使用ceres库将经纬度坐标GCJ02到WGS84精确转换

    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.youkuaiyun.com/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 = Wg