C语言实现卡尔曼滤波算法：带中文注释的代码示例

由于卡尔曼滤波程序代码较长，此处仅给出部分代码，并附带简要注释，以供参考。

//定义状态变量和观测变量的维度 #define STATE_DIM 4 #define OBS_DIM 2

//定义卡尔曼滤波器结构体 typedef struct { float x[STATE_DIM]; //状态变量 float P[STATE_DIM][STATE_DIM]; //状态协方差矩阵 float F[STATE_DIM][STATE_DIM]; //状态转移矩阵 float H[OBS_DIM][STATE_DIM]; //观测矩阵 float Q[STATE_DIM][STATE_DIM]; //过程噪声协方差矩阵 float R[OBS_DIM][OBS_DIM]; //观测噪声协方差矩阵 } KalmanFilter;

//初始化卡尔曼滤波器 void KalmanFilterInit(KalmanFilter *filter) { int i, j; //初始化状态变量为0 for (i = 0; i < STATE_DIM; i++) { filter->x[i] = 0.0f; } //初始化状态协方差矩阵为单位矩阵 for (i = 0; i < STATE_DIM; i++) { for (j = 0; j < STATE_DIM; j++) { filter->P[i][j] = (i == j) ? 1.0f : 0.0f; } } //初始化状态转移矩阵为单位矩阵 for (i = 0; i < STATE_DIM; i++) { for (j = 0; j < STATE_DIM; j++) { filter->F[i][j] = (i == j) ? 1.0f : 0.0f; } } //初始化观测矩阵为单位矩阵 for (i = 0; i < OBS_DIM; i++) { for (j = 0; j < STATE_DIM; j++) { filter->H[i][j] = (i == j) ? 1.0f : 0.0f; } } //初始化过程噪声协方差矩阵和观测噪声协方差矩阵为单位矩阵 for (i = 0; i < STATE_DIM; i++) { for (j = 0; j < STATE_DIM; j++) { filter->Q[i][j] = (i == j) ? 1.0f : 0.0f; } } for (i = 0; i < OBS_DIM; i++) { for (j = 0; j < OBS_DIM; j++) { filter->R[i][j] = (i == j) ? 1.0f : 0.0f; } } }

//卡尔曼滤波器预测 void KalmanFilterPredict(KalmanFilter *filter) { int i, j, k; float x[STATE_DIM]; float P[STATE_DIM][STATE_DIM];

//计算状态变量的预测值
for (i = 0; i < STATE_DIM; i++) {
    x[i] = 0.0f;
    for (j = 0; j < STATE_DIM; j++) {
        x[i] += filter->F[i][j] * filter->x[j];
    }
}
//计算状态协方差矩阵的预测值
for (i = 0; i < STATE_DIM; i++) {
    for (j = 0; j < STATE_DIM; j++) {
        P[i][j] = 0.0f;
        for (k = 0; k < STATE_DIM; k++) {
            P[i][j] += filter->F[i][k] * filter->P[k][j];
        }
        P[i][j] += filter->Q[i][j];
    }
}
//更新状态变量和状态协方差矩阵
for (i = 0; i < STATE_DIM; i++) {
    filter->x[i] = x[i];
    for (j = 0; j < STATE_DIM; j++) {
        filter->P[i][j] = P[i][j];
    }
}

}

//卡尔曼滤波器更新 void KalmanFilterUpdate(KalmanFilter *filter, float *z) { int i, j, k; float y[OBS_DIM]; float S[OBS_DIM][OBS_DIM]; float K[STATE_DIM][OBS_DIM];

//计算观测残差
for (i = 0; i < OBS_DIM; i++) {
    y[i] = z[i];
    for (j = 0; j < STATE_DIM; j++) {
        y[i] -= filter->H[i][j] * filter->x[j];
    }
}
//计算观测噪声协方差矩阵
for (i = 0; i < OBS_DIM; i++) {
    for (j = 0; j < OBS_DIM; j++) {
        S[i][j] = 0.0f;
        for (k = 0; k < STATE_DIM; k++) {
            S[i][j] += filter->H[i][k] * filter->P[k][j];
        }
        S[i][j] += filter->R[i][j];
    }
}
//计算卡尔曼增益
for (i = 0; i < STATE_DIM; i++) {
    for (j = 0; j < OBS_DIM; j++) {
        K[i][j] = 0.0f;
        for (k = 0; k < OBS_DIM; k++) {
            K[i][j] += filter->P[i][k] * filter->H[k][j];
        }
        K[i][j] /= S[j][j];
    }
}
//更新状态变量和状态协方差矩阵
for (i = 0; i < STATE_DIM; i++) {
    filter->x[i] += K[i][0] * y[0] + K[i][1] * y[1];
    for (j = 0; j < STATE_DIM; j++) {
        filter->P[i][j] -= K[i][0] * S[0][j] * K[j][0] + K[i][1] * S[1][j] * K[j][1];
    }
}

}

//示例代码 int main() { KalmanFilter filter; float z[OBS_DIM];

//初始化卡尔曼滤波器
KalmanFilterInit(&filter);

while (1) {
    //读取传感器数据，存储在z中
    ReadSensorData(z);

    //卡尔曼滤波器预测
    KalmanFilterPredict(&filter);

    //卡尔曼滤波器更新
    KalmanFilterUpdate(&filter, z);

    //输出滤波结果
    printf('Filtered data: %f	%f\n', filter.x[0], filter.x[1]);
}

return 0;