geoid.c

/*
 * 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.
 *
 * This file is Copyright (c) 2010 by the GPSD project
 * BSD terms apply: see the file COPYING in the distribution root for details.
 */

#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->speed )
	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);
}