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/**
******************************************************************************
*
* @file coordinateconversions.cpp
* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
* @brief General conversions with different coordinate systems.
* - all angles in deg
* - distances in meters
* - altitude above WGS-84 elipsoid
*
* @see The GNU Public License (GPL) Version 3
*
*****************************************************************************/
/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "coordinateconversions.h"
#include <stdint.h>
#include <QDebug>
#include <math.h>
#include <qmath.h>
#define RAD2DEG (180.0/M_PI)
#define DEG2RAD (M_PI/180.0)
namespace Utils {
CoordinateConversions::CoordinateConversions()
{
}
/**
* Get rotation matrix from ECEF to NED for that LLA
* @param[in] LLA Longitude latitude altitude for this location
* @param[out] Rne[3][3] Rotation matrix
*/
void CoordinateConversions::RneFromLLA(double LLA[3], double Rne[3][3]){
float sinLat, sinLon, cosLat, cosLon;
sinLat=(float)sin(DEG2RAD*LLA[0]);
sinLon=(float)sin(DEG2RAD*LLA[1]);
cosLat=(float)cos(DEG2RAD*LLA[0]);
cosLon=(float)cos(DEG2RAD*LLA[1]);
Rne[0][0] = -sinLat*cosLon; Rne[0][1] = -sinLat*sinLon; Rne[0][2] = cosLat;
Rne[1][0] = -sinLon; Rne[1][1] = cosLon; Rne[1][2] = 0;
Rne[2][0] = -cosLat*cosLon; Rne[2][1] = -cosLat*sinLon; Rne[2][2] = -sinLat;
}
/**
* Convert from LLA coordinates to ECEF coordinates
* @param[in] LLA[3] latitude longitude alititude coordinates in
* @param[out] ECEF[3] location in ECEF coordinates
*/
void CoordinateConversions::LLA2ECEF(double LLA[3], double ECEF[3]){
const double a = 6378137.0; // Equatorial Radius
const double e = 8.1819190842622e-2; // Eccentricity
double sinLat, sinLon, cosLat, cosLon;
double N;
sinLat=sin(DEG2RAD*LLA[0]);
sinLon=sin(DEG2RAD*LLA[1]);
cosLat=cos(DEG2RAD*LLA[0]);
cosLon=cos(DEG2RAD*LLA[1]);
N = a / sqrt(1.0 - e*e*sinLat*sinLat); //prime vertical radius of curvature
ECEF[0] = (N+LLA[2])*cosLat*cosLon;
ECEF[1] = (N+LLA[2])*cosLat*sinLon;
ECEF[2] = ((1-e*e)*N + LLA[2]) * sinLat;
}
/**
* Convert from ECEF coordinates to LLA coordinates
* @param[in] ECEF[3] location in ECEF coordinates
* @param[out] LLA[3] latitude longitude alititude coordinates
*/
int CoordinateConversions::ECEF2LLA(double ECEF[3], double LLA[3])
{
const double a = 6378137.0; // Equatorial Radius
const double e = 8.1819190842622e-2; // Eccentricity
double x=ECEF[0], y=ECEF[1], z=ECEF[2];
double Lat, N, NplusH, delta, esLat;
uint16_t iter;
LLA[1] = RAD2DEG*atan2(y,x);
N = a;
NplusH = N;
delta = 1;
Lat = 1;
iter=0;
while (((delta > 1.0e-14)||(delta < -1.0e-14)) && (iter < 100))
{
delta = Lat - atan(z / (sqrt(x*x + y*y)*(1-(N*e*e/NplusH))));
Lat = Lat-delta;
esLat = e*sin(Lat);
N = a / sqrt(1 - esLat*esLat);
NplusH = sqrt(x*x + y*y)/cos(Lat);
iter += 1;
}
LLA[0] = RAD2DEG*Lat;
LLA[2] = NplusH - N;
if (iter==500) return (0);
else return (1);
}
/**
* Get the current location in Longitude, Latitude Altitude (above WSG-48 ellipsoid)
* @param[in] BaseECEF the ECEF of the home location (in cm)
* @param[in] NED the offset from the home location (in m)
* @param[out] position three element double for position in degrees and meters
* @returns
* @arg 0 success
* @arg -1 for failure
*/
int CoordinateConversions::GetLLA(double BaseECEFcm[3], double NED[3], double position[3])
{
int i;
// stored value is in cm, convert to m
double BaseECEFm[3] = {BaseECEFcm[0], BaseECEFcm[1], BaseECEFcm[2]};
double BaseLLA[3];
double ECEF[3];
double Rne [3][3];
// Get LLA address to compute conversion matrix
ECEF2LLA(BaseECEFm, BaseLLA);
RneFromLLA(BaseLLA, Rne);
/* P = ECEF + Rne' * NED */
for(i = 0; i < 3; i++)
ECEF[i] = BaseECEFm[i] + Rne[0][i]*NED[0] + Rne[1][i]*NED[1] + Rne[2][i]*NED[2];
ECEF2LLA(ECEF,position);
return 0;
}
void CoordinateConversions::LLA2Base(double LLA[3], double BaseECEF[3], float Rne[3][3], float NED[3])
{
double ECEF[3];
float diff[3];
LLA2ECEF(LLA, ECEF);
diff[0] = (float)(ECEF[0] - BaseECEF[0]);
diff[1] = (float)(ECEF[1] - BaseECEF[1]);
diff[2] = (float)(ECEF[2] - BaseECEF[2]);
NED[0] = Rne[0][0] * diff[0] + Rne[0][1] * diff[1] + Rne[0][2] * diff[2];
NED[1] = Rne[1][0] * diff[0] + Rne[1][1] * diff[1] + Rne[1][2] * diff[2];
NED[2] = Rne[2][0] * diff[0] + Rne[2][1] * diff[1] + Rne[2][2] * diff[2];
}
// ****** find roll, pitch, yaw from quaternion ********
void CoordinateConversions::Quaternion2RPY(const float q[4], float rpy[3])
{
float R13, R11, R12, R23, R33;
float q0s = q[0] * q[0];
float q1s = q[1] * q[1];
float q2s = q[2] * q[2];
float q3s = q[3] * q[3];
R13 = 2 * (q[1] * q[3] - q[0] * q[2]);
R11 = q0s + q1s - q2s - q3s;
R12 = 2 * (q[1] * q[2] + q[0] * q[3]);
R23 = 2 * (q[2] * q[3] + q[0] * q[1]);
R33 = q0s - q1s - q2s + q3s;
rpy[1] = RAD2DEG * asinf(-R13); // pitch always between -pi/2 to pi/2
rpy[2] = RAD2DEG * atan2f(R12, R11);
rpy[0] = RAD2DEG * atan2f(R23, R33);
//TODO: consider the cases where |R13| ~= 1, |pitch| ~= pi/2
}
// ****** find quaternion from roll, pitch, yaw ********
void CoordinateConversions::RPY2Quaternion(const float rpy[3], float q[4])
{
float phi, theta, psi;
float cphi, sphi, ctheta, stheta, cpsi, spsi;
phi = DEG2RAD * rpy[0] / 2;
theta = DEG2RAD * rpy[1] / 2;
psi = DEG2RAD * rpy[2] / 2;
cphi = cosf(phi);
sphi = sinf(phi);
ctheta = cosf(theta);
stheta = sinf(theta);
cpsi = cosf(psi);
spsi = sinf(psi);
q[0] = cphi * ctheta * cpsi + sphi * stheta * spsi;
q[1] = sphi * ctheta * cpsi - cphi * stheta * spsi;
q[2] = cphi * stheta * cpsi + sphi * ctheta * spsi;
q[3] = cphi * ctheta * spsi - sphi * stheta * cpsi;
if (q[0] < 0) { // q0 always positive for uniqueness
q[0] = -q[0];
q[1] = -q[1];
q[2] = -q[2];
q[3] = -q[3];
}
}
//** Find Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
void CoordinateConversions::Quaternion2R(const float q[4], float Rbe[3][3])
{
float q0s = q[0] * q[0], q1s = q[1] * q[1], q2s = q[2] * q[2], q3s = q[3] * q[3];
Rbe[0][0] = q0s + q1s - q2s - q3s;
Rbe[0][1] = 2 * (q[1] * q[2] + q[0] * q[3]);
Rbe[0][2] = 2 * (q[1] * q[3] - q[0] * q[2]);
Rbe[1][0] = 2 * (q[1] * q[2] - q[0] * q[3]);
Rbe[1][1] = q0s - q1s + q2s - q3s;
Rbe[1][2] = 2 * (q[2] * q[3] + q[0] * q[1]);
Rbe[2][0] = 2 * (q[1] * q[3] + q[0] * q[2]);
Rbe[2][1] = 2 * (q[2] * q[3] - q[0] * q[1]);
Rbe[2][2] = q0s - q1s - q2s + q3s;
}
}