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/*
* geoid.c -- ECEF to WGS84 conversions, including ellipsoid-to-MSL height
*
* This code does not specify, but given the creation date, I assume it
* is using the EGM96 geoid revised 2004.
*
* Geoid separation code by Oleg Gusev, from data by Peter Dana.
* ECEF conversion by Rob Janssen.
*
* This file is Copyright (c) 2010-2018 by the GPSD project
* SPDX-License-Identifier: BSD-2-clause
*/
#include <math.h>
#include "gpsd.h"
static double fix_minuz(double d);
static double bilinear(double x1, double y1, double x2, double y2, double x,
double y, double z11, double z12, double z21,
double z22)
{
double delta;
#define EQ(a, b) (fabs((a) - (b)) < 0.001)
if (EQ(y1, y2) && EQ(x1, x2))
return (z11);
if (EQ(y1, y2) && !EQ(x1, x2))
return (z22 * (x - x1) + z11 * (x2 - x)) / (x2 - x1);
if (EQ(x1, x2) && !EQ(y1, y2))
return (z22 * (y - y1) + z11 * (y2 - y)) / (y2 - y1);
#undef EQ
delta = (y2 - y1) * (x2 - x1);
return (z22 * (y - y1) * (x - x1) + z12 * (y2 - y) * (x - x1) +
z21 * (y - y1) * (x2 - x) + z11 * (y2 - y) * (x2 - x)) / delta;
}
double wgs84_separation(double lat, double lon)
/* return geoid separation (MSL-WGS84) in meters, given a lat/lon in degrees */
{
#define GEOID_ROW 19
#define GEOID_COL 37
/* *INDENT-OFF* */
const int geoid_delta[GEOID_COL*GEOID_ROW]={
/* 90S */ -30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30, -30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,
/* 80S */ -53,-54,-55,-52,-48,-42,-38,-38,-29,-26,-26,-24,-23,-21,-19,-16,-12, -8, -4, -1, 1, 4, 4, 6, 5, 4, 2, -6,-15,-24,-33,-40,-48,-50,-53,-52,-53,
/* 70S */ -61,-60,-61,-55,-49,-44,-38,-31,-25,-16, -6, 1, 4, 5, 4, 2, 6, 12, 16, 16, 17, 21, 20, 26, 26, 22, 16, 10, -1,-16,-29,-36,-46,-55,-54,-59,-61,
/* 60S */ -45,-43,-37,-32,-30,-26,-23,-22,-16,-10, -2, 10, 20, 20, 21, 24, 22, 17, 16, 19, 25, 30, 35, 35, 33, 30, 27, 10, -2,-14,-23,-30,-33,-29,-35,-43,-45,
/* 50S */ -15,-18,-18,-16,-17,-15,-10,-10, -8, -2, 6, 14, 13, 3, 3, 10, 20, 27, 25, 26, 34, 39, 45, 45, 38, 39, 28, 13, -1,-15,-22,-22,-18,-15,-14,-10,-15,
/* 40S */ 21, 6, 1, -7,-12,-12,-12,-10, -7, -1, 8, 23, 15, -2, -6, 6, 21, 24, 18, 26, 31, 33, 39, 41, 30, 24, 13, -2,-20,-32,-33,-27,-14, -2, 5, 20, 21,
/* 30S */ 46, 22, 5, -2, -8,-13,-10, -7, -4, 1, 9, 32, 16, 4, -8, 4, 12, 15, 22, 27, 34, 29, 14, 15, 15, 7, -9,-25,-37,-39,-23,-14, 15, 33, 34, 45, 46,
/* 20S */ 51, 27, 10, 0, -9,-11, -5, -2, -3, -1, 9, 35, 20, -5, -6, -5, 0, 13, 17, 23, 21, 8, -9,-10,-11,-20, -40,-47,-45,-25, 5, 23, 45, 58, 57, 63, 51,
/* 10S */ 36, 22, 11, 6, -1, -8,-10, -8,-11, -9, 1, 32, 4,-18,-13, -9, 4, 14, 12, 13, -2,-14,-25,-32,-38,-60, -75,-63,-26, 0, 35, 52, 68, 76, 64, 52, 36,
/* 00N */ 22, 16, 17, 13, 1,-12,-23,-20,-14, -3, 14, 10,-15,-27,-18, 3, 12, 20, 18, 12,-13, -9,-28,-49,-62,-89,-102,-63, -9, 33, 58, 73, 74, 63, 50, 32, 22,
/* 10N */ 13, 12, 11, 2,-11,-28,-38,-29,-10, 3, 1,-11,-41,-42,-16, 3, 17, 33, 22, 23, 2, -3, -7,-36,-59,-90, -95,-63,-24, 12, 53, 60, 58, 46, 36, 26, 13,
/* 20N */ 5, 10, 7, -7,-23,-39,-47,-34, -9,-10,-20,-45,-48,-32, -9, 17, 25, 31, 31, 26, 15, 6, 1,-29,-44,-61, -67,-59,-36,-11, 21, 39, 49, 39, 22, 10, 5,
/* 30N */ -7, -5, -8,-15,-28,-40,-42,-29,-22,-26,-32,-51,-40,-17, 17, 31, 34, 44, 36, 28, 29, 17, 12,-20,-15,-40, -33,-34,-34,-28, 7, 29, 43, 20, 4, -6, -7,
/* 40N */ -12,-10,-13,-20,-31,-34,-21,-16,-26,-34,-33,-35,-26, 2, 33, 59, 52, 51, 52, 48, 35, 40, 33, -9,-28,-39, -48,-59,-50,-28, 3, 23, 37, 18, -1,-11,-12,
/* 50N */ -8, 8, 8, 1,-11,-19,-16,-18,-22,-35,-40,-26,-12, 24, 45, 63, 62, 59, 47, 48, 42, 28, 12,-10,-19,-33, -43,-42,-43,-29, -2, 17, 23, 22, 6, 2, -8,
/* 60N */ 2, 9, 17, 10, 13, 1,-14,-30,-39,-46,-42,-21, 6, 29, 49, 65, 60, 57, 47, 41, 21, 18, 14, 7, -3,-22, -29,-32,-32,-26,-15, -2, 13, 17, 19, 6, 2,
/* 70N */ 2, 2, 1, -1, -3, -7,-14,-24,-27,-25,-19, 3, 24, 37, 47, 60, 61, 58, 51, 43, 29, 20, 12, 5, -2,-10, -14,-12,-10,-14,-12, -6, -2, 3, 6, 4, 2,
/* 80N */ 3, 1, -2, -3, -3, -3, -1, 3, 1, 5, 9, 11, 19, 27, 31, 34, 33, 34, 33, 34, 28, 23, 17, 13, 9, 4, 4, 1, -2, -2, 0, 2, 3, 2, 1, 1, 3,
/* 90N */ 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13
};
/* *INDENT-ON* */
int ilat, ilon;
int ilat1, ilat2, ilon1, ilon2;
ilat = (int)floor((90. + lat) / 10);
ilon = (int)floor((180. + lon) / 10);
/* sanity checks to prevent segfault on bad data */
if ((GEOID_ROW <= ilat) || (0 > ilat) ||
(GEOID_COL <= ilon) || (0 > ilon))
return 0.0;
ilat1 = ilat;
ilon1 = ilon;
ilat2 = (ilat < GEOID_ROW - 1) ? ilat + 1 : ilat;
ilon2 = (ilon < GEOID_COL - 1) ? ilon + 1 : ilon;
return bilinear(ilon1 * 10.0 - 180.0, ilat1 * 10.0 - 90.0,
ilon2 * 10.0 - 180.0, ilat2 * 10.0 - 90.0,
lon, lat,
(double)geoid_delta[ilon1 + ilat1 * GEOID_COL],
(double)geoid_delta[ilon2 + ilat1 * GEOID_COL],
(double)geoid_delta[ilon1 + ilat2 * GEOID_COL],
(double)geoid_delta[ilon2 + ilat2 * GEOID_COL]
);
}
void ecef_to_wgs84fix(struct gps_fix_t *fix, double *separation,
double x, double y, double z,
double vx, double vy, double vz)
/* fill in WGS84 position/velocity fields from ECEF coordinates
* x, y, z are all in meters
* vx, vy, vz are all in meters/second
*/
{
double lambda, phi, p, theta, n, h, vnorth, veast, heading;
const double a = WGS84A; /* equatorial radius */
const double b = WGS84B; /* polar radius */
const double e2 = (a * a - b * b) / (a * a);
const double e_2 = (a * a - b * b) / (b * b);
/* geodetic location */
lambda = atan2(y, x);
p = sqrt(pow(x, 2) + pow(y, 2));
theta = atan2(z * a, p * b);
phi =
atan2(z + e_2 * b * pow(sin(theta), 3),
p - e2 * a * pow(cos(theta), 3));
n = a / sqrt(1.0 - e2 * pow(sin(phi), 2));
h = p / cos(phi) - n;
fix->latitude = phi * RAD_2_DEG;
fix->longitude = lambda * RAD_2_DEG;
*separation = wgs84_separation(fix->latitude, fix->longitude);
fix->altitude = h - *separation;
/* velocity computation */
vnorth =
-vx * sin(phi) * cos(lambda) - vy * sin(phi) * sin(lambda) +
vz * cos(phi);
veast = -vx * sin(lambda) + vy * cos(lambda);
fix->climb =
vx * cos(phi) * cos(lambda) + vy * cos(phi) * sin(lambda) +
vz * sin(phi);
/* sanity check the climb, 10,000 m/s should be a nice max */
if ( 9999.9 < fix->climb )
fix->climb = NAN;
else if ( -9999.9 > fix->climb )
fix->climb = NAN;
fix->speed = sqrt(pow(vnorth, 2) + pow(veast, 2));
/* sanity check the speed, 10,000 m/s should be a nice max */
if ( 9999.9 < fix->speed )
fix->speed = NAN;
else if ( -9999.9 > fix->speed )
fix->speed = NAN;
heading = atan2(fix_minuz(veast), fix_minuz(vnorth));
if (heading < 0)
heading += 2 * GPS_PI;
fix->track = heading * RAD_2_DEG;
}
/*
* Some systems propagate the sign along with zero. This messes up
* certain trig functions, like atan2():
* atan2(+0, +0) = 0
* atan2(+0, -0) = PI
* Obviously that will break things. Luckily the "==" operator thinks
* that -0 == +0; we will use this to return an unambiguous value.
*
* I hereby decree that zero is not allowed to have a negative sign!
*/
static double fix_minuz(double d)
{
return ((d == 0.0) ? 0.0 : d);
}
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