以下是一个使用C++实现自定义线性系统的卡尔曼滤波拟合的示例代码：

以下是一个使用C++实现自定义线性系统的卡尔曼滤波拟合的示例代码：

#include 
#include 

using namespace std;
using namespace cv;

int main()
{
    // 初始化卡尔曼滤波器
    KalmanFilter kf(4, 2, 0);

    // 状态转移矩阵
    kf.transitionMatrix = (Mat_<float>(4, 4) <<
        1, 0, 1, 0,
        0, 1, 0, 1,
        0, 0, 1, 0,
        0, 0, 0, 1);

    // 测量矩阵
    Mat_<float> measurement(2, 1);
    measurement.setTo(Scalar(0));

    // 初始化测量矩阵
    kf.measurementMatrix = (Mat_<float>(2, 4) <<
        1, 0, 0, 0,
        0, 1, 0, 0);

    // 过程噪声协方差矩阵
    kf.processNoiseCov = (Mat_<float>(4, 4) <<
        0.1, 0, 0, 0,
        0, 0.1, 0, 0,
        0, 0, 0.01, 0,
        0, 0, 0, 0.01);

    // 测量噪声协方差矩阵
    kf.measurementNoiseCov = (Mat_<float>(2, 2) <<
        0.1, 0,
        0, 0.1);

    // 初始化状态估计
    kf.statePre.setTo(Scalar(0));
    kf.statePost.setTo(Scalar(0));

    // 创建窗口
    namedWindow("Kalman Filter", WINDOW_NORMAL);

    // 创建随机数生成器
    RNG rng;

    // 生成一些初始点
    vector<Point> points;
    for (int i = 0; i < 100; ++i)
    {
        int x = rng.uniform(0, 500);
        int y = rng.uniform(0, 500);
        points.push_back(Point(x, y));
    }

    // 进行滤波拟合
    for (int i = 0; i < points.size(); ++i)
    {
        // 测量值
        measurement(0) = points[i].x;
        measurement(1) = points[i].y;

        // 预测
        Mat prediction = kf.predict();

        // 修正
        Mat estimated = kf.correct(measurement);

        // 绘制滤波前原始点
        circle(estimated, points[i], 3, Scalar(0, 0, 255), -1);

        // 绘制预测点
        circle(estimated, Point(prediction.at<float>(0), prediction.at<float>(1)), 3, Scalar(0, 255, 0), -1);

        // 绘制拟合曲线
        line(estimated, Point(0, estimated.at<float>(1)), Point(500, estimated.at<float>(1) + estimated.at<float>(3) * 500), Scalar(255, 0, 0), 2);

        // 显示结果
        imshow("Kalman Filter", estimated);
        waitKey(100);
    }

    return 0;
}