geofunctions.h File Reference

A set of coordinate transformations functions and helpers, some of them migrated from MATLAB, for geographic information systems. More...

#include <armadillo>

Go to the source code of this file.

Functions
arma::mat	Skew_symmetric (const arma::vec &a)
	Calculates skew-symmetric matrix. More...
double	WGS84_g0 (double Lat_rad)
double	WGS84_geocentric_radius (double Lat_geodetic_rad)
int	topocent (double *Az, double *El, double *D, const arma::vec &x, const arma::vec &dx)
	Transformation of vector dx into topocentric coordinate system with origin at x Inputs: x - vector origin coordinates (in ECEF system [X; Y; Z;]) dx - vector ([dX; dY; dZ;]). More...
int	togeod (double *dphi, double *dlambda, double *h, double a, double finv, double X, double Y, double Z)
	Subroutine to calculate geodetic coordinates latitude, longitude, height given Cartesian coordinates X,Y,Z, and reference ellipsoid values semi-major axis (a) and the inverse of flattening (finv). More...
arma::vec	Gravity_ECEF (const arma::vec &r_eb_e)
	Calculates acceleration due to gravity resolved about ECEF-frame. More...
arma::vec	cart2geo (const arma::vec &XYZ, int elipsoid_selection)
	Conversion of Cartesian coordinates (X,Y,Z) to geographical coordinates (latitude, longitude, h) on a selected reference ellipsoid. More...
arma::vec	LLH_to_deg (const arma::vec &LLH)
double	degtorad (double angleInDegrees)
double	radtodeg (double angleInRadians)
double	mstoknotsh (double MetersPerSeconds)
double	mstokph (double MetersPerSeconds)
arma::vec	CTM_to_Euler (const arma::mat &C)
arma::mat	Euler_to_CTM (const arma::vec &eul)
void	ECEF_to_Geo (const arma::vec &r_eb_e, const arma::vec &v_eb_e, const arma::mat &C_b_e, arma::vec &LLH, arma::vec &v_eb_n, arma::mat &C_b_n)
void	Geo_to_ECEF (const arma::vec &LLH, const arma::vec &v_eb_n, const arma::mat &C_b_n, arma::vec &r_eb_e, arma::vec &v_eb_e, arma::mat &C_b_e)
	From Geographic to ECEF coordinates. More...
void	pv_Geo_to_ECEF (double L_b, double lambda_b, double h_b, const arma::vec &v_eb_n, arma::vec &r_eb_e, arma::vec &v_eb_e)
	Converts curvilinear to Cartesian position and velocity resolving axes from NED to ECEF This function created 11/4/2012 by Paul Groves. More...
double	great_circle_distance (double lat1, double lon1, double lat2, double lon2)
	The Haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. More...
void	cart2utm (const arma::vec &r_eb_e, int zone, arma::vec &r_enu)
	Transformation of ECEF (X,Y,Z) to (E,N,U) in UTM, zone 'zone'. More...
int	findUtmZone (double latitude_deg, double longitude_deg)
	Function finds the UTM zone number for given longitude and latitude. More...
double	clsin (const arma::colvec &ar, int degree, double argument)
	Clenshaw summation of sinus of argument. More...
void	clksin (const arma::colvec &ar, int degree, double arg_real, double arg_imag, double *re, double *im)
	Clenshaw summation of sinus with complex argument. More...

Detailed Description

A set of coordinate transformations functions and helpers, some of them migrated from MATLAB, for geographic information systems.

Author

Javier Arribas, 2018. jarribas(at)cttc.es

---

Copyright (C) 2010-2020 (see AUTHORS file for a list of contributors)

GNSS-SDR is a software defined Global Navigation Satellite Systems receiver

This file is part of GNSS-SDR.

SPDX-License-Identifier: GPL-3.0-or-later

---

Definition in file geofunctions.h.

Function Documentation

cart2geo()

arma::vec cart2geo	(	const arma::vec &	XYZ,
		int	elipsoid_selection
	)

Conversion of Cartesian coordinates (X,Y,Z) to geographical coordinates (latitude, longitude, h) on a selected reference ellipsoid.

Choices of Reference Ellipsoid for Geographical Coordinates 0. International Ellipsoid 1924

1. International Ellipsoid 1967
2. World Geodetic System 1972
3. Geodetic Reference System 1980
4. World Geodetic System 1984

cart2utm()

void cart2utm	(	const arma::vec &	r_eb_e,
		int	zone,
		arma::vec &	r_enu
	)

Transformation of ECEF (X,Y,Z) to (E,N,U) in UTM, zone 'zone'.

clksin()

void clksin	(	const arma::colvec &	ar,
		int	degree,
		double	arg_real,
		double	arg_imag,
		double *	re,
		double *	im
	)

Clenshaw summation of sinus with complex argument.

clsin()

double clsin	(	const arma::colvec &	ar,
		int	degree,
		double	argument
	)

Clenshaw summation of sinus of argument.

findUtmZone()

int findUtmZone	(	double	latitude_deg,
		double	longitude_deg
	)

Function finds the UTM zone number for given longitude and latitude.

Geo_to_ECEF()

void Geo_to_ECEF	(	const arma::vec &	LLH,
		const arma::vec &	v_eb_n,
		const arma::mat &	C_b_n,
		arma::vec &	r_eb_e,
		arma::vec &	v_eb_e,
		arma::mat &	C_b_e
	)

From Geographic to ECEF coordinates.

Inputs: LLH latitude (rad), longitude (rad), height (m) v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along north, east, and down (m/s) C_b_n body-to-NED coordinate transformation matrix

Outputs: r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved along ECEF-frame axes (m) v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along ECEF-frame axes (m/s) C_b_e body-to-ECEF-frame coordinate transformation matrix

Gravity_ECEF()

arma::vec Gravity_ECEF

(

const arma::vec &

r_eb_e

)

Calculates acceleration due to gravity resolved about ECEF-frame.

great_circle_distance()

double great_circle_distance	(	double	lat1,
		double	lon1,
		double	lat2,
		double	lon2
	)

The Haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.

pv_Geo_to_ECEF()

void pv_Geo_to_ECEF	(	double	L_b,
		double	lambda_b,
		double	h_b,
		const arma::vec &	v_eb_n,
		arma::vec &	r_eb_e,
		arma::vec &	v_eb_e
	)

Converts curvilinear to Cartesian position and velocity resolving axes from NED to ECEF This function created 11/4/2012 by Paul Groves.

Inputs: L_b latitude (rad) lambda_b longitude (rad) h_b height (m) v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along north, east, and down (m/s)

Outputs: r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved along ECEF-frame axes (m) v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along ECEF-frame axes (m/s)

Skew_symmetric()

arma::mat Skew_symmetric

(

const arma::vec &

a

)

Calculates skew-symmetric matrix.

togeod()

int togeod	(	double *	dphi,
		double *	dlambda,
		double *	h,
		double	a,
		double	finv,
		double	X,
		double	Y,
		double	Z
	)

Subroutine to calculate geodetic coordinates latitude, longitude, height given Cartesian coordinates X,Y,Z, and reference ellipsoid values semi-major axis (a) and the inverse of flattening (finv).

The output units of angular quantities will be in decimal degrees (15.5 degrees not 15 deg 30 min). The output units of h will be the same as the units of X,Y,Z,a.

  Inputs:
      a           - semi-major axis of the reference ellipsoid
      finv        - inverse of flattening of the reference ellipsoid
      X,Y,Z       - Cartesian coordinates

  Outputs:
      dphi        - latitude
      dlambda     - longitude
      h           - height above reference ellipsoid

      Based in a Matlab function by Kai Borre

topocent()

int topocent	(	double *	Az,
		double *	El,
		double *	D,
		const arma::vec &	x,
		const arma::vec &	dx
	)

Transformation of vector dx into topocentric coordinate system with origin at x Inputs: x - vector origin coordinates (in ECEF system [X; Y; Z;]) dx - vector ([dX; dY; dZ;]).

Outputs: D - vector length. Units like the input Az - azimuth from north positive clockwise, degrees El - elevation angle, degrees

Based on a Matlab function by Kai Borre