使用ceres库将经纬度坐标GCJ02到WGS84精确转换
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在之前的一篇博客中，介绍了经纬度坐标系的关系，WGS84是世界大地坐标系，属于原始坐标系，在商用中，需要通过火星加密算法将经纬度做转换，转换之后的坐标，称为国测局坐标，也叫火星坐标系，简称GCJ02。这个过程称为坐标偏移算法。反过来，我们将GCJ02坐标系转为WGS84就是纠偏算法，严格来说，他们不是一对正向与反向的可逆操作，但是有理论公式可以推导。
ceres库是一个c++开源库，用来解决非线性优化问题，可以解决边界约束鲁棒非线性最小二乘法优化问题（Ceres Solver 1 is an open source C++ library for modeling and solving large, complicated optimization problems. It can be used to solve Non-linear Least Squares problems with bounds constraints and general unconstrained optimization problems），通过这个库，我们几乎可以将GCJ02精确转换为WGS84坐标。下面来看示例。
代码是从github上拿过来的。
c++头文件：
/***************************************************************************
*
* This class WGStoGCJ implements geodetic coordinate transform between geodetic
* coordinate in WGS84 coordinate system and geodetic coordinate in GCJ-02
* coordinate system.
*
* details: https://blog.csdn.net/gudufuyun/article/details/106738942
*
* Copyright (c) 2020. All rights reserved.
*
* kikkimo
* School of Remote Sensing and Information Engineering,
* WuHan University,
* Wuhan, Hubei, P.R. China. 430079
* fywhu@outlook.com
*
***************************************************************************
* *
* This program 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 2 of the License, or *
* (at your option) any later version. *
* *
***************************************************************************/
#pragma once
#include <utility>
#ifdef _WGSTOGCJ_API
#if (defined _WIN32 || defined WINCE || defined __CYGWIN__)
#define WGSTOGCJ_API_EXPORTS __declspec(dllexport)
#elif defined __GNUC__ && __GNUC__ >= 4
#define WGSTOGCJ_API_EXPORTS __attribute__((visibility("default")))
#endif
#endif
#ifndef WGSTOGCJ_API_EXPORTS
#define WGSTOGCJ_API_EXPORTS
#endif
/**
* \\brief Covert geodetic coordinate in WGS84 coordinate system to geodetic coordinate
* in GCJ-02 coordinate system
*
* \\param [in] wgs84lon: longitude in WGS84 coordinate system [unit:degree]
* \\param [in] wgs84lat: latitude in WGS84 coordinate system [unit:degree]
* \\return Returns geodetic coordinate in GCJ-02 coordinate system
* \\time 15:47:38 2020/06/12
*/
WGSTOGCJ_API_EXPORTS std::pair<double, double>
Wgs2Gcj(const double& wgs84lon, const double& wgs84lat);
/**
* \\brief Covert geodetic coordinate in GCJ-02 coordinate system to geodetic coordinate
* in WGS84 coordinate system
*
* \\param [in] gcj02lon: longitude in GCJ-02 coordinate system [unit:degree]
* \\param [in] gcj02lat: latitude in GCJ-02 coordinate system [unit:degree]
* \\return Returns geodetic coordinate in WGS84 coordinate system
* \\remark simple linear iteration
* \\detail
* \\time 15:51:13 2020/06/12
*/
std::pair<double, double> __declspec(dllexport)
Gcj2Wgs_SimpleIteration(const double& gcj02lon, const double& gcj02lat);
/**
* \\brief Covert geodetic coordinate in GCJ-02 coordinate system to geodetic coordinate
* in WGS84 coordinate system
*
* \\param [in] gcj02lon: longitude in GCJ-02 coordinate system [unit:degree]
* \\param [in] gcj02lat: latitude in GCJ-02 coordinate system [unit:degree]
* \\return Returns geodetic coordinate in WGS84 coordinate system
* \\remark the encryption formula is known and use an auto-differentiable cost function
* \\time 15:51:13 2020/06/12
*/
WGSTOGCJ_API_EXPORTS std::pair<double, double>
Gcj2Wgs_AutoDiff(const double& gcj02lon, const double& gcj02lat);
/**
* \\brief Covert geodetic coordinate in GCJ-02 coordinate system to geodetic coordinate
* in WGS84 coordinate system
*
* \\param [in] gcj02lon: longitude in GCJ-02 coordinate system [unit:degree]
* \\param [in] gcj02lat: latitude in GCJ-02 coordinate system [unit:degree]
* \\return Returns geodetic coordinate in WGS84 coordinate system
* \\remark the encryption formula is unknown but we can covert point in WGS84 to point
* in GCJ-02 with an API,then use the numerical derivation method to solve the
* problem
* \\detail Assuming the encryption formula is
*
* gcj02lon = Wgs2Gcj(wgs84lon, wgs84lat)
* gcj02lat = Wgs2Gcj(wgs84lon, wgs84lat)
*
* In the rectification process, (wgs84lon, wgs84lat) are unknown items. Obviously,
* this is a system of nonlinear equations.
*
* The linear formed error functions of forward intersection come from
* consideration of a Taylor series expansion.
* V = AX - b
* here:
* V: The residuals of the observed values
* A: The jacobian matrix
* X: The modification of the unknown items
* b: The constant terms of the error functions
*
* Then the error functions written in vector form are:
* | V_lon | = | dlongcj_dlonwgs dlongcj_dlatwgs | | d_lonwgs | - | l_lon |
* | V_lat | = | 0 dlatgcj_dlatwgs | | d_latwgs | - | l_lat |
* here:
* l_lon = longcj - longcj' // the modification of longcj
* l_lat = latgcj - latgcj' // the modification of latgcj
* longcj : the observed longitude in GCJ-02
* latgcj : the observed latitude in GCJ-02
* longcj' = Wgs2Gcj(wgs84lon',wgs84lat') // estimated longitude in GCJ-02
* latgcj' = Wgs2Gcj(wgs84lon',wgs84lat') // estimated latitude in GCJ-02
* wgs84lon' : estimated longitude in WGS84
* wgs84lat' : estimated latitude in WGS84
* d_lonwgs : unknown items
* d_latwgs : unknown items
* wgs84lon = wgs84lon' + d_lonwgs // update
* wgs84lat = wgs84lat' + d_latwgs
*
* let V = [V_lon V_lat]T = 0, then
* d_latwgs = (l_lon * dlatgcj_dlonwgs - l_lat * dlongcj_dlonwgs) /
* (dlongcj_dlatwgs * dlatgcj_dlonwgs - dlatgcj_dlatwgs * dlongcj_dlonwgs)
* d_lonwgs = (l_lon - dlongcj_dlatwgs * d_latwgs) / dlongcj_dlonwgs
*
* This iterative procedure is repeated until X= [d_lonwgs d_latwgs]T are
* sufficiently small.
* \\time 17:42:01 2020/06/12
*/
WGSTOGCJ_API_EXPORTS std::pair<double, double>
Gcj2Wgs_NumbericDiff(const double& gcj02lon, const double& gcj02lat);
/**
* \\brief Covert geodetic coordinate in GCJ-02 coordinate system to geodetic coordinate
* in WGS84 coordinate system
*
* \\param [in] gcj02lon: longitude in GCJ-02 coordinate system [unit:degree]
* \\param [in] gcj02lat: latitude in GCJ-02 coordinate system [unit:degree]
* \\return Returns geodetic coordinate in WGS84 coordinate system
* \\remark The encryption formula is known,and use the analytical derivation method to
* solve the problem with high precision.
* \\detail Assuming the encryption formula is
*
* gcj02lon = Wgs2Gcj(wgs84lon, wgs84lat)
* gcj02lat = Wgs2Gcj(wgs84lon, wgs84lat)
*
* In the rectification process, (wgs84lon, wgs84lat) are unknown items. Obviously,
* this is a system of nonlinear equations.
*
* The linear formed error functions of forward intersection come from
* consideration of a Taylor series expansion.
* V = AX - b
* here:
* V: The residuals of the observed values
* A: The jacobian matrix
* X: The modification of the unknown items
* b: The constant terms of the error functions
*
* Then the error functions written in vector form are:
* | V_lon | = | dlongcj_dlonwgs dlongcj_dlatwgs | | d_lonwgs | - | l_lon |
* | V_lat | = | dlatgcj_dlonwgs dlatgcj_dlatwgs | | d_latwgs | - | l_lat |
* here:
* l_lon = longcj - longcj' // the modification of longcj
* l_lat = latgcj - latgcj' // the modification of latgcj
* longcj : the observed longitude in GCJ-02
* latgcj : the observed latitude in GCJ-02
* longcj' = Wgs2Gcj(wgs84lon',wgs84lat') // estimated longitude in GCJ-02
* latgcj' = Wgs2Gcj(wgs84lon',wgs84lat') // estimated latitude in GCJ-02
* wgs84lon' : estimated longitude in WGS84
* wgs84lat' : estimated latitude in WGS84
* d_lonwgs : unknown items
* d_latwgs : unknown items
* wgs84lon = wgs84lon' + d_lonwgs // update
* wgs84lat = wgs84lat' + d_latwgs
*
* let V = [V_lon V_lat]T = 0, then
* d_latwgs = (l_lon * dlatgcj_dlonwgs - l_lat * dlongcj_dlonwgs) /
* (dlongcj_dlatwgs * dlatgcj_dlonwgs - dlatgcj_dlatwgs * dlongcj_dlonwgs)
* d_lonwgs = (l_lon - dlongcj_dlatwgs * d_latwgs) / dlongcj_dlonwgs
*
* This iterative procedure is repeated until X= [d_lonwgs d_latwgs]T are
* sufficiently small.
* \\time 01:54:46 2020/06/13
*/
WGSTOGCJ_API_EXPORTS std::pair<double, double>
Gcj2Wgs_AnalyticDiff(const double& gcj02lon, const double& gcj02lat);
c++源文件：
#include <iostream>
#include <cmath>
#include "WGS84GCJ02.h"
#include <ceres/ceres.h>
constexpr double kKRASOVSKY_A = 6378245.0; // equatorial radius [unit: meter]
constexpr double kKRASOVSKY_B = 6356863.0187730473; // polar radius
constexpr double kKRASOVSKY_ECCSQ = 6.6934216229659332e-3; // first eccentricity squared
constexpr double kKRASOVSKY_ECC2SQ = 6.7385254146834811e-3; // second eccentricity squared
constexpr double PI = 3.14159265358979323846; //π
constexpr double kDEG2RAD = PI / 180.0;
constexpr double kRAD2DEG = 180.0 / PI;
constexpr inline double Deg2Rad(const double deg) {
return deg * kDEG2RAD;
}
constexpr inline double Rad2Deg(const double rad) {
return rad * kRAD2DEG;
}
std::pair<double, double> GetGeodeticOffset(const double& wgs84lon, const double& wgs84lat)
{
//get geodetic offset relative to 'center china'
double lon0 = wgs84lon - 105.0;
double lat0 = wgs84lat - 35.0;
//generate an pair offset roughly in meters
double lon1 = 300.0 + lon0 + 2.0 * lat0 + 0.1 * lon0 * lon0 + 0.1 * lon0 * lat0 + 0.1 * sqrt(fabs(lon0));
lon1 = lon1 + (20.0 * sin(6.0 * lon0 * PI) + 20.0 * sin(2.0 * lon0 * PI)) * 2.0 / 3.0;
lon1 = lon1 + (20.0 * sin(lon0 * PI) + 40.0 * sin(lon0 / 3.0 * PI)) * 2.0 / 3.0;
lon1 = lon1 + (150.0 * sin(lon0 / 12.0 * PI) + 300.0 * sin(lon0 * PI / 30.0)) * 2.0 / 3.0;
double lat1 = -100.0 + 2.0 * lon0 + 3.0 * lat0 + 0.2 * lat0 * lat0 + 0.1 * lon0 * lat0 + 0.2 * sqrt(fabs(lon0));
lat1 = lat1 + (20.0 * sin(6.0 * lon0 * PI) + 20.0 * sin(2.0 * lon0 * PI)) * 2.0 / 3.0;
lat1 = lat1 + (20.0 * sin(lat0 * PI) + 40.0 * sin(lat0 / 3.0 * PI)) * 2.0 / 3.0;
lat1 = lat1 + (160.0 * sin(lat0 / 12.0 * PI) + 320.0 * sin(lat0 * PI / 30.0)) * 2.0 / 3.0;
//latitude in radian
double B = Deg2Rad(wgs84lat);
double sinB = sin(B), cosB = cos(B);
double W = sqrt(1 - kKRASOVSKY_ECCSQ * sinB * sinB);
double N = kKRASOVSKY_A / W;
//geodetic offset used by GCJ-02
double lon2 = Rad2Deg(lon1 / (N * cosB));
double lat2 = Rad2Deg(lat1 * W * W / (N * (1 - kKRASOVSKY_ECCSQ)));
return { lon2, lat2 };
}
std::pair<double, double> Wgs2Gcj(const double& wgs84lon, const double& wgs84lat)
{
std::pair<double, double> dlonlat = GetGeodeticOffset(wgs84lon, wgs84lat);
double gcj02lon = wgs84lon + dlonlat.first;
double gcj02lat = wgs84lat + dlonlat.second;
return { gcj02lon, gcj02lat };
}
std::pair<double, double> Gcj2Wgs_SimpleIteration(const double& gcj02lon,
const double& gcj02lat)
{
std::pair<double, double> lonlat = Wgs2Gcj(gcj02lon, gcj02lat);
double lon0 = lonlat.first;
double lat0 = lonlat.second;
int iterCounts = 0;
while (++iterCounts < 1000)
{
std::pair<double, double> lonlat1 = Wgs2Gcj(lon0, lat0);
double lon1 = lonlat1.first;
double lat1 = lonlat1.second;
double dlon = lon1 - gcj02lon;
double dlat = lat1 - gcj02lat;
lon1 = lon0 - dlon;
lat1 = lat0 - dlat;
//1.0e-9 degree corresponding to 0.1mm
if (fabs(dlon) < 1.0e-9 && fabs(dlat) < 1.0e-9)
break;
lon0 = lon1;
lat0 = lat1;
}
return { lon0 , lat0 };
}
class AutoDiffCostFunc
{
public:
AutoDiffCostFunc(const double lon, const double lat) :
mlonGcj(lon), mlatGcj(lat) {}
template <typename T>
bool operator() (const T* const lonWgs, const T* const latWgs, T* residuals) const
{
//get geodetic offset relative to 'center china'
T lon0 = lonWgs[0] - T(105.0);
T lat0 = latWgs[0] - T(35.0);
//generate an pair offset roughly in meters
T lon1 = T(300.0) + lon0 + T(2.0) * lat0 + T(0.1) * lon0 * lon0 + T(0.1) * lon0 * lat0
+ T(0.1) * ceres::sqrt(ceres::abs(lon0));
lon1 = lon1 + (T(20.0) * ceres::sin(T(6.0) * lon0 * T(PI)) + T(20.0) * ceres::sin(T(2.0) * lon0 * T(PI))) * T(2.0) / T(3.0);
lon1 = lon1 + (T(20.0) * ceres::sin(lon0 * T(PI)) + T(40.0) * ceres::sin(lon0 / T(3.0) * T(PI))) * T(2.0) / T(3.0);
lon1 = lon1 + (T(150.0) * ceres::sin(lon0 / T(12.0) * T(PI)) + T(300.0) * ceres::sin(lon0 * T(PI) / T(30.0))) * T(2.0) / T(3.0);
T lat1 = T(-100.0) + T(2.0) * lon0 + T(3.0) * lat0 + T(0.2) * lat0 * lat0 + T(0.1) * lon0 * lat0
+ T(0.2) * ceres::sqrt(ceres::abs(lon0));
lat1 = lat1 + (T(20.0) * ceres::sin(T(6.0) * lon0 * T(PI)) + T(20.0) * ceres::sin(T(2.0) * lon0 * T(PI))) * T(2.0) / T(3.0);
lat1 = lat1 + (T(20.0) * ceres::sin(lat0 * T(PI)) + T(40.0) * ceres::sin(lat0 / T(3.0) * T(PI))) * T(2.0) / T(3.0);
lat1 = lat1 + (T(160.0) * ceres::sin(lat0 / T(12.0) * T(PI)) + T(320.0) * ceres::sin(lat0 * T(PI) / T(30.0))) * T(2.0) / T(3.0);
//latitude in radian
T B = latWgs[0] * T(kDEG2RAD);
T sinB = ceres::sin(B), cosB = ceres::cos(B);
T W = ceres::sqrt(T(1) - T(kKRASOVSKY_ECCSQ) * sinB * sinB);
T N = T(kKRASOVSKY_A) / W;
//geodetic offset used by GCJ-02
T lon2 = T(kRAD2DEG) * lon1 / (N * cosB);
T lat2 = T(kRAD2DEG) * (lat1 * W * W / (N * (1 - kKRASOVSKY_ECCSQ)));
//residuals
residuals[0] = lonWgs[0] + lon2 - mlonGcj;
residuals[1] = latWgs[0] + lat2 - mlatGcj;
return true;
}
private:
double mlonGcj;
double mlatGcj;
};
std::pair<double, double> Gcj2Wgs_AutoDiff(const double& gcj02lon,
const double& gcj02lat)
{
ceres::Problem * poProblem = new ceres::Problem;
AutoDiffCostFunc* pCostFunc = new AutoDiffCostFunc(gcj02lon, gcj02lat);
double wgslon = gcj02lon, wgslat = gcj02lat;
poProblem->AddResidualBlock(new ceres::AutoDiffCostFunction<AutoDiffCostFunc, 2, 1, 1>(pCostFunc),
nullptr,
&wgslon,
&wgslat);
ceres::Solver::Options options;
options.max_num_iterations = 30;
options.linear_solver_type = ceres::DENSE_QR;
options.minimizer_progress_to_stdout = false;
options.gradient_tolerance = 1e-16;
options.function_tolerance = 1e-12;
options.parameter_tolerance = 1e-14;
ceres::Solver::Summary summary;
ceres::Solve(options, poProblem, &summary);
delete poProblem; //auto free memory of cost function "pCostFunc"
return { wgslon, wgslat };
}
std::pair<double, double> GetPartialDerivative_Lon(const double& wgs84lon, const double& wgs84lat, const double& dlon)
{
double lonBk = wgs84lon + dlon;
double lonFw = wgs84lon - dlon;
std::pair<double, double > gcjlatlonBk = Wgs2Gcj(lonBk, wgs84lat);
double gcjlonBk = gcjlatlonBk.first;
double gcjlatBk = gcjlatlonBk.second;
std::pair<double, double > gcjlatlonFw = Wgs2Gcj(lonFw, wgs84lat);
double gcjlonFw = gcjlatlonFw.first;
double gcjlatFw = gcjlatlonFw.second;
double dlongcj_dlonwgs = (gcjlonBk - gcjlonFw) / (dlon * 2.0);
double dlatgcj_dlonwgs = (gcjlatBk - gcjlatFw) / (dlon * 2.0);
return { dlongcj_dlonwgs , dlatgcj_dlonwgs };
}
std::pair<double, double> GetPartialDerivative_Lat(const double& wgs84lon, const double& wgs84lat, const double& dlat)
{
double latBk = wgs84lat + dlat;
double latFw = wgs84lat - dlat;
std::pair<double, double> gcjlonlatBk = Wgs2Gcj(wgs84lon, latBk);
double gcjlonBk = gcjlonlatBk.first;
double gcjlatBk = gcjlonlatBk.second;
std::pair<double, double> gcjlonlatFw = Wgs2Gcj(wgs84lon, latFw);
double gcjlonFw = gcjlonlatFw.first;
double gcjlatFw = gcjlonlatFw.second;
double dlongcj_dlatwgs = (gcjlonBk - gcjlonFw) / (dlat * 2.0);
double dlatgcj_dlatwgs = (gcjlatBk - gcjlatFw) / (dlat * 2.0);
return { dlongcj_dlatwgs , dlatgcj_dlatwgs };
}
std::pair<double, double> Gcj2Wgs_NumbericDiff(const double& gcj02lon,
const double& gcj02lat)
{
double wgs84lon = gcj02lon, wgs84lat = gcj02lat;
int nIterCount = 0;
double tol = 1e-9;
while (++nIterCount < 1000)
{
std::pair<double, double > data1 = GetPartialDerivative_Lon(wgs84lon, wgs84lat, tol);
double dlongcj_dlonwgs = data1.first;
double dlatgcj_dlonwgs = data1.second;
std::pair<double, double > data2 = GetPartialDerivative_Lat(wgs84lon, wgs84lat, tol);
double dlongcj_dlatwgs = data2.first;
double dlatgcj_dlatwgs = data2.second;
std::pair<double, double > data3 = Wgs2Gcj(wgs84lon, wgs84lat);
double gcj02lonEst = data3.first;
double gcj02latEst = data3.second;
double l_lon = gcj02lon - gcj02lonEst;
double l_lat = gcj02lat - gcj02latEst;
double d_latwgs = (l_lon * dlatgcj_dlonwgs - l_lat * dlongcj_dlonwgs) /
(dlongcj_dlatwgs * dlatgcj_dlonwgs - dlatgcj_dlatwgs * dlongcj_dlonwgs);
double d_lonwgs = (l_lon - dlongcj_dlatwgs * d_latwgs) / dlongcj_dlonwgs;
if (fabs(d_latwgs) < tol && fabs(d_lonwgs) < tol)
break;
wgs84lon = wgs84lon + d_lonwgs;
wgs84lat = wgs84lat + d_latwgs;
}
return { wgs84lon, wgs84lat };
}
std::pair<double, double> Gcj2Wgs_AnalyticDiff(const double& gcj02lon,
const double& gcj02lat)
{
double wgs84lon = gcj02lon, wgs84lat = gcj02lat;
int nIterCount = 0;
while (++nIterCount < 1000)
{
//get geodetic offset relative to 'center china'
double lon0 = wgs84lon - 105.0;
double lat0 = wgs84lat - 35.0;
//generate an pair offset roughly in meters
double lon1 = 300.0 + lon0 + 2.0 * lat0 + 0.1 * lon0 * lon0 + 0.1 * lon0 * lat0 + 0.1 * sqrt(fabs(lon0));
lon1 = lon1 + (20.0 * sin(6.0 * lon0 * PI) + 20.0 * sin(2.0 * lon0 * PI)) * 2.0 / 3.0;
lon1 = lon1 + (20.0 * sin(lon0 * PI) + 40.0 * sin(lon0 / 3.0 * PI)) * 2.0 / 3.0;
lon1 = lon1 + (150.0 * sin(lon0 / 12.0 * PI) + 300.0 * sin(lon0 * PI / 30.0)) * 2.0 / 3.0;
double lat1 = -100.0 + 2.0 * lon0 + 3.0 * lat0 + 0.2 * lat0 * lat0 + 0.1 * lon0 * lat0 + 0.2 * sqrt(fabs(lon0));
lat1 = lat1 + (20.0 * sin(6.0 * lon0 * PI) + 20.0 * sin(2.0 * lon0 * PI)) * 2.0 / 3.0;
lat1 = lat1 + (20.0 * sin(lat0 * PI) + 40.0 * sin(lat0 / 3.0 * PI)) * 2.0 / 3.0;
lat1 = lat1 + (160.0 * sin(lat0 / 12.0 * PI) + 320.0 * sin(lat0 * PI / 30.0)) * 2.0 / 3.0;
double g_lon0 = 0;
if (lon0 > 0)
g_lon0 = 0.05 / sqrt(lon0);
else
if (lon0 < 0)
g_lon0 = -0.05 / sqrt(-lon0);
else
g_lon0 = 0;
double PIlon0 = PI * lon0, PIlat0 = PI * lat0;
double dlon1_dlonwgs = 1 + 0.2 * lon0 + 0.1 * lat0 + g_lon0
+ ((120 * PI * cos(6 * PIlon0) + 40 * PI * cos(2 * PIlon0))
+ (20 * PI * cos(PIlon0) + 40 * PI / 3.0 * cos(PIlon0 / 3.0))
+ (12.5 * PI * cos(PIlon0 / 12.0) + 10 * PI * cos(PIlon0 / 30.0))) * 2.0 / 3.0;
double dlon1_dlatwgs = 2 + 0.1 * lon0;
double dlat1_dlonwgs = 2 + 0.1 * lat0 + 2 * g_lon0
+ (120 * PI * cos(6 * PIlon0) + 40 * PI * cos(2 * PIlon0)) * 2.0 / 3.0;
double dlat1_dlatwgs = 3 + 0.4 * lat0 + 0.1 * lon0
+ ((20 * PI * cos(PIlat0) + 40.0 * PI / 3.0 * cos(PIlat0 / 3.0))
+ (40 * PI / 3.0 * cos(PIlat0 / 12.0) + 32.0 * PI / 3.0 * cos(PIlat0 / 30.0))) * 2.0 / 3.0;
//latitude in radian
double B = Deg2Rad(wgs84lat);
double sinB = sin(B), cosB = cos(B);
double WSQ = 1 - kKRASOVSKY_ECCSQ * sinB * sinB;
double W = sqrt(WSQ);
double N = kKRASOVSKY_A / W;
double dW_dlatwgs = -PI * kKRASOVSKY_ECCSQ * sinB * cosB / (180.0 * W);
double dN_dlatwgs = -kKRASOVSKY_A * dW_dlatwgs / WSQ;
double PIxNxCosB = PI * N * cosB;
double dlongcj_dlonwgs = 1.0 + 180.0 * dlon1_dlonwgs / PIxNxCosB;
double dlongcj_dlatwgs = 180 * dlon1_dlatwgs / PIxNxCosB -
180 * lon1 * PI * (dN_dlatwgs * cosB - PI * N * sinB / 180.0) / (PIxNxCosB * PIxNxCosB);
double PIxNxSubECCSQ = PI * N * (1 - kKRASOVSKY_ECCSQ);
double dlatgcj_dlonwgs = 180 * WSQ * dlat1_dlonwgs / PIxNxSubECCSQ;
double dlatgcj_dlatwgs = 1.0 + 180 * (N * (dlat1_dlatwgs * WSQ + 2.0 * lat1 * W * dW_dlatwgs) - lat1 * WSQ * dN_dlatwgs) /
(N * PIxNxSubECCSQ);
std::pair<double, double> gcj02lonlatEst = Wgs2Gcj(wgs84lon, wgs84lat);
double gcj02lonEst = gcj02lonlatEst.first;
double gcj02latEst = gcj02lonlatEst.second;
double l_lon = gcj02lon - gcj02lonEst;
double l_lat = gcj02lat - gcj02latEst;
double d_latwgs = (l_lon * dlatgcj_dlonwgs - l_lat * dlongcj_dlonwgs) /
(dlongcj_dlatwgs * dlatgcj_dlonwgs - dlatgcj_dlatwgs * dlongcj_dlonwgs);
double d_lonwgs = (l_lon - dlongcj_dlatwgs * d_latwgs) / dlongcj_dlonwgs;
if (fabs(d_latwgs) < 1.0e-9 && fabs(d_lonwgs) < 1.0e-9)
break;
wgs84lon = wgs84lon + d_lonwgs;
wgs84lat = wgs84lat + d_latwgs;
}
return { wgs84lon, wgs84lat };
}
void TestCase1()
{
double lonWgs = 116.39123343289631;
double latWgs = 39.9072885060602;
std::cout.precision(16);
std::cout << "WGS84 Point: (" << latWgs << ", " << lonWgs << ")\\n";
std::pair<double, double> lonlatGcj = Wgs2Gcj(lonWgs, latWgs);
double lonGcj = lonlatGcj.first;
double latGcj = lonlatGcj.second;
std::cout << "GCJ-02 Point [Wgs2Gcj]: (" << latGcj << ", " << lonGcj << ")\\n";
//simple linear iteration
std::pair<double, double> lonlatWgsNS = Gcj2Wgs_SimpleIteration(lonGcj, latGcj);
double lonWgsNS = lonlatWgsNS.first;
double latWgsNS = lonlatWgsNS.second;
std::cout << "WGS84 Point [simple linear iteration]: (" << latWgsNS << ", " << lonWgsNS << ")\\n";
//numerically differentiated cost function
std::pair<double, double> lonlatWgsND = Gcj2Wgs_NumbericDiff(lonGcj, latGcj);
double lonWgsND = lonlatWgsND.first;
double latWgsND = lonlatWgsND.second;
std::cout << "WGS84 Point [numerically derivation]: (" << latWgsND << ", " << lonWgsND << ")\\n";
//analytical differentiated cost function
std::pair<double, double> lonlatWgsNAn = Gcj2Wgs_AnalyticDiff(lonGcj, latGcj);
double lonWgsNAn = lonlatWgsNAn.first;
double latWgsNAn = lonlatWgsNAn.second;
std::cout << "WGS84 Point [analytical derivation]: (" << latWgsNAn << ", " << lonWgsNAn << ")\\n";
//auto differentiable, use ceres
std::pair<double, double> lonlatWgsNA = Gcj2Wgs_AutoDiff(lonGcj, latGcj);
double lonWgsNA = lonlatWgsNA.first;
double latWgsNA = lonlatWgsNA.second;
std::cout << "WGS84 Point [auto differentiable]: (" << latWgsNA << ", " << lonWgsNA << ")\\n";
}
int main() {
TestCase1();
return 0;
}
运行结果： 
从打印结果来看，普通的转换，虽然精度上可以接近原始gps坐标，但是都无法完全还原，只有ceres代码执行的结果才能达到完全还原的效果。
有关ceres库的编译以及与c++项目结合，可以移步这里。
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