We have updated to the python code in our git repo.

It now includes;

• The elusive Kalman filter.
• Math needed when the IMU is upside down
• Automatically calculate loop period.
• A lot more comments.

What is a Kalman filter?  In a nutshell;
A Kalman filter is, it is an algorithm which uses a series of measurements observed over time, in this context an accelerometer and a gyroscope. These measurements will contain noise that will contribute to the error of the measurement. The Kalman filter will then try to estimate the state of the system, based on the current and previous states, that tend to be more precise that than the measurements alone.

A Kalman filter is more precise than a Complementary filter. This can be seen in the image below, which is the output of a complementary filter (CFangleX) and a Kalman filter (kalmanX) from the X axis plotted in a graph.

The red line (KalmanX) is better at filtering out noisep;

The code can be found here in our Git repository here
And  can be pulled down to your Raspberry Pi with;

A summary of the code;

def kalmanFilterY ( accAngle, gyroRate, DT):
        y=0.0
        S=0.0
        global KFangleY
        global Q_angle
        global Q_gyro
        global y_bias
        global XP_00
        global XP_01
        global XP_10
        global XP_11
        global YP_00
        global YP_01
        global YP_10
        global YP_11
        KFangleY = KFangleY + DT * (gyroRate - y_bias)
        YP_00 = YP_00 + ( - DT * (YP_10 + YP_01) + Q_angle * DT )
        YP_01 = YP_01 + ( - DT * YP_11 )
        YP_10 = YP_10 + ( - DT * YP_11 )
        YP_11 = YP_11 + ( + Q_gyro * DT )
        y = accAngle - KFangleY
        S = YP_00 + R_angle
        K_0 = YP_00 / S
        K_1 = YP_10 / S
        KFangleY = KFangleY + ( K_0 * y )
        y_bias = y_bias + ( K_1 * y )
        YP_00 = YP_00 - ( K_0 * YP_00 )
        YP_01 = YP_01 - ( K_0 * YP_01 )
        YP_10 = YP_10 - ( K_1 * YP_00 )
        YP_11 = YP_11 - ( K_1 * YP_01 )
        return KFangleY