Kalman Filter

A Python implementation of the Kalman Filter using NumPy.

Description

This class provides an implementation of a Kalman Filter for state estimation and prediction.

Attributes

• F (numpy.ndarray): The state-transition model matrix.
• H (numpy.ndarray): The observation model matrix.
• Q (numpy.ndarray): The covariance matrix for the process noise.
• R (numpy.ndarray): The covariance matrix for the observation noise.
• x (numpy.ndarray): The current state estimate.
• P (numpy.ndarray): The current state covariance matrix.

Example Usage

import numpy as np
from kalman_filter import KalmanFilter

# Initialize the system matrices
F = np.array([[1, 1], [0, 1]])
H = np.array([[1, 0]])
Q = np.array([[0.1, 0], [0, 0.1]])
R = np.array([[0.5]])
x0 = np.array([0, 0])
P0 = np.array([[1, 0], [0, 1]])

# Create a Kalman Filter object
kf = KalmanFilter(F, H, Q, R, x0, P0)

# Simulate measurements and update the filter
measurements = [0.5, 1.0, 1.5, 2.0, 2.5]
for z in measurements:
    kf.predict()
    kf.update(np.array([z]))
    print("State estimate:", kf.x)

Methods

__init__(self, F, H, Q, R, x0, P0)

Initializes the KalmanFilter class with initial values.

Arguments

• F (numpy.ndarray): The state-transition model matrix.
• H (numpy.ndarray): The observation model matrix.
• Q (numpy.ndarray): The covariance matrix for the process noise.
• R (numpy.ndarray): The covariance matrix for the observation noise.
• x0 (numpy.ndarray): The initial state estimate.
• P0 (numpy.ndarray): The initial state covariance matrix.

predict(self)

Predicts the next state and updates the state covariance matrix.

Returns

• numpy.ndarray: The predicted state.

update(self, z)

Updates the state estimate and state covariance matrix based on the given observation.

Arguments

• z (numpy.ndarray): The observation vector.