The Lab

import numpy as np

class KalmanFilter1D:
    """1D Kalman filter for IMU sensor fusion."""

    def __init__(self, process_noise=0.01, measurement_noise=0.1):
        self.Q = process_noise      # Process noise covariance
        self.R = measurement_noise  # Measurement noise covariance
        self.P = 1.0               # Estimation error covariance
        self.x = 0.0               # Initial state estimate

    def update(self, measurement: float) -> float:
        # --- Predict ---
        self.P += self.Q

        # --- Kalman gain ---
        K = self.P / (self.P + self.R)

        # --- Update state ---
        self.x += K * (measurement - self.x)
        self.P *= (1 - K)

        return self.x

# Usage: fusing gyroscope + accelerometer angle
kf = KalmanFilter1D(process_noise=0.001, measurement_noise=0.05)
filtered_angle = kf.update(raw_imu_reading)