kalman filter in python

Kalman filter is a popular technique used for state estimation in various fields, such as engineering, physics, and economics. In Python, the filterpy library provides a variety of Kalman filter implementations for different use cases. Here's an example of how to use a Kalman filter to estimate the state of a system, given noisy measurements.

main.py
from filterpy.kalman import KalmanFilter
import numpy as np

# Define the Kalman filter model
kf = KalmanFilter(dim_x=2, dim_z=1)

# Initialize the state and covariance estimates
x = np.array([0, 0])
P = np.diag([1, 1])

kf.x = x
kf.P = P

# Define the state transition matrix and measurement matrix
dt = 0.1
kf.F = np.array([[1, dt],
                 [0, 1]])
kf.H = np.array([[1, 0]])

# Define the process noise and measurement noise covariance matrices
kf.Q = np.diag([0.1, 0.1])
kf.R = np.array([[2]])

# Generate some noisy measurements
measurements = [10, 12, 15, 20, 18, 22, 24, 28, 25, 29]

# Run the Kalman filter on the measurements
filtered_states = []
for z in measurements:
    kf.predict()
    kf.update(np.array([z]))
    filtered_states.append(kf.x)

# Plot the filtered result against the measurements
import matplotlib.pyplot as plt

plt.plot(range(len(measurements)), measurements, 'ro-', label='Measurements')
plt.plot(range(len(filtered_states)), [x[0] for x in filtered_states], 'bx-', label='Filtered')
plt.legend(loc='best')
plt.show()
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In this example, we first create a KalmanFilter object with a state dimension of 2 and measurement dimension of 1. We then initialize the state and covariance estimates, as well as the state transition and measurement matrices. We also specify the process noise and measurement noise covariance matrices.

We then generate a list of noisy measurements, and run the Kalman filter on each measurement. The filtered state estimates are stored in a list, which we then plot against the measurements using Matplotlib.

This is just a simple example, and there are many variations and extensions of the Kalman filter for different use cases. However, this should serve as a good starting point for implementing Kalman filters in Python for state estimation and data analysis.