Statistical Insights Guiding Decisions … And Precision In Actions …
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1. Generates a noisy quadratic signal
2. Applies a Kalman filter to estimate the true signal
3. Visualizes the results with 3 lines:
Blue: The noisy signal
Red: The Kalman filter estimate
Green (dashed): The true quadratic signalThe Kalman filter parameters are tuned for this specific case:
1. Uses a 3rd order model (position, velocity, acceleration)
2. The measurement noise R is set to 50
3. Process noise Q is set to 0.1 on the diagonal
4. Initial uncertainty P0 is set high (1000) to give more weight to measurements initially
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import numpy as np
import matplotlib.pyplot as plt# Generate noisy data
np.random.seed(0) # For reproducibility
mu, sigma = 0, 500
x = np.arange(1, 100, 0.1)
z = np.random.normal(mu, sigma, len(x))
y = x ** 2 + z # Noisy quadratic signal
class KalmanFilter:
def __init__(self, F, B, H, Q, R, x0, P0):
self.F = F
self.B = B
self.H = H
self.Q = Q
self.R = R
self.x = x0
self.P = P0
def predict(self, u):
self.x = np.dot(self.F, self.x) + np.dot(self.B, u)
self.P = np.dot(np.dot(self.F, self.P), self.F.T) + self.Q…