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/*
* geoid.c -- ECEF to WGS84 conversions, including ellipsoid-to-MSL height
*
* Geoid separation code by Oleg Gusev, from data by Peter Dana.
* ECEF conversion by Rob Janssen.
*/
#include <math.h>
#include "gpsd.h"
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;
if (y1 == y2 && x1 == x2 ) return (z11);
if (y1 == y2 && x1 != x2 ) return (z22*(x-x1)+z11*(x2-x))/(x2-x1);
if (x1 == x2 && y1 != y2 ) return (z22*(y-y1)+z11*(y2-y))/(y2-y1);
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;
}
/* return geoid separtion (MSL - WGS84) in meters, given a lat/lot in degrees */
double wgs84_separation(double lat, double lon)
{
#define GEOID_ROW 19
#define GEOID_COL 37
const char 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};
int ilat, ilon;
int ilat1, ilat2, ilon1, ilon2;
ilat=(int)floor(( 90.+lat)/10);
ilon=(int)floor((180.+lon)/10);
ilat1=ilat;
ilon1=ilon;
ilat2=(ilat < GEOID_ROW-1)? ilat+1:ilat;
ilon2=(ilon < GEOID_COL-1)? ilon+1:ilon;
return bilinear(
ilon1*10.-180.,ilat1*10.-90.,
ilon2*10.-180.,ilat2*10.-90.,
lon, lat,
geoid_delta[ilon1+ilat1*GEOID_COL], geoid_delta[ilon2+ilat1*GEOID_COL],
geoid_delta[ilon1+ilat2*GEOID_COL], geoid_delta[ilon2+ilat2*GEOID_COL]
);
}
void ecef_to_wgs84fix(struct gps_fix_t *fix,
double x, double y, double z,
double vx, double vy, double vz)
/* fill in WGS84 position/velocity fields from ECEF coordinates */
{
double lambda,phi,p,theta,n,h,vnorth,veast,heading;
const double a = 6378137; /* equatorial radius */
const double f = 1 / 298.257223563; /* flattening */
const double b = a * (1 - f); /* 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;
fix->altitude = h - wgs84_separation(fix->latitude, fix->longitude);
/* 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);
fix->speed = RAD_2_DEG * sqrt(pow(vnorth,2) + pow(veast,2));
heading = atan2(veast,vnorth);
if (heading < 0)
heading += 2 * PI;
fix->track = heading * RAD_2_DEG;
}
#ifdef TESTMAIN
#include <stdio.h>
#include <stdlib.h>
int main(int argc, char **argv)
{
double lat, lon;
if (argc != 3) {
fprintf(stderr,"Usage: %s lat lon\n",argv[0]);
return 1;
}
lat=atof(argv[1]);
lon=atof(argv[2]);
if (lat > 90. || lat < -90.)
{
fprintf(stderr," -90 <= lat=%s(%.f) <= 90 ?\n",argv[1],lat);
return 1;
}
if (lon > 180. || lat < -180.)
{
fprintf(stderr," -180 <= lon=%s(%.f) <= 180 ?\n",argv[2],lon);
return 1;
}
printf(" lat= %f lon= %f geoid correction= %f\n",
lat, lon, wgs84_separation(lat, lon));
return 0;
}
#endif /* TESTMAIN */
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