cpr.c

// Part of dump1090, a Mode S message decoder for RTLSDR devices.
//
// cpr.c - Compact Position Reporting decoder and tests
//
// Copyright (c) 2014,2015 Oliver Jowett <oliver@mutability.co.uk>
//
// This file is free software: you may copy, redistribute and/or modify it  
// under the terms of the GNU General Public License as published by the
// Free Software Foundation, either version 2 of the License, or (at your  
// option) any later version.  
//
// This file 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, see <http://www.gnu.org/licenses/>.

// This file incorporates work covered by the following copyright and  
// permission notice:
//
//   Copyright (C) 2012 by Salvatore Sanfilippo <antirez@gmail.com>
//
//   All rights reserved.
//
//   Redistribution and use in source and binary forms, with or without
//   modification, are permitted provided that the following conditions are
//   met:
//
//    *  Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//
//    *  Redistributions in binary form must reproduce the above copyright
//       notice, this list of conditions and the following disclaimer in the
//       documentation and/or other materials provided with the distribution.
//
//   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
//   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
//   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
//   A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
//   HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
//   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
//   LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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//   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
//   OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

#include <math.h>
#include <stdio.h>

//
//=========================================================================
//
// Always positive MOD operation, used for CPR decoding.
//
static int cprModInt(int a, int b) {
    int res = a % b;
    if (res < 0) res += b;
    return res;
}

static double cprModDouble(double a, double b) {
    double res = fmod(a, b);
    if (res < 0) res += b;
    return res;
}

//
//=========================================================================
//
// The NL function uses the precomputed table from 1090-WP-9-14
//
static int cprNLFunction(double lat) {
    if (lat < 0) lat = -lat; // Table is simmetric about the equator
    if (lat < 10.47047130) return 59;
    if (lat < 14.82817437) return 58;
    if (lat < 18.18626357) return 57;
    if (lat < 21.02939493) return 56;
    if (lat < 23.54504487) return 55;
    if (lat < 25.82924707) return 54;
    if (lat < 27.93898710) return 53;
    if (lat < 29.91135686) return 52;
    if (lat < 31.77209708) return 51;
    if (lat < 33.53993436) return 50;
    if (lat < 35.22899598) return 49;
    if (lat < 36.85025108) return 48;
    if (lat < 38.41241892) return 47;
    if (lat < 39.92256684) return 46;
    if (lat < 41.38651832) return 45;
    if (lat < 42.80914012) return 44;
    if (lat < 44.19454951) return 43;
    if (lat < 45.54626723) return 42;
    if (lat < 46.86733252) return 41;
    if (lat < 48.16039128) return 40;
    if (lat < 49.42776439) return 39;
    if (lat < 50.67150166) return 38;
    if (lat < 51.89342469) return 37;
    if (lat < 53.09516153) return 36;
    if (lat < 54.27817472) return 35;
    if (lat < 55.44378444) return 34;
    if (lat < 56.59318756) return 33;
    if (lat < 57.72747354) return 32;
    if (lat < 58.84763776) return 31;
    if (lat < 59.95459277) return 30;
    if (lat < 61.04917774) return 29;
    if (lat < 62.13216659) return 28;
    if (lat < 63.20427479) return 27;
    if (lat < 64.26616523) return 26;
    if (lat < 65.31845310) return 25;
    if (lat < 66.36171008) return 24;
    if (lat < 67.39646774) return 23;
    if (lat < 68.42322022) return 22;
    if (lat < 69.44242631) return 21;
    if (lat < 70.45451075) return 20;
    if (lat < 71.45986473) return 19;
    if (lat < 72.45884545) return 18;
    if (lat < 73.45177442) return 17;
    if (lat < 74.43893416) return 16;
    if (lat < 75.42056257) return 15;
    if (lat < 76.39684391) return 14;
    if (lat < 77.36789461) return 13;
    if (lat < 78.33374083) return 12;
    if (lat < 79.29428225) return 11;
    if (lat < 80.24923213) return 10;
    if (lat < 81.19801349) return 9;
    if (lat < 82.13956981) return 8;
    if (lat < 83.07199445) return 7;
    if (lat < 83.99173563) return 6;
    if (lat < 84.89166191) return 5;
    if (lat < 85.75541621) return 4;
    if (lat < 86.53536998) return 3;
    if (lat < 87.00000000) return 2;
    else return 1;
}
//
//=========================================================================
//
static int cprNFunction(double lat, int fflag) {
    int nl = cprNLFunction(lat) - (fflag ? 1 : 0);
    if (nl < 1) nl = 1;
    return nl;
}
//
//=========================================================================
//
static double cprDlonFunction(double lat, int fflag, int surface) {
    return (surface ? 90.0 : 360.0) / cprNFunction(lat, fflag);
}
//
//=========================================================================
//
// This algorithm comes from:
// http://www.lll.lu/~edward/edward/adsb/DecodingADSBposition.html.
//
// A few remarks:
// 1) 131072 is 2^17 since CPR latitude and longitude are encoded in 17 bits.
//
int decodeCPRairborne(int even_cprlat, int even_cprlon,
                      int odd_cprlat, int odd_cprlon,
                      int fflag,
                      double *out_lat, double *out_lon)
{
    double AirDlat0 = 360.0 / 60.0;
    double AirDlat1 = 360.0 / 59.0;
    double lat0 = even_cprlat;
    double lat1 = odd_cprlat;
    double lon0 = even_cprlon;
    double lon1 = odd_cprlon;

    double rlat, rlon;

    // Compute the Latitude Index "j"
    int    j     = (int) floor(((59*lat0 - 60*lat1) / 131072) + 0.5);
    double rlat0 = AirDlat0 * (cprModInt(j,60) + lat0 / 131072);
    double rlat1 = AirDlat1 * (cprModInt(j,59) + lat1 / 131072);

    if (rlat0 >= 270) rlat0 -= 360;
    if (rlat1 >= 270) rlat1 -= 360;

    // Check to see that the latitude is in range: -90 .. +90
    if (rlat0 < -90 || rlat0 > 90 || rlat1 < -90 || rlat1 > 90)
        return (-2); // bad data

    // Check that both are in the same latitude zone, or abort.
    if (cprNLFunction(rlat0) != cprNLFunction(rlat1))
        return (-1); // positions crossed a latitude zone, try again later

    // Compute ni and the Longitude Index "m"
    if (fflag) { // Use odd packet.
        int ni = cprNFunction(rlat1,1);
        int m = (int) floor((((lon0 * (cprNLFunction(rlat1)-1)) -
                              (lon1 * cprNLFunction(rlat1))) / 131072.0) + 0.5);
        rlon = cprDlonFunction(rlat1, 1, 0) * (cprModInt(m, ni)+lon1/131072);
        rlat = rlat1;
    } else {     // Use even packet.
        int ni = cprNFunction(rlat0,0);
        int m = (int) floor((((lon0 * (cprNLFunction(rlat0)-1)) -
                              (lon1 * cprNLFunction(rlat0))) / 131072) + 0.5);
        rlon = cprDlonFunction(rlat0, 0, 0) * (cprModInt(m, ni)+lon0/131072);
        rlat = rlat0;
    }

    // Renormalize to -180 .. +180
    rlon -= floor( (rlon + 180) / 360 ) * 360;

    *out_lat = rlat;
    *out_lon = rlon;

    return 0;
}

int decodeCPRsurface(double reflat, double reflon,
                     int even_cprlat, int even_cprlon,
                     int odd_cprlat, int odd_cprlon,
                     int fflag,
                     double *out_lat, double *out_lon)
{
    double AirDlat0 = 90.0 / 60.0;
    double AirDlat1 = 90.0 / 59.0;
    double lat0 = even_cprlat;
    double lat1 = odd_cprlat;
    double lon0 = even_cprlon;
    double lon1 = odd_cprlon;
    double rlon, rlat;

    // Compute the Latitude Index "j"
    int    j     = (int) floor(((59*lat0 - 60*lat1) / 131072) + 0.5);
    double rlat0 = AirDlat0 * (cprModInt(j,60) + lat0 / 131072);
    double rlat1 = AirDlat1 * (cprModInt(j,59) + lat1 / 131072);

    // Pick the quadrant that's closest to the reference location -
    // this is not necessarily the same quadrant that contains the
    // reference location.
    //
    // There are also only two valid quadrants: -90..0 and 0..90;
    // no correct message would try to encoding a latitude in the
    // ranges -180..-90 and 90..180.
    //
    // If the computed latitude is more than 45 degrees north of
    // the reference latitude (using the northern hemisphere
    // solution), then the southern hemisphere solution will be
    // closer to the refernce latitude.
    //
    // e.g. reflat=0, rlat=44, use rlat=44
    //      reflat=0, rlat=46, use rlat=46-90 = -44
    //      reflat=40, rlat=84, use rlat=84
    //      reflat=40, rlat=86, use rlat=86-90 = -4
    //      reflat=-40, rlat=4, use rlat=4
    //      reflat=-40, rlat=6, use rlat=6-90 = -84

    // As a special case, -90, 0 and +90 all encode to zero, so
    // there's a little extra work to do there.

    if (rlat0 == 0) {
        if (reflat < -45)
            rlat0 = -90;
        else if (reflat > 45)
            rlat0 = 90;
    } else if ((rlat0 - reflat) > 45) {
        rlat0 -= 90;
    }

    if (rlat1 == 0) {
        if (reflat < -45)
            rlat1 = -90;
        else if (reflat > 45)
            rlat1 = 90;
    } else if ((rlat1 - reflat) > 45) {
        rlat1 -= 90;
    }

    // Check to see that the latitude is in range: -90 .. +90
    if (rlat0 < -90 || rlat0 > 90 || rlat1 < -90 || rlat1 > 90)
        return (-2); // bad data

    // Check that both are in the same latitude zone, or abort.
    if (cprNLFunction(rlat0) != cprNLFunction(rlat1))
        return (-1); // positions crossed a latitude zone, try again later

    // Compute ni and the Longitude Index "m"
    if (fflag) { // Use odd packet.
        int ni = cprNFunction(rlat1,1);
        int m = (int) floor((((lon0 * (cprNLFunction(rlat1)-1)) -
                              (lon1 * cprNLFunction(rlat1))) / 131072.0) + 0.5);
        rlon = cprDlonFunction(rlat1, 1, 1) * (cprModInt(m, ni)+lon1/131072);
        rlat = rlat1;
    } else {     // Use even packet.
        int ni = cprNFunction(rlat0,0);
        int m = (int) floor((((lon0 * (cprNLFunction(rlat0)-1)) -
                              (lon1 * cprNLFunction(rlat0))) / 131072) + 0.5);
        rlon = cprDlonFunction(rlat0, 0, 1) * (cprModInt(m, ni)+lon0/131072);
        rlat = rlat0;
    }

    // Pick the quadrant that's closest to the reference location -
    // this is not necessarily the same quadrant that contains the
    // reference location. Unlike the latitude case, all four
    // quadrants are valid.

    // if reflon is more than 45 degrees away, move some multiple of 90 degrees towards it
    rlon += floor( (reflon - rlon + 45) / 90 ) * 90;  // this might move us outside (-180..+180), we fix this below

    // Renormalize to -180 .. +180
    rlon -= floor( (rlon + 180) / 360 ) * 360;

    *out_lat = rlat;
    *out_lon = rlon;
    return 0;
}

//
//=========================================================================
//
// This algorithm comes from:
// 1090-WP29-07-Draft_CPR101 (which also defines decodeCPR() )
//
// Despite what the earlier comment here said, we should *not* be using trunc().
// See Figure 5-5 / 5-6 and note that floor is applied to (0.5 + fRP - fEP), not
// directly to (fRP - fEP). Eq 38 is correct.
//
int decodeCPRrelative(double reflat, double reflon,
                      int cprlat, int cprlon,
                      int fflag, int surface,
                      double *out_lat, double *out_lon)
{
    double AirDlat;
    double AirDlon;
    double fractional_lat = cprlat / 131072.0;
    double fractional_lon = cprlon / 131072.0;
    double rlon, rlat;
    int j,m;

    AirDlat = (surface ? 90.0 : 360.0) / (fflag ? 59.0 : 60.0);

    // Compute the Latitude Index "j"
    j = (int) (floor(reflat/AirDlat) +
               floor(0.5 + cprModDouble(reflat, AirDlat)/AirDlat - fractional_lat));
    rlat = AirDlat * (j + fractional_lat);
    if (rlat >= 270) rlat -= 360;

    // Check to see that the latitude is in range: -90 .. +90
    if (rlat < -90 || rlat > 90) {
        return (-1);                               // Time to give up - Latitude error
    }

    // Check to see that answer is reasonable - ie no more than 1/2 cell away 
    if (fabs(rlat - reflat) > (AirDlat/2)) {
        return (-1);                               // Time to give up - Latitude error 
    }

    // Compute the Longitude Index "m"
    AirDlon = cprDlonFunction(rlat, fflag, surface);
    m = (int) (floor(reflon/AirDlon) +
               floor(0.5 + cprModDouble(reflon, AirDlon)/AirDlon - fractional_lon));
    rlon = AirDlon * (m + fractional_lon);
    if (rlon > 180) rlon -= 360;

    // Check to see that answer is reasonable - ie no more than 1/2 cell away
    if (fabs(rlon - reflon) > (AirDlon/2))
        return (-1);                               // Time to give up - Longitude error

    *out_lat = rlat;
    *out_lon = rlon;
    return (0);
}