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ardupilot/libraries/AP_Math/location.cpp

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/*
* location.cpp
* Copyright (C) Andrew Tridgell 2011
*
* This file 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 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 module deals with calculations involving struct Location
*/
#include <AP_HAL/AP_HAL.h>
#include <stdlib.h>
#include "AP_Math.h"
#include "location.h"
float longitude_scale(const struct Location &loc)
{
float scale = cosf(loc.lat * 1.0e-7f * DEG_TO_RAD);
return constrain_float(scale, 0.01f, 1.0f);
}
// return distance in meters between two locations
float get_distance(const struct Location &loc1, const struct Location &loc2)
{
float dlat = (float)(loc2.lat - loc1.lat);
float dlong = ((float)(loc2.lng - loc1.lng)) * longitude_scale(loc2);
return norm(dlat, dlong) * LOCATION_SCALING_FACTOR;
}
// return distance in centimeters to between two locations
uint32_t get_distance_cm(const struct Location &loc1, const struct Location &loc2)
{
return get_distance(loc1, loc2) * 100;
}
// return bearing in centi-degrees between two locations
int32_t get_bearing_cd(const struct Location &loc1, const struct Location &loc2)
{
int32_t off_x = loc2.lng - loc1.lng;
int32_t off_y = (loc2.lat - loc1.lat) / longitude_scale(loc2);
int32_t bearing = 9000 + atan2f(-off_y, off_x) * 5729.57795f;
if (bearing < 0) bearing += 36000;
return bearing;
}
// see if location is past a line perpendicular to
// the line between point1 and point2. If point1 is
// our previous waypoint and point2 is our target waypoint
// then this function returns true if we have flown past
// the target waypoint
bool location_passed_point(const struct Location &location,
const struct Location &point1,
const struct Location &point2)
{
return location_path_proportion(location, point1, point2) >= 1.0f;
}
/*
return the proportion we are along the path from point1 to
point2, along a line parallel to point1<->point2.
This will be less than >1 if we have passed point2
*/
float location_path_proportion(const struct Location &location,
const struct Location &point1,
const struct Location &point2)
{
Vector2f vec1 = location_diff(point1, point2);
Vector2f vec2 = location_diff(point1, location);
float dsquared = sq(vec1.x) + sq(vec1.y);
if (dsquared < 0.001f) {
// the two points are very close together
return 1.0f;
}
return (vec1 * vec2) / dsquared;
}
/*
* extrapolate latitude/longitude given bearing and distance
* Note that this function is accurate to about 1mm at a distance of
* 100m. This function has the advantage that it works in relative
* positions, so it keeps the accuracy even when dealing with small
* distances and floating point numbers
*/
void location_update(struct Location &loc, float bearing, float distance)
{
float ofs_north = cosf(radians(bearing))*distance;
float ofs_east = sinf(radians(bearing))*distance;
location_offset(loc, ofs_north, ofs_east);
}
/*
* extrapolate latitude/longitude given distances north and east
*/
void location_offset(struct Location &loc, float ofs_north, float ofs_east)
{
if (!is_zero(ofs_north) || !is_zero(ofs_east)) {
int32_t dlat = ofs_north * LOCATION_SCALING_FACTOR_INV;
int32_t dlng = (ofs_east * LOCATION_SCALING_FACTOR_INV) / longitude_scale(loc);
loc.lat += dlat;
loc.lng += dlng;
}
}
/*
return the distance in meters in North/East plane as a N/E vector
from loc1 to loc2
*/
Vector2f location_diff(const struct Location &loc1, const struct Location &loc2)
{
return Vector2f((loc2.lat - loc1.lat) * LOCATION_SCALING_FACTOR,
(loc2.lng - loc1.lng) * LOCATION_SCALING_FACTOR * longitude_scale(loc1));
}
/*
return the distance in meters in North/East/Down plane as a N/E/D vector
from loc1 to loc2
*/
Vector3f location_3d_diff_NED(const struct Location &loc1, const struct Location &loc2)
{
return Vector3f((loc2.lat - loc1.lat) * LOCATION_SCALING_FACTOR,
(loc2.lng - loc1.lng) * LOCATION_SCALING_FACTOR * longitude_scale(loc1),
(loc1.alt - loc2.alt) * 0.01f);
}
/*
return true if lat and lng match. Ignores altitude and options
*/
bool locations_are_same(const struct Location &loc1, const struct Location &loc2) {
return (loc1.lat == loc2.lat) && (loc1.lng == loc2.lng);
}
/*
* convert invalid waypoint with useful data. return true if location changed
*/
bool location_sanitize(const struct Location &defaultLoc, struct Location &loc)
{
bool has_changed = false;
// convert lat/lng=0 to mean current point
if (loc.lat == 0 && loc.lng == 0) {
loc.lat = defaultLoc.lat;
loc.lng = defaultLoc.lng;
has_changed = true;
}
// convert relative alt=0 to mean current alt
if (loc.alt == 0 && loc.flags.relative_alt) {
loc.flags.relative_alt = false;
loc.alt = defaultLoc.alt;
has_changed = true;
}
// limit lat/lng to appropriate ranges
if (!check_latlng(loc)) {
loc.lat = defaultLoc.lat;
loc.lng = defaultLoc.lng;
has_changed = true;
}
return has_changed;
}
/*
print a int32_t lat/long in decimal degrees
*/
void print_latlon(AP_HAL::BetterStream *s, int32_t lat_or_lon)
{
int32_t dec_portion, frac_portion;
int32_t abs_lat_or_lon = labs(lat_or_lon);
// extract decimal portion (special handling of negative numbers to ensure we round towards zero)
dec_portion = abs_lat_or_lon / 10000000UL;
// extract fractional portion
frac_portion = abs_lat_or_lon - dec_portion*10000000UL;
// print output including the minus sign
if( lat_or_lon < 0 ) {
s->printf("-");
}
s->printf("%ld.%07ld",(long)dec_portion,(long)frac_portion);
}
void wgsllh2ecef(const Vector3d &llh, Vector3d &ecef) {
double d = WGS84_E * sin(llh[0]);
double N = WGS84_A / sqrt(1 - d*d);
ecef[0] = (N + llh[2]) * cos(llh[0]) * cos(llh[1]);
ecef[1] = (N + llh[2]) * cos(llh[0]) * sin(llh[1]);
ecef[2] = ((1 - WGS84_E*WGS84_E)*N + llh[2]) * sin(llh[0]);
}
void wgsecef2llh(const Vector3d &ecef, Vector3d &llh) {
/* Distance from polar axis. */
const double p = sqrt(ecef[0]*ecef[0] + ecef[1]*ecef[1]);
/* Compute longitude first, this can be done exactly. */
if (!is_zero(p))
llh[1] = atan2(ecef[1], ecef[0]);
else
llh[1] = 0;
/* If we are close to the pole then convergence is very slow, treat this is a
* special case. */
if (p < WGS84_A * double(1e-16)) {
llh[0] = copysign(M_PI_2, ecef[2]);
llh[2] = fabs(ecef[2]) - WGS84_B;
return;
}
/* Calculate some other constants as defined in the Fukushima paper. */
const double P = p / WGS84_A;
const double e_c = sqrt(1 - WGS84_E*WGS84_E);
const double Z = fabs(ecef[2]) * e_c / WGS84_A;
/* Initial values for S and C correspond to a zero height solution. */
double S = Z;
double C = e_c * P;
/* Neither S nor C can be negative on the first iteration so
* starting prev = -1 will not cause and early exit. */
double prev_C = -1;
double prev_S = -1;
double A_n, B_n, D_n, F_n;
/* Iterate a maximum of 10 times. This should be way more than enough for all
* sane inputs */
for (int i=0; i<10; i++)
{
/* Calculate some intermmediate variables used in the update step based on
* the current state. */
A_n = sqrt(S*S + C*C);
D_n = Z*A_n*A_n*A_n + WGS84_E*WGS84_E*S*S*S;
F_n = P*A_n*A_n*A_n - WGS84_E*WGS84_E*C*C*C;
B_n = double(1.5) * WGS84_E*S*C*C*(A_n*(P*S - Z*C) - WGS84_E*S*C);
/* Update step. */
S = D_n*F_n - B_n*S;
C = F_n*F_n - B_n*C;
/* The original algorithm as presented in the paper by Fukushima has a
* problem with numerical stability. S and C can grow very large or small
* and over or underflow a double. In the paper this is acknowledged and
* the proposed resolution is to non-dimensionalise the equations for S and
* C. However, this does not completely solve the problem. The author caps
* the solution to only a couple of iterations and in this period over or
* underflow is unlikely but as we require a bit more precision and hence
* more iterations so this is still a concern for us.
*
* As the only thing that is important is the ratio T = S/C, my solution is
* to divide both S and C by either S or C. The scaling is chosen such that
* one of S or C is scaled to unity whilst the other is scaled to a value
* less than one. By dividing by the larger of S or C we ensure that we do
* not divide by zero as only one of S or C should ever be zero.
*
* This incurs an extra division each iteration which the author was
* explicityl trying to avoid and it may be that this solution is just
* reverting back to the method of iterating on T directly, perhaps this
* bears more thought?
*/
if (S > C) {
C = C / S;
S = 1;
} else {
S = S / C;
C = 1;
}
/* Check for convergence and exit early if we have converged. */
if (fabs(S - prev_S) < double(1e-16) && fabs(C - prev_C) < double(1e-16)) {
break;
} else {
prev_S = S;
prev_C = C;
}
}
A_n = sqrt(S*S + C*C);
llh[0] = copysign(1.0, ecef[2]) * atan(S / (e_c*C));
llh[2] = (p*e_c*C + fabs(ecef[2])*S - WGS84_A*e_c*A_n) / sqrt(e_c*e_c*C*C + S*S);
}
// return true when lat and lng are within range
bool check_lat(float lat)
{
return fabsf(lat) <= 90;
}
bool check_lng(float lng)
{
return fabsf(lng) <= 180;
}
bool check_lat(int32_t lat)
{
return labs(lat) <= 90*1e7;
}
bool check_lng(int32_t lng)
{
return labs(lng) <= 180*1e7;
}
bool check_latlng(float lat, float lng)
{
return check_lat(lat) && check_lng(lng);
}
bool check_latlng(int32_t lat, int32_t lng)
{
return check_lat(lat) && check_lng(lng);
}
bool check_latlng(Location loc)
{
return check_lat(loc.lat) && check_lng(loc.lng);
}
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