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I wish to get my phone's current orientation by the following method: Get the initial orientation (azimuth) first via the getRotationMatrix() and getOrientation() . Add the integration of gyroscope reading over time to it to get the current orientation. Phone Orientation: The phone's x-y plane is fixed parallel with the ground plane. i.e., is in a "texting-while-walking" orientation. " getOrientation() " Returnings: Android API allows me to easily get the orientation, i.e., azimuth, pitch, roll, from getOrientation() . Please note that this method always returns its value within the range: [0, -PI] and [o, PI] . My Problem: Since the integration of the gyroscope reading, denoted by dR , may be quite big, so when I do CurrentOrientation += dR , the CurrentOrientation may exceed the [0, -PI] and [o, PI] ranges. What manipulations are needed so that I can ALWAYS get the current orientation within the the [0, -PI] and [o, PI] ranges? I have tried the following in Python, but I highly doubt its correctness. rotation = scipy.integrate.trapz(gyroSeries, timeSeries) # integration if (headingDirection - rotation) < -np.pi: headingDirection += 2 * np.pi elif (headingDirection - rotation) > np.pi: headingDirection -= 2 * np.pi # Complementary Filter headingDirection = ALPHA * (headingDirection - rotation) + (1 - ALPHA) * np.mean(azimuth[np.array(stepNo.tolist()) == i]) if headingDirection < -np.pi: headingDirection += 2 * np.pi elif headingDirection > np.pi: headingDirection -= 2 * np.pi <

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