用c语言写卡尔曼滤波GPS与IMU融合导航的代码

以下是一个简单的C语言程序，演示了如何使用卡尔曼滤波对GPS和IMU的测量结果进行融合，实现导航定位：

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

#define N 4   // 状态向量的维度
#define M 2   // 测量向量的维度

void matrix_multiply(float a[N][N], float b[N][N], float c[N][N]) {
    int i, j, k;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            c[i][j] = 0;
            for (k = 0; k < N; k++) {
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

void matrix_add(float a[N][N], float b[N][N], float c[N][N]) {
    int i, j;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            c[i][j] = a[i][j] + b[i][j];
        }
    }
}

void matrix_subtract(float a[N][N], float b[N][N], float c[N][N]) {
    int i, j;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            c[i][j] = a[i][j] - b[i][j];
        }
    }
}

void matrix_transpose(float a[N][N], float b[N][N]) {
    int i, j;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            b[j][i] = a[i][j];
        }
    }
}

void matrix_inverse(float a[N][N], float b[N][N]) {
    int i, j, k;
    float t;
    float c[N][N];
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            c[i][j] = a[i][j];
            b[i][j] = (i == j) ? 1 : 0;
        }
    }
    for (k = 0; k < N; k++) {
        t = c[k][k];
        for (j = 0; j < N; j++) {
            c[k][j] /= t;
            b[k][j] /= t;
        }
        for (i = k + 1; i < N; i++) {
            t = c[i][k];
            for (j = 0; j < N; j++) {
                c[i][j] -= t * c[k][j];
                b[i][j] -= t * b[k][j];
            }
        }
    }
    for (k = N - 1; k > 0; k--) {
        for (i = k - 1; i >= 0; i--) {
            t = c[i][k];
            for (j = 0; j < N; j++) {
                c[i][j] -= t * c[k][j];
                b[i][j] -= t * b[k][j];
            }
        }
    }
}

void kalman_filter(float x[N], float P[N][N], float z[M], float R[M][M], float Q[N][N], float A[N][N], float H[M][N]) {
    float xp[N], Pp[N][N], K[N][M], y[M], S[M][M], S_inv[M][M];
    matrix_multiply(A, x, xp);
    matrix_multiply(A, P, Pp);
    matrix_multiply(Pp, A, Pp);
    matrix_add(Pp, Q, Pp);
    matrix_multiply(H, Pp, S);
    matrix_multiply(S, H, S);
    matrix_add(S, R, S);
    matrix_inverse(S, S_inv);
    matrix_multiply(Pp, H, K);
    matrix_multiply(K, S_inv, K);
    matrix_subtract(z, xp, y);
    matrix_multiply(K, y, x);
    matrix_multiply(K, H, K);
    matrix_subtract(Pp, K, P);
}

int main() {
    // 初始化状态向量和协方差矩阵
    float x[N] = {0, 0, 0, 0};
    float P[N][N] = {{100, 0, 0, 0},
                     {0, 100, 0, 0},
                     {0, 0, 100, 0},
                     {0, 0, 0, 100}};

    // 初始化测量向量和协方差矩阵
    float z[M] = {0, 0};
    float R[M][M] = {{0.1, 0},
                     {0, 0.1}};

    // 初始化过程噪声协方差矩阵和状态转移矩阵
    float Q[N][N] = {{0.01, 0, 0, 0},
                     {0, 0.01, 0, 0},
                     {0, 0, 0.01, 0},
                     {0, 0, 0, 0.01}};
    float dt = 0.01;
    float A[N][N] = {{1, 0, dt, 0},
                     {0, 1, 0, dt},
                     {0, 0, 1, 0},
                     {0, 0, 0, 1}};

    // 初始化测量矩阵
    float H[M][N] = {{1, 0, 0, 0},
                     {0, 1, 0, 0}};

    // 读取GPS和IMU的测量结果，并进行融合
    float gps_x, gps_y;
    float imu_ax, imu_ay;
    while (1) {
        // 读取GPS和IMU的测量结果
        // ...

        // 更新状态向量和协方差矩阵
        z[0] = gps_x;
        z[1] = gps_y;
        float imu_noise = 0.1;
        float Q_imu[N][N] = {{imu_noise, 0, 0, 0},
                             {0, imu_noise, 0, 0},
                             {0, 0, imu_noise, 0},
                             {0, 0, 0, imu_noise}};
        float A_imu[N][N] = {{1, 0, dt, 0},
                             {0, 1, 0, dt},
                             {0, 0, 1 - imu_noise, 0},
                             {0, 0, 0, 1 - imu_noise}};
        kalman_filter(x, P, z, R, Q, A, H);
        kalman_filter(x, P, imu_ax, Q_imu, A_imu, H);
    }

    return 0;
}

以上是一个简单的卡尔曼滤波的实现，具体的实现需要根据实际情况进行调整和优化。