org.orekit.estimation.measurements.gnss

Class AbstractLambdaMethod

java.lang.Object

org.orekit.estimation.measurements.gnss.AbstractLambdaMethod

All Implemented Interfaces:

IntegerLeastSquareSolver

Direct Known Subclasses:

LambdaMethod, ModifiedLambdaMethod

public abstract class AbstractLambdaMethod
extends Object
implements IntegerLeastSquareSolver

Base class for decorrelation/reduction engine for LAMBDA type methods.

This class is based on both the 1996 paper The LAMBDA method for integer ambiguity estimation: implementation aspects by Paul de Jonge and Christian Tiberius and on the 2005 paper A modified LAMBDA method for integer least-squares estimation by X.-W Chang, X. Yang and T. Zhou, Journal of Geodesy 79(9):552-565, DOI: 10.1007/s00190-005-0004-x

Since:

10.0

Author:

Luc Maisonobe

Constructor Summary

Constructors

Constructor and Description
AbstractLambdaMethod()

Method Summary

Modifier and Type	Method and Description
protected void	addSolution(long[] fixed, double squaredNorm) Add a new solution.
protected abstract void	discreteSearch() Find the best solutions to the Integer Least Square problem.
protected double[]	getDecorrelatedReference() Get the reference decorrelated ambiguities.
protected double[]	getDiagReference() Get a reference to the diagonal matrix of the decomposition.
protected double[]	getLowReference() Get a reference to the lower triangular matrix of the decomposition.
protected double	getMaxDistance() Get the maximum of distance among the solutions found.
protected int	getMaxSolution() Get the maximum number of solutions seeked.
protected int	getSize() Get the size of the problem.
protected int	getSolutionsSize() Get the number of solutions found.
protected int[]	getZInverseTransformationReference() Get a reference to the Z inverse transformation matrix.
protected void	integerGaussTransformation(int row, int col) Perform one integer Gauss transformation.
protected abstract void	inverseDecomposition() Inverse the decomposition.
protected int	lIndex(int row, int col) Get the index of an entry in the lower triangular matrix.
protected abstract void	ltdlDecomposition() Perform Lᵀ.D.L = Q decomposition of the covariance matrix.
protected void	permutation(int k0, double delta) Perform one symmetric permutation involving rows/columns k0 and k0+1.
protected IntegerLeastSquareSolution[]	recoverAmbiguities() Recover ambiguities prior to the Z-transformation.
protected abstract void	reduction() Perform LAMBDA reduction.
protected void	removeSolution() Remove spurious solution.
IntegerLeastSquareSolution[]	solveILS(int nbSol, double[] floatAmbiguities, int[] indirection, RealMatrix covariance) Find the best solutions to an Integer Least Square problem.
protected int	zIndex(int row, int col) Get the index of an entry in the Z transformation matrix.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

AbstractLambdaMethod

public AbstractLambdaMethod()

Method Detail

solveILS

public IntegerLeastSquareSolution[] solveILS(int nbSol,
                                             double[] floatAmbiguities,
                                             int[] indirection,
                                             RealMatrix covariance)

Find the best solutions to an Integer Least Square problem.

Specified by:

solveILS in interface IntegerLeastSquareSolver

Parameters:

nbSol - number of solutions to search for

floatAmbiguities - float estimates of ambiguities

indirection - indirection array to extract ambiguity covariances from global covariance matrix

covariance - global covariance matrix (includes ambiguities among other parameters)

Returns:

at most nbSol solutions a to the Integer Least Square problem, in increasing squared distance order

getDiagReference

protected double[] getDiagReference()

Get a reference to the diagonal matrix of the decomposition.

BEWARE: the returned value is a reference to an internal array, it is only intended for subclasses use (hence the method is protected and not public).

Returns:

reference to the diagonal matrix of the decomposition

getLowReference

protected double[] getLowReference()

Get a reference to the lower triangular matrix of the decomposition.

BEWARE: the returned value is a reference to an internal array, it is only intended for subclasses use (hence the method is protected and not public).

Returns:

reference to the lower triangular matrix of the decomposition

getDecorrelatedReference

protected double[] getDecorrelatedReference()

Get the reference decorrelated ambiguities.

Returns:

reference to the decorrelated ambiguities.

getMaxSolution

protected int getMaxSolution()

Get the maximum number of solutions seeked.

Returns:

the maximum number of solutions seeked

addSolution

protected void addSolution(long[] fixed,
                           double squaredNorm)

Add a new solution.

Parameters:

fixed - solution array

squaredNorm - squared distance to the corresponding float solution

removeSolution

protected void removeSolution()

Remove spurious solution.

getSolutionsSize

protected int getSolutionsSize()

Get the number of solutions found.

Returns:

the number of solutions found

getMaxDistance

protected double getMaxDistance()

Get the maximum of distance among the solutions found. getting last of solutions as they are sorted in SortesSet

Returns:

greatest distance of the solutions

Since:

10.2

getZInverseTransformationReference

protected int[] getZInverseTransformationReference()

Get a reference to the Z inverse transformation matrix.

BEWARE: the returned value is a reference to an internal array, it is only intended for subclasses use (hence the method is protected and not public). BEWARE: for the MODIFIED LAMBDA METHOD, the returned matrix Z is such that Q = Z'L'DLZ where Q is the covariance matrix and ' refers to the transposition operation

Returns:

array of integer corresponding to Z matrix

Since:

10.2

getSize

protected int getSize()

Get the size of the problem. In the ILS problem, the integer returned is the size of the covariance matrix.

Returns:

the size of the ILS problem

Since:

10.2

ltdlDecomposition

protected abstract void ltdlDecomposition()

Perform Lᵀ.D.L = Q decomposition of the covariance matrix.

reduction

protected abstract void reduction()

Perform LAMBDA reduction.

discreteSearch

protected abstract void discreteSearch()

Find the best solutions to the Integer Least Square problem.

inverseDecomposition

protected abstract void inverseDecomposition()

Inverse the decomposition.

This method transforms the Lᵀ.D.L = Q decomposition of covariance into the L⁻¹.D⁻¹.L⁻ᵀ = Q⁻¹ decomposition of the inverse of covariance.

integerGaussTransformation

protected void integerGaussTransformation(int row,
                                          int col)

Perform one integer Gauss transformation.

This method corresponds to algorithm 2.1 in X.-W Chang, X. Yang and T. Zhou paper.

Parameters:

row - row index (counting from 0)

col - column index (counting from 0)

permutation

protected void permutation(int k0,
                           double delta)

Perform one symmetric permutation involving rows/columns k0 and k0+1.

This method corresponds to algorithm 2.2 in X.-W Chang, X. Yang and T. Zhou paper.

Parameters:

k0 - diagonal index (counting from 0)

delta - new value for diag[k0+1]

recoverAmbiguities

protected IntegerLeastSquareSolution[] recoverAmbiguities()

Recover ambiguities prior to the Z-transformation.

Returns:

recovered ambiguities

lIndex

protected int lIndex(int row,
                     int col)

Get the index of an entry in the lower triangular matrix.

Parameters:

row - row index (counting from 0)

col - column index (counting from 0)

Returns:

index in the single dimension array

zIndex

protected int zIndex(int row,
                     int col)

Get the index of an entry in the Z transformation matrix.

Parameters:

row - row index (counting from 0)

col - column index (counting from 0)

Returns:

index in the single dimension array