The code of the Kalman filter is shown below:
// KasBot V1 - Kalman filter module
float Q_angle = 0.01; //0.001 //0.005
float Q_gyro = 0.0003; //0.003 //0.0003
float R_angle = 0.01; //0.03 //0.008
float x_bias = 0;
float P_00 = 0, P_01 = 0, P_10 = 0, P_11 = 0;
float y, S;
float K_0, K_1;
float kalmanCalculate(float newAngle, float newRate,int looptime)
{
float dt = float(looptime)/1000; // XXXXXXX arevoir
x_angle += dt * (newRate - x_bias);
P_00 += - dt * (P_10 + P_01) + Q_angle * dt;
P_01 += - dt * P_11;
P_10 += - dt * P_11;
P_11 += + Q_gyro * dt;
y = newAngle - x_angle;
S = P_00 + R_angle;
K_0 = P_00 / S;
K_1 = P_10 / S;
x_angle += K_0 * y;
x_bias += K_1 * y;
P_00 -= K_0 * P_00;
P_01 -= K_0 * P_01;
P_10 -= K_1 * P_00;
P_11 -= K_1 * P_01;
return x_angle;
}