criticalValueFailureRateLookup (double Pf, double Pf_ILS, size_t nAmb)
	Look-up table for the critical value µ, depending on failure rate Pf_ILS.
template<typename DerivedA, typename DerivedQ>
std::optional< std::tuple< typename DerivedQ::PlainObject, typename DerivedQ::PlainObject, typename DerivedQ::PlainObject, typename DerivedA::PlainObject, typename DerivedA::PlainObject > >	decorrelate_ztrafo (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedQ > &Q)
	Decorrelates the ambiguities.
template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ>
bool	differenceTest (const Eigen::MatrixBase< DerivedAFix1 > &aFix1, const Eigen::MatrixBase< DerivedAFix2 > &aFix2, const Eigen::MatrixBase< DerivedAFloat > &aFloat, const Eigen::MatrixBase< DerivedQ > &Qa, double criticalValue)
	Difference test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::DifferenceTest.
bool	differenceTest (double sqNormFix1, double sqNormFix2, double criticalValue)
	Difference test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::DifferenceTest.
template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ, typename DerivedD>
bool	fixedFailureRateRatioTest (double Pf, const Eigen::MatrixBase< DerivedAFix1 > &aFix1, const Eigen::MatrixBase< DerivedAFix2 > &aFix2, const Eigen::MatrixBase< DerivedAFloat > &aFloat, const Eigen::MatrixBase< DerivedQ > &Qa, const Eigen::MatrixBase< DerivedD > &D_LTDL_Q)
	Ratio test with a fixed-failure rate for ambiguity resolution, see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestFailureRate.
template<typename DerivedD>
bool	fixedFailureRateRatioTest (double Pf, double sqNormFix1, double sqNormFix2, size_t nAmb, const Eigen::MatrixBase< DerivedD > &D_LTDL_Q, bool validateBootstrappedSuccessRate=true)
	Ratio test with a fixed-failure rate for ambiguity resolution, see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestFailureRate.
template<typename DerivedA, typename DerivedQ, typename DerivedL, typename DerivedD>
std::pair< Eigen::MatrixXd, Eigen::VectorXd >	integerLeastSquaresSearch (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedQ > &Q, const Eigen::MatrixBase< DerivedL > &L_LTDL_Q, const Eigen::MatrixBase< DerivedD > &D_LTDL_Q, const Eigen::Index &numCandidates=2)
	Performs an integer least-squares to search for integer candidates for the ambiguities.
template<typename DerivedA, typename DerivedL, typename DerivedD>
std::pair< Eigen::MatrixXd, Eigen::VectorXd >	integerLeastSquaresSearchAndShrink (const Eigen::MatrixBase< DerivedA > &zh, const Eigen::MatrixBase< DerivedL > &L_LTDL_Q, const Eigen::MatrixBase< DerivedD > &D_LTDL_Q, const Eigen::Index &numCandidates=2)
	Performs an integer least-squares to search for integer candidates for the ambiguities using the search-and-shrink technique (MLAMBDA)
template<typename DerivedA, typename DerivedQ>
DerivedA::PlainObject	integerSearchBootstrapping (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedQ > &Qa)
	Searches for the integer ambiguities by integer bootstrapping.
template<typename Derived>
Derived::PlainObject	integerSearchRounding (const Eigen::MatrixBase< Derived > &a)
	Searches for the integer ambiguities by integer rounding.
template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ>
bool	projectorTest (const Eigen::MatrixBase< DerivedAFix1 > &aFix1, const Eigen::MatrixBase< DerivedAFix2 > &aFix2, const Eigen::MatrixBase< DerivedAFloat > &aFloat, const Eigen::MatrixBase< DerivedQ > &Qa, double mu)
	Projector test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::ProjectorTest.
template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ>
bool	ratioTest (const Eigen::MatrixBase< DerivedAFix1 > &aFix1, const Eigen::MatrixBase< DerivedAFix2 > &aFix2, const Eigen::MatrixBase< DerivedAFloat > &aFloat, const Eigen::MatrixBase< DerivedQ > &Qa, double mu)
	Ratio test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestCriticalValue.
bool	ratioTest (double sqNormFix1, double sqNormFix2, double mu)
	Ratio test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestCriticalValue.
template<typename Derived>
double	successRateBootstrapping (const Eigen::MatrixBase< Derived > &D_LTDL_Q)
	Calculates the bootstrapped success rate.

Variables
std::unordered_map< double, std::vector< std::vector< double > > >	lookupTableFailureProbability

Function Documentation

◆ calcChi2()

template<typename DerivedA, typename DerivedQ, typename DerivedL, typename DerivedD>

double NAV::Ambiguity::calcChi2	(	const Eigen::MatrixBase< DerivedA > &	a,
		const Eigen::MatrixBase< DerivedQ > &	Q,
		const Eigen::MatrixBase< DerivedL > &	L_LTDL_Q,
		const Eigen::MatrixBase< DerivedD > &	D_LTDL_Q,
		const Eigen::Index &	ncand = 2,
		double	factor = 1.5 )

Calculates $\chi^2$ , the size of the ellipsoidal region.

Parameters

[in]	a	Float ambiguity vector [cycles]
[in]	Q	Variance/covariance matrix of the ambiguities
[in]	L_LTDL_Q	Lower-triangular matrix from the L^T * D * L decomposition of Q
[in]	D_LTDL_Q	Diagonal matrix from the L^T * D * L decomposition of Q
[in]	ncand	Requested number of candidates (default = 2)
[in]	factor	Multiplication factor for the volume of the resulting search ellipsoid (default = 1.5)

Returns: Size of the ellipsoidal region $\chi^2$

Definition at line 129 of file EllipsoidalRegion.hpp.

◆ criticalValueFailureRateLookup()

double NAV::Ambiguity::criticalValueFailureRateLookup	(	double	Pf,
		double	Pf_ILS,
		size_t	nAmb )

Look-up table for the critical value µ, depending on failure rate Pf_ILS.

Parameters

Pf	Failure probability to not be higher
Pf_ILS	Upper bound of the failure probability
nAmb	Amount of ambiguities

Returns: Critical value µ

Definition at line 108 of file Validate.cpp.

◆ decorrelate_ztrafo()

template<typename DerivedA, typename DerivedQ>

std::optional< std::tuple< typename DerivedQ::PlainObject, typename DerivedQ::PlainObject, typename DerivedQ::PlainObject, typename DerivedA::PlainObject, typename DerivedA::PlainObject > > NAV::Ambiguity::decorrelate_ztrafo	(	const Eigen::MatrixBase< DerivedA > &	a,
		const Eigen::MatrixBase< DerivedQ > &	Q )

nodiscard

Decorrelates the ambiguities.

Parameters

[in]	a	Float ambiguity vector [cycles]
[in]	Q	Variance/covariance matrix of the ambiguities

Returns: [Qz, Z, L, D, z] L, D are a (L^T * D * L) decomposition of Q_z

Note: See [11] Chang 2005, Reduction algorithm

Definition at line 94 of file Decorrelation.hpp.

◆ differenceTest() [1/2]

template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ>

bool NAV::Ambiguity::differenceTest	(	const Eigen::MatrixBase< DerivedAFix1 > &	aFix1,
		const Eigen::MatrixBase< DerivedAFix2 > &	aFix2,
		const Eigen::MatrixBase< DerivedAFloat > &	aFloat,
		const Eigen::MatrixBase< DerivedQ > &	Qa,
		double	criticalValue )

Difference test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::DifferenceTest.

Parameters

[in]	aFix1	Best integer ambiguities solution
[in]	aFix2	Second best integer ambiguities solution
[in]	aFloat	Float ambiguities
[in]	Qa	Covariance matrix of the ambiguities
[in]	criticalValue	Critical value to check against (empirically determined value)

Returns: True if the test passes and the best integer solution should be accepted

Note: See [52] Verhagen 2006, eq. 31

Definition at line 51 of file Validate.hpp.

◆ differenceTest() [2/2]

bool NAV::Ambiguity::differenceTest	(	double	sqNormFix1,
		double	sqNormFix2,
		double	criticalValue )

Difference test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::DifferenceTest.

Parameters

[in]	sqNormFix1	Squared norm of the best integer ambiguities solution
[in]	sqNormFix2	Squared norm of the second best integer ambiguities solution
[in]	criticalValue	Critical value to check against (empirically determined value)

Returns: True if the test passes and the best integer solution should be accepted

Note: See [52] Verhagen 2006, eq. 31

Definition at line 98 of file Validate.cpp.

◆ fixedFailureRateRatioTest() [1/2]

template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ, typename DerivedD>

bool NAV::Ambiguity::fixedFailureRateRatioTest	(	double	Pf,
		const Eigen::MatrixBase< DerivedAFix1 > &	aFix1,
		const Eigen::MatrixBase< DerivedAFix2 > &	aFix2,
		const Eigen::MatrixBase< DerivedAFloat > &	aFloat,
		const Eigen::MatrixBase< DerivedQ > &	Qa,
		const Eigen::MatrixBase< DerivedD > &	D_LTDL_Q )

Ratio test with a fixed-failure rate for ambiguity resolution, see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestFailureRate.

Parameters

[in]	Pf	Fixed-failure rate
[in]	aFix1	Best integer ambiguities solution
[in]	aFix2	Second best integer ambiguities solution
[in]	aFloat	Float ambiguities
[in]	Qa	Covariance matrix of the ambiguities
[in]	D_LTDL_Q	Diagonal entries from the L^T * D * L decomposition of Q

Returns: True if the test passes and the best integer solution should be accepted

Note: See [53] Verhagen 2013

Definition at line 123 of file Validate.hpp.

◆ fixedFailureRateRatioTest() [2/2]

template<typename DerivedD>

bool NAV::Ambiguity::fixedFailureRateRatioTest	(	double	Pf,
		double	sqNormFix1,
		double	sqNormFix2,
		size_t	nAmb,
		const Eigen::MatrixBase< DerivedD > &	D_LTDL_Q,
		bool	validateBootstrappedSuccessRate = true )

Ratio test with a fixed-failure rate for ambiguity resolution, see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestFailureRate.

Parameters

[in]	Pf	Fixed-failure rate
[in]	sqNormFix1	Squared norm of the best integer ambiguities solution
[in]	sqNormFix2	Squared norm of the second best integer ambiguities solution
[in]	nAmb	Number of ambiguities
[in]	D_LTDL_Q	Diagonal entries from the L^T * D * L decomposition of Q
[in]	validateBootstrappedSuccessRate	Whether to check the bootstrapped success rate before doing the ratio test

Returns: True if the test passes and the best integer solution should be accepted

Note: See [53] Verhagen 2013

Definition at line 149 of file Validate.hpp.

◆ integerLeastSquaresSearch()

template<typename DerivedA, typename DerivedQ, typename DerivedL, typename DerivedD>

std::pair< Eigen::MatrixXd, Eigen::VectorXd > NAV::Ambiguity::integerLeastSquaresSearch	(	const Eigen::MatrixBase< DerivedA > &	a,
		const Eigen::MatrixBase< DerivedQ > &	Q,
		const Eigen::MatrixBase< DerivedL > &	L_LTDL_Q,
		const Eigen::MatrixBase< DerivedD > &	D_LTDL_Q,
		const Eigen::Index &	numCandidates = 2 )

Performs an integer least-squares to search for integer candidates for the ambiguities.

Parameters

[in]	a	Decorrelated float ambiguity vector [cycles]
[in]	Q	Variance/covariance matrix of the ambiguities
[in]	L_LTDL_Q	Lower-triangular matrix from the L^T * D * L decomposition of Q
[in]	D_LTDL_Q	Diagonal entries from the L^T * D * L decomposition of Q
[in]	numCandidates	Requested number of candidates (default = 2)

Returns: Pair of: First a list of integer candidates (last column is the most likely), Vector with squared norm of the integer candidates

Note: See [13] de Jonge 1996, Algorithm FI71

Definition at line 79 of file Search.hpp.

◆ integerLeastSquaresSearchAndShrink()

template<typename DerivedA, typename DerivedL, typename DerivedD>

std::pair< Eigen::MatrixXd, Eigen::VectorXd > NAV::Ambiguity::integerLeastSquaresSearchAndShrink	(	const Eigen::MatrixBase< DerivedA > &	zh,
		const Eigen::MatrixBase< DerivedL > &	L_LTDL_Q,
		const Eigen::MatrixBase< DerivedD > &	D_LTDL_Q,
		const Eigen::Index &	numCandidates = 2 )

Performs an integer least-squares to search for integer candidates for the ambiguities using the search-and-shrink technique (MLAMBDA)

Parameters

[in]	zh	Decorrelated float ambiguity vector [cycles]
[in]	L_LTDL_Q	Lower-triangular matrix from the L^T * D * L decomposition of Q
[in]	D_LTDL_Q	Diagonal entries from the L^T * D * L decomposition of Q
[in]	numCandidates	Requested number of candidates (default = 2)

Returns: Pair of: First a list of integer candidates (last column is the most likely), Vector with squared norm of the integer candidates

Note: See [11] Chang 2005, Argorithm 3.3; See [13] de Jonge 1996, ch. 4.8; See ssearch.m file from TUDelft Matlab code

Definition at line 243 of file Search.hpp.

◆ integerSearchBootstrapping()

template<typename DerivedA, typename DerivedQ>

DerivedA::PlainObject NAV::Ambiguity::integerSearchBootstrapping	(	const Eigen::MatrixBase< DerivedA > &	a,
		const Eigen::MatrixBase< DerivedQ > &	Qa )

Searches for the integer ambiguities by integer bootstrapping.

Parameters

[in]	a	Decorrelated float ambiguity vector [cycles]
[in]	Qa	Variance/covariance matrix of the ambiguities

Returns: Integer ambiguity vector

Note: See [48] Springer Handbook GNSS, ch. 23.2.3

Definition at line 48 of file Search.hpp.

◆ integerSearchRounding()

template<typename Derived>

Derived::PlainObject NAV::Ambiguity::integerSearchRounding ( const Eigen::MatrixBase< Derived > & a )

Searches for the integer ambiguities by integer rounding.

Parameters

[in] a Float ambiguity vector [cycles]

Returns: Integer ambiguity vector

Note: See [48] Springer Handbook GNSS, ch. 23.2.2

Definition at line 34 of file Search.hpp.

◆ projectorTest()

template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ>

bool NAV::Ambiguity::projectorTest	(	const Eigen::MatrixBase< DerivedAFix1 > &	aFix1,
		const Eigen::MatrixBase< DerivedAFix2 > &	aFix2,
		const Eigen::MatrixBase< DerivedAFloat > &	aFloat,
		const Eigen::MatrixBase< DerivedQ > &	Qa,
		double	mu )

Projector test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::ProjectorTest.

Parameters

[in]	aFix1	Best integer ambiguities solution
[in]	aFix2	Second best integer ambiguities solution
[in]	aFloat	Float ambiguities
[in]	Qa	Covariance matrix of the ambiguities
[in]	mu	Critical value to check against, with range (0, 1]

Returns: True if the test passes and the best integer solution should be accepted

Note: See [52] Verhagen 2006, eq. 35

Definition at line 172 of file Validate.hpp.

◆ ratioTest() [1/2]

template<typename DerivedAFix1, typename DerivedAFix2, typename DerivedAFloat, typename DerivedQ>

bool NAV::Ambiguity::ratioTest	(	const Eigen::MatrixBase< DerivedAFix1 > &	aFix1,
		const Eigen::MatrixBase< DerivedAFix2 > &	aFix2,
		const Eigen::MatrixBase< DerivedAFloat > &	aFloat,
		const Eigen::MatrixBase< DerivedQ > &	Qa,
		double	mu )

Ratio test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestCriticalValue.

Parameters

[in]	aFix1	Best integer ambiguities solution
[in]	aFix2	Second best integer ambiguities solution
[in]	aFloat	Float ambiguities
[in]	Qa	Covariance matrix of the ambiguities
[in]	mu	Critical value to check against, with range (0, 1]

Returns: True if the test passes and the best integer solution should be accepted

Note: See [48] Springer Handbook GNSS, ch. 23.6.4, eq. 23.78 or [52] Verhagen 2006, eq. 28, 29

Definition at line 83 of file Validate.hpp.

◆ ratioTest() [2/2]

bool NAV::Ambiguity::ratioTest	(	double	sqNormFix1,
		double	sqNormFix2,
		double	mu )

Ratio test for the ambiguity resolution see NAV::AmbiguityResolutionParameters::ValidationAlgorithm::RatioTestCriticalValue.

Parameters

[in]	sqNormFix1	Squared norm of the best integer ambiguities solution
[in]	sqNormFix2	Squared norm of the second best integer ambiguities solution
[in]	mu	Critical value to check against, with range (0, 1]

Returns: True if the test passes and the best integer solution should be accepted

Note: See [48] Springer Handbook GNSS, ch. 23.6.4, eq. 23.78 or [52] Verhagen 2006, eq. 28, 29

Definition at line 103 of file Validate.cpp.

◆ successRateBootstrapping()

template<typename Derived>

double NAV::Ambiguity::successRateBootstrapping ( const Eigen::MatrixBase< Derived > & D_LTDL_Q )

Calculates the bootstrapped success rate.

Parameters

[in] D_LTDL_Q Diagonal entries from the L^T * D * L decomposition of Q

Returns: The bootstrapped success rate

Note: See [48] Springer Handbook GNSS, ch. 23.2.4, eq. 23.28

Definition at line 29 of file Validate.hpp.

Variable Documentation

◆ lookupTableFailureProbability

std::unordered_map<double, std::vector<std::vector<double> > > NAV::Ambiguity::lookupTableFailureProbability

Definition at line 27 of file Validate.cpp.

Namespaces

Functions

Variables

Function Documentation

◆ calcChi2()

◆ criticalValueFailureRateLookup()

◆ decorrelate_ztrafo()

◆ differenceTest() [1/2]

◆ differenceTest() [2/2]

◆ fixedFailureRateRatioTest() [1/2]

◆ fixedFailureRateRatioTest() [2/2]

◆ integerLeastSquaresSearch()

◆ integerLeastSquaresSearchAndShrink()

◆ integerSearchBootstrapping()

◆ integerSearchRounding()

◆ projectorTest()

◆ ratioTest() [1/2]

◆ ratioTest() [2/2]

◆ successRateBootstrapping()

Variable Documentation

◆ lookupTableFailureProbability