理解不了你的回答,请你重新给我提供一个正确的WGS84海拔转EGM96椭球高的程序,用C语言实现
时间: 2024-03-17 18:43:38 浏览: 128
非常抱歉之前的回答没有能够很好地解决您的问题。下面是一个用C语言实现的WGS84海拔转EGM96椭球高的程序:
```c
#include <stdio.h>
#include <math.h>
double WGS84ToEGM96(double lat, double lon, double alt)
{
double a = 6378137.0; // WGS84椭球体长半轴
double f = 1 / 298.257223563; // WGS84椭球体扁率
double GM = 3986004.418E8; // 地球万有引力常数
double omega = 7292115.0E-11; // 地球自转角速度
double b = a * (1 - f); // WGS84椭球体短半轴
double e2 = 1 - (b / a) * (b / a); // WGS84椭球体第一偏心率的平方
double ep2 = (a / b) * (a / b) - 1; // WGS84椭球体第二偏心率的平方
double N, X, Y, Z, p, theta, sin_theta, cos_theta, W;
double M = GM / pow(a, 3); // 地球质量引力常数
double J2 = 1.0826158E-3; // 地球重力场J2项
double J4 = -1.65597E-6; // 地球重力场J4项
double J6 = 3.35152E-9; // 地球重力场J6项
double C20 = -4.8416514379082E-4; // EGM96中的C20项
double C22 = 2.439383573283E-6; // EGM96中的C22项
double C40 = 1.3969712789723E-6; // EGM96中的C40项
double C42 = 2.947703080281E-7; // EGM96中的C42项
double C60 = -5.4068123919322E-9; // EGM96中的C60项
double C62 = 9.394327107043E-9; // EGM96中的C62项
// 计算地心经纬度坐标系下的坐标
lat = lat * M_PI / 180.0; // 将经纬度转换为弧度
lon = lon * M_PI / 180.0;
N = a / sqrt(1 - e2 * sin(lat) * sin(lat)); // 计算子午圈曲率半径
X = (N + alt) * cos(lat) * cos(lon); // 计算地心直角坐标系下的X坐标
Y = (N + alt) * cos(lat) * sin(lon); // 计算地心直角坐标系下的Y坐标
Z = (N * (1 - e2) + alt) * sin(lat); // 计算地心直角坐标系下的Z坐标
// 计算EGM96中的地球引力势函数
p = sqrt(X * X + Y * Y);
theta = atan((Z * a) / (p * b));
sin_theta = sin(theta);
cos_theta = cos(theta);
W = sqrt(1 - e2 * sin_theta * sin_theta);
double r = sqrt(X * X + Y * Y + Z * Z);
double V = GM / r * (1 - (3.0 / 2.0) * J2 * (a / r) * (a / r) * W * W * (1 - 5 * sin_theta * sin_theta) - (5.0 / 4.0) * J4 * (a / r) * (a / r) * (a / r) * (a / r) * W * W * (1 - 14 * sin_theta * sin_theta + 21 * sin_theta * sin_theta * sin_theta * sin_theta) - (35.0 / 8.0) * J6 * (a / r) * (a / r) * (a / r) * (a / r) * (a / r) * (a / r) * W * W * (1 - 45 * sin_theta * sin_theta + 210 * sin_theta * sin_theta * sin_theta * sin_theta - 231 * sin_theta * sin_theta * sin_theta * sin_theta * sin_theta * sin_theta));
// 计算EGM96中的椭球高
double delta_V = 0;
double delta_W = 0;
double H = 0;
do {
delta_V = -M * (a / r) * cos_theta * (C20 * (a / r) / 2.0 * (3.0 * cos_theta * cos_theta - 1.0) + C22 * (a / r) / 2.0 * sin_theta * sin(2.0 * theta) + C40 * (a / r) * (a / r) / 8.0 * (35.0 * cos_theta * cos_theta * cos_theta * cos_theta - 30.0 * cos_theta * cos_theta + 3.0) + C42 * (a / r) * (a / r) / 4.0 * sin_theta * sin(2.0 * theta) * (7.0 * cos_theta * cos_theta - 1.0) + C60 * (a / r) * (a / r) / 16.0 * (231.0 * cos_theta * cos_theta * cos_theta * cos_theta * cos_theta * cos_theta - 315.0 * cos_theta * cos_theta * cos_theta * cos_theta + 105.0 * cos_theta * cos_theta - 5.0) + C62 * (a / r) * (a / r) / 8.0 * sin_theta * sin(2.0 * theta) * (33.0 * cos_theta * cos_theta - 11.0));
delta_W = -M * (a / r) * sin_theta * (C20 * (a / r) / 2.0 * (5.0 * cos_theta * cos_theta - 1.0) + C22 * (a / r) * sin(2.0 * theta) + C40 * (a / r) * (a / r) / 4.0 * (7.0 * cos_theta * cos_theta * cos_theta - 3.0 * cos_theta) + C42 * (a / r) * (a / r) / 2.0 * cos_theta * sin(2.0 * theta) * (7.0 * cos_theta * cos_theta - 3.0) + C60 * (a / r) * (a / r) / 8.0 * (429.0 * cos_theta * cos_theta * cos_theta * cos_theta * cos_theta - 693.0 * cos_theta * cos_theta * cos_theta + 315.0 * cos_theta * cos_theta - 35.0) + C62 * (a / r) * (a / r) / 4.0 * cos_theta * sin(2.0 * theta) * (33.0 * cos_theta * cos_theta - 26.0));
alt = V - delta_V - H;
H = W - delta_W;
} while (fabs(delta_V) > 0.001 && fabs(delta_W) > 0.001);
return H; // 返回EGM96中的椭球高
}
int main()
{
double lat = 39.9042; // 北京市的纬度
double lon = 116.4074; // 北京市的经度
double alt = 43.54; // 北京市的WGS84海拔高度
double egm96_alt = WGS84ToEGM96(lat, lon, alt); // 计算北京市的EGM96椭球高
printf("The EGM96 ellipsoidal height of Beijing is: %lf meters\n", egm96_alt);
return 0;
}
```
在这个程序中,我们使用了EGM96重力模型中的C20、C22、C40、C42、C60和C62系数,利用牛顿-拉夫逊迭代法计算EGM96中的椭球高,最终返回计算出的EGM96椭球高。
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