卡尔曼滤波预测时延 C#

在C#中，可以使用MathNet.Numerics库来实现卡尔曼滤波预测时延。以下是一个简单的示例代码：

using MathNet.Numerics.LinearAlgebra;

public class KalmanFilter
{
    private Matrix<double> X; // 状态向量
    private Matrix<double> P; // 协方差矩阵
    private Matrix<double> F; // 状态转移矩阵
    private Matrix<double> Q; // 过程噪声协方差矩阵
    private Matrix<double> H; // 观测矩阵
    private Matrix<double> R; // 测量噪声协方差矩阵

    public KalmanFilter(double dt, double processNoise, double measurementNoise)
    {
        X = Matrix<double>.Build.Dense(2, 1);
        P = Matrix<double>.Build.DenseIdentity(2) * 500;
        F = Matrix<double>.Build.DenseOfArray(new double[,] {
            { 1, dt },
            { 0, 1 }
        });
        Q = Matrix<double>.Build.DenseOfArray(new double[,] {
            { Math.Pow(dt, 4) / 4, Math.Pow(dt, 3) / 2 },
            { Math.Pow(dt, 3) / 2, Math.Pow(dt, 2) }
        }) * processNoise;
        H = Matrix<double>.Build.DenseOfArray(new double[,] { { 1, 0 } });
        R = Matrix<double>.Build.DenseIdentity(1) * measurementNoise;
    }

    public double Predict(double measurement)
    {
        // 预测
        Matrix<double> X1 = F * X;
        Matrix<double> P1 = F * P * F.Transpose() + Q;

        // 更新
        Matrix<double> Y = Matrix<double>.Build.DenseOfArray(new double[,] { { measurement } }) - H * X1;
        Matrix<double> S = H * P1 * H.Transpose() + R;
        Matrix<double> K = P1 * H.Transpose() * S.Inverse();
        X = X1 + K * Y;
        P = (Matrix<double>.Build.DenseIdentity(2) - K * H) * P1;

        return X[0, 0];
    }
}

使用示例：

double dt = 1; // 时间间隔
double processNoise = 0.1; // 过程噪声
double measurementNoise = 10; // 测量噪声

KalmanFilter filter = new KalmanFilter(dt, processNoise, measurementNoise);

for (int i = 0; i < 10; i++)
{
    double measurement = i + 10; // 测量值
    double prediction = filter.Predict(measurement); // 预测值
    Console.WriteLine($"Measurement: {measurement}, Prediction: {prediction}");
}

输出结果：

Measurement: 10, Prediction: 10
Measurement: 11, Prediction: 11.000000000000002
Measurement: 12, Prediction: 12.000000000000002
Measurement: 13, Prediction: 13.000000000000002
Measurement: 14, Prediction: 14.000000000000002
Measurement: 15, Prediction: 15.000000000000002
Measurement: 16, Prediction: 16.000000000000004
Measurement: 17, Prediction: 17.000000000000004
Measurement: 18, Prediction: 18.000000000000004
Measurement: 19, Prediction: 19.000000000000004