请基于python写一份基于卡尔曼滤波的数据去噪代码

好的，以下是一份基于Python的卡尔曼滤波数据去噪代码：

import numpy as np

class KalmanFilter:
    def __init__(self, x0, P0, F, Q, H, R):
        self.x = x0
        self.P = P0
        self.F = F
        self.Q = Q
        self.H = H
        self.R = R

    def predict(self):
        self.x = np.dot(self.F, self.x)
        self.P = np.dot(self.F, np.dot(self.P, self.F.T)) + self.Q

    def update(self, z):
        K = np.dot(self.P, np.dot(self.H.T, np.linalg.inv(np.dot(self.H, np.dot(self.P, self.H.T)) + self.R)))
        self.x = self.x + np.dot(K, (z - np.dot(self.H, self.x)))
        self.P = np.dot((np.eye(self.P.shape[0]) - np.dot(K, self.H)), self.P)

def kalman_filter(data):
    x0 = np.array([data[0], 0])
    P0 = np.diag([1, 1])
    F = np.array([[1, 1], [0, 1]])
    Q = np.diag([0.1, 0.1])
    H = np.array([[1, 0]])
    R = np.array([[0.1]])

    kf = KalmanFilter(x0, P0, F, Q, H, R)
    n = len(data)
    result = np.zeros(n)
    for i in range(n):
        kf.predict()
        kf.update(data[i])
        result[i] = kf.x[0]
    return result

使用方法：

import matplotlib.pyplot as plt

# 生成原始数据
t = np.linspace(0, 10, 100)
data = np.sin(t) + np.random.normal(0, 0.1, 100)

# 进行卡尔曼滤波去噪
filtered_data = kalman_filter(data)

# 绘制原始数据与滤波后的数据
plt.plot(t, data, label='Raw Data')
plt.plot(t, filtered_data, label='Filtered Data')
plt.legend()
plt.show()

运行后会生成一张原始数据与滤波后的数据的对比图。