假设有三个可以测量航向角的传感器 A 、 B和C，通过联邦卡尔曼滤波器来融合各自的估计结果。在每个时间步骤中，三个传感器分别执行局部卡尔曼滤波器的预测和更新步骤，然后将结果传递给全局融合器。全局融合器通过加权平均来融合三个局部滤波器的结果，得到更准确的状态估计。你可以给出相应的c语言程序么

以下是用 C 语言实现联邦卡尔曼滤波器的示例代码。由于代码比较长，我会分步骤进行解释：

1. 定义状态向量、控制向量和观测向量的数据类型：

typedef struct {
    double x;
    double y;
    double theta;
    double dx;
    double dy;
    double dtheta;
} state_t;

typedef struct {
    double u;
} control_t;

typedef struct {
    double z;
} observation_t;

2. 定义状态转移矩阵 A、控制输入矩阵 B、观测矩阵 H、过程噪声协方差矩阵 Q 和观测噪声协方差矩阵 R：

double A_data[6][6] = {{1, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}};
matrix_t A = {6, 6, &A_data[0][0]};

double B_data[6][1] = {{0}, {0}, {0}, {0.1}, {0.1}, {0.1}};
matrix_t B = {6, 1, &B_data[0][0]};

double H_data[1][6] = {{0, 0, 1, 0, 0, 0}};
matrix_t H = {1, 6, &H_data[0][0]};

double Q_data[6][6] = {{0.001, 0, 0, 0, 0, 0}, {0, 0.001, 0, 0, 0, 0}, {0, 0, 0.001, 0, 0, 0}, {0, 0, 0, 0.001, 0, 0}, {0, 0, 0, 0, 0.001, 0}, {0, 0, 0, 0, 0, 0.001}};
matrix_t Q = {6, 6, &Q_data[0][0]};

double R_data[1][1] = {{1}};
matrix_t R = {1, 1, &R_data[0][0]};

3. 定义局部滤波器的状态向量和协方差矩阵：

typedef struct {
    state_t x;
    matrix_t P;
} local_filter_t;

4. 定义全局融合器的权重：

double w_A = 0.3;
double w_B = 0.3;
double w_C = 0.4;

5. 定义卡尔曼滤波器的辅助函数：

// 计算卡尔曼增益 K
matrix_t kalman_gain(matrix_t P, matrix_t H, matrix_t R) {
    matrix_t PHt = matrix_multiply(P, matrix_transpose(H));
    matrix_t HPHtR = matrix_add(matrix_multiply(matrix_multiply(H, P), matrix_transpose(H)), R);
    matrix_t K = matrix_multiply(PHt, matrix_inverse(HPHtR));
    matrix_free(PHt);
    matrix_free(HPHtR);
    return K;
}

// 局部滤波器的预测步骤
void local_predict(local_filter_t *filter, control_t u) {
    matrix_t x = matrix_from_array(6, 1, &filter->x);
    matrix_t P = filter->P;
    matrix_t u_mat = matrix_from_array(1, 1, &u.u);
    matrix_t Ax = matrix_add(matrix_multiply(A, x), matrix_multiply(B, u_mat));
    matrix_t APAtQ = matrix_add(matrix_multiply(matrix_multiply(matrix_multiply(A, P), matrix_transpose(A)), Q), Q);
    matrix_t P_new = matrix_clone(APAtQ);
    state_t x_new = {matrix_get(Ax, 0, 0), matrix_get(Ax, 1, 0), matrix_get(Ax, 2, 0), matrix_get(Ax, 3, 0), matrix_get(Ax, 4, 0), matrix_get(Ax, 5, 0)};
    matrix_free(x);
    matrix_free(u_mat);
    matrix_free(APAtQ);
    filter->x = x_new;
    filter->P = P_new;
}

// 局部滤波器的更新步骤
void local_update(local_filter_t *filter, observation_t z) {
    matrix_t x = matrix_from_array(6, 1, &filter->x);
    matrix_t P = filter->P;
    matrix_t z_mat = matrix_from_array(1, 1, &z.z);
    matrix_t Hx = matrix_multiply(H, x);
    matrix_t z_Hx = matrix_subtract(z_mat, Hx);
    matrix_t K = kalman_gain(P, H, R);
    matrix_t KH = matrix_multiply(K, H);
    matrix_t I_KH = matrix_subtract(matrix_identity(6), KH);
    matrix_t P_new = matrix_multiply(I_KH, P);
    matrix_t x_new = matrix_add(x, matrix_multiply(K, z_Hx));
    state_t x_new_array = {matrix_get(x_new, 0, 0), matrix_get(x_new, 1, 0), matrix_get(x_new, 2, 0), matrix_get(x_new, 3, 0), matrix_get(x_new, 4, 0), matrix_get(x_new, 5, 0)};
    matrix_free(x);
    matrix_free(P);
    matrix_free(z_mat);
    matrix_free(Hx);
    matrix_free(z_Hx);
    matrix_free(K);
    matrix_free(I_KH);
    filter->x = x_new_array;
    filter->P = P_new;
}

// 全局融合器
state_t global_fusion(local_filter_t *filter_A, local_filter_t *filter_B, local_filter_t *filter_C, double w_A, double w_B, double w_C) {
    matrix_t x_A = matrix_from_array(6, 1, &filter_A->x);
    matrix_t x_B = matrix_from_array(6, 1, &filter_B->x);
    matrix_t x_C = matrix_from_array(6, 1, &filter_C->x);
    matrix_t P_A = filter_A->P;
    matrix_t P_B = filter_B->P;
    matrix_t P_C = filter_C->P;
    matrix_t w_A_mat = matrix_from_array(1, 1, &w_A);
    matrix_t w_B_mat = matrix_from_array(1, 1, &w_B);
    matrix_t w_C_mat = matrix_from_array(1, 1, &w_C);
    matrix_t x = matrix_multiply(w_A_mat, x_A);
    matrix_add_to(x, matrix_multiply(w_B_mat, x_B));
    matrix_add_to(x, matrix_multiply(w_C_mat, x_C));
    matrix_t P = matrix_add(matrix_add(matrix_multiply(matrix_multiply(w_A_mat, P_A), matrix_subtract(matrix_identity(6), matrix_multiply(w_A_mat, matrix_transpose(w_A_mat)))), matrix_add(matrix_multiply(matrix_multiply(w_B_mat, P_B), matrix_subtract(matrix_identity(6), matrix_multiply(w_B_mat, matrix_transpose(w_B_mat)))), matrix_multiply(matrix_multiply(w_C_mat, P_C), matrix_subtract(matrix_identity(6), matrix_multiply(w_C_mat, matrix_transpose(w_C_mat))))));
    state_t x_array = {matrix_get(x, 0, 0), matrix_get(x, 1, 0), matrix_get(x, 2, 0), matrix_get(x, 3, 0), matrix_get(x, 4, 0), matrix_get(x, 5, 0)};
    matrix_free(x_A);
    matrix_free(x_B);
    matrix_free(x_C);
    matrix_free(P_A);
    matrix_free(P_B);
    matrix_free(P_C);
    matrix_free(w_A_mat);
    matrix_free(w_B_mat);
    matrix_free(w_C_mat);
    matrix_free(x);
    return x_array;
}

6. 在主函数中执行卡尔曼滤波器：

int main() {
    // 定义局部滤波器 A、B 和 C
    local_filter_t filter_A = {{0, 0, 0, 0, 0, 0}, matrix_identity(6)};
    local_filter_t filter_B = {{0, 0, 0, 0, 0, 0}, matrix_identity(6)};
    local_filter_t filter_C = {{0, 0, 0, 0, 0, 0}, matrix_identity(6)};

    // 定义观测值 z
    observation_t z_A = {1.2};
    observation_t z_B = {1.3};
    observation_t z_C = {1.1};

    for (int i = 0; i < 10; i++) {
        // 机器人 A 的局部滤波器
        control_t u_A = {0.1};
        local_predict(&filter_A, u_A);
        local_update(&filter_A, z_A);

        // 机器人 B 的局部滤波器
        control_t u_B = {0.2};
        local_predict(&filter_B, u_B);
        local_update(&filter_B, z_B);

        // 机器人 C 的局部滤波器
        control_t u_C = {0.3};
        local_predict(&filter_C, u_C);
        local_update(&filter_C, z_C);

        // 全局融合器
        state_t x = global_fusion(&filter_A, &filter_B, &filter_C, w_A, w_B, w_C);
        
        printf("State estimate: (%lf, %lf, %lf, %lf, %lf, %lf)\n", x.x, x.y, x.theta, x.dx, x.dy, x.dtheta);
    }

    return 0;
}

该示例中假设有三个可以测量航向角的传感器 A、B 和 C，它们分别执行局部卡尔曼滤波器的预测和更新步骤，然后将结果传递给全局融合器。全局融合器通过加权平均来融合三个局部滤波器的结果，得到更准确的状态估计。在每个时间步骤中，传感器 A、B 和 C 分别测量航向角，并将观测值传递给各自的局部滤波器进行处理。最后，主函数中执行全局融合器来融合三个局部滤波器的结果，并输出状态估计值。