提供基于C++的卫星/微惯性组合导航系统示例代码

以下是一个基于C的卫星/微惯性组合导航系统示例代码：

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

#define PI 3.14159265358979323846

typedef struct {
double x; // 位置
double y;
double z;
} Vector;

typedef struct {
double w; // 旋转角
Vector v; // 旋转轴
} Quaternion;

typedef struct {
double lat; // 纬度
double lon; // 经度
double alt; // 高度
Vector vel; // 速度
Quaternion q; // 姿态四元数
} State;

typedef struct {
double a; // 卫星的半长轴
double e; // 卫星的离心率
double i; // 卫星的轨道倾角
double omega; // 卫星的升交点赤经
double w; // 卫星的近地点角距
double M0; // 卫星的平近点角
double n; // 卫星的平均角速度
double t0; // 卫星的时刻
} KeplerOrbit;

double norm(Vector v) {
return sqrt(v.x * v.x + v.y * v.y + v.z * v.z);
}

Vector add(Vector a, Vector b) {
Vector c;
c.x = a.x + b.x;
c.y = a.y + b.y;
c.z = a.z + b.z;
return c;
}

Vector sub(Vector a, Vector b) {
Vector c;
c.x = a.x - b.x;
c.y = a.y - b.y;
c.z = a.z - b.z;
return c;
}

Vector mul(Vector v, double s) {
Vector c;
c.x = v.x * s;
c.y = v.y * s;
c.z = v.z * s;
return c;
}

Quaternion mul(Quaternion q1, Quaternion q2) {
Quaternion q;
q.w = q1.w * q2.w - q1.v.x * q2.v.x - q1.v.y * q2.v.y - q1.v.z * q2.v.z;
q.v.x = q1.w * q2.v.x + q1.v.x * q2.w + q1.v.y * q2.v.z - q1.v.z * q2.v.y;
q.v.y = q1.w * q2.v.y - q1.v.x * q2.v.z + q1.v.y * q2.w + q1.v.z * q2.v.x;
q.v.z = q1.w * q2.v.z + q1.v.x * q2.v.y - q1.v.y * q2.v.x + q1.v.z * q2.w;
return q;
}

Vector rotate(Vector v, Quaternion q) {
Quaternion p;
p.w = 0;
p.v = v;
Quaternion q_inv;
q_inv.w = q.w;
q_inv.v = mul(q.v, -1);
Quaternion r = mul(mul(q, p), q_inv);
return r.v;
}

State propagate(State s, double dt) {
// 计算卫星的轨道位置
double n = s.q.w;
Vector qv = s.q.v;
KeplerOrbit orbit = {6378137+500000, 0.001, 0, 0, 0, 0, 2*PI/(24*60*60), 0};
double M = orbit.M0 + orbit.n * (s.t - orbit.t0);
double E = M;
double E_old;
do {
E_old = E;
E = M + orbit.e * sin(E);
} while (fabs(E - E_old) > 1e-6);
double v = 2 * atan(sqrt((1 + orbit.e) / (1 - orbit.e)) * tan(E / 2));
double r = orbit.a * (1 - orbit.e * cos(E));
Vector p;
p.x = r * cos(v);
p.y = r * sin(v);
p.z = 0;
Vector v_p;
v_p.x = -orbit.n * orbit.a * sin(E) / sqrt(1 - orbit.e * orbit.e);
v_p.y = orbit.n * orbit.a * sqrt(1 - orbit.e * orbit.e) / (1 - orbit.e * cos(E));
v_p.z = 0;
v_p = rotate(v_p, s.q);
// 计算加速度
Vector a;
a.x = -6.67428e-11 * 5.97e24 / (r * r);
a.y = 0;
a.z = 0;
// 计算速度
Vector v_new = add(s.vel, mul(a, dt));
// 计算位置
Vector p_new = add(p, mul(v_new, dt));
// 计算姿态
Quaternion q_new;
Vector w;
w.x = 0;
w.y = 0;
w.z = orbit.n;
q_new.w = cos(norm(w) * dt / 2);
q_new.v = mul(w, sin(norm(w) * dt / 2) / norm(w));
q_new = mul(q_new, s.q);
// 更新状态
State s_new;
s_new.lat = asin(p_new.z / norm(p_new));
s_new.lon = atan2(p_new.y, p_new.x);
s_new.alt = norm(p_new) - 6378137;
s_new.vel = v_new;
s_new.q = q_new;
s_new.t = s.t + dt;
return s_new;
}

int main() {
State s = {0, 0, 0, {0, 0, 0}, {1, {0, 0, 0}}};
double dt = 1;
for (int i = 0; i < 60; i++) {
s = propagate(s, dt);
printf("%f,%f,%f\n", s.lat, s.lon, s.alt);
}
return 0;
}