# Remove Bias from Angular Velocity Measurement

This example shows how to remove gyroscope bias from an IMU using `imufilter`.

Use `kinematicTrajectory` to create a trajectory with two parts. The first part has a constant angular velocity about the y- and z-axes. The second part has a varying angular velocity in all three axes.

```duration = 60*8; fs = 20; numSamples = duration * fs; rng('default') % Seed the RNG to reproduce noisy sensor measurements. initialAngVel = [0,0.5,0.25]; finalAngVel = [-0.2,0.6,0.5]; constantAngVel = repmat(initialAngVel,floor(numSamples/2),1); varyingAngVel = [linspace(initialAngVel(1), finalAngVel(1), ceil(numSamples/2)).', ... linspace(initialAngVel(2), finalAngVel(2), ceil(numSamples/2)).', ... linspace(initialAngVel(3), finalAngVel(3), ceil(numSamples/2)).']; angVelBody = [constantAngVel; varyingAngVel]; accBody = zeros(numSamples,3); traj = kinematicTrajectory('SampleRate',fs); [~,qNED,~,accNED,angVelNED] = traj(accBody,angVelBody);```

Create an `imuSensor` System object™, `IMU`, with a nonideal gyroscope. Call `IMU` with the ground-truth acceleration, angular velocity, and orientation.

```IMU = imuSensor('accel-gyro', ... 'Gyroscope',gyroparams('RandomWalk',0.003,'ConstantBias',0.3), ... 'SampleRate',fs); [accelReadings, gyroReadingsBody] = IMU(accNED,angVelNED,qNED);```

Create an `imufilter` System object, `fuse`. Call `fuse` with the modeled accelerometer readings and gyroscope readings.

```fuse = imufilter('SampleRate',fs, 'GyroscopeDriftNoise', 1e-6); [~,angVelBodyRecovered] = fuse(accelReadings,gyroReadingsBody);```

Plot the ground-truth angular velocity, the gyroscope readings, and the recovered angular velocity for each axis.

The angular velocity returned from the `imufilter` compensates for the effect of the gyroscope bias over time and converges to the true angular velocity.

```time = (0:numSamples-1)'/fs; figure(1) plot(time,angVelBody(:,1), ... time,gyroReadingsBody(:,1), ... time,angVelBodyRecovered(:,1)) title('X-axis') legend('True Angular Velocity', ... 'Gyroscope Readings', ... 'Recovered Angular Velocity') ylabel('Angular Velocity (rad/s)')```

```figure(2) plot(time,angVelBody(:,2), ... time,gyroReadingsBody(:,2), ... time,angVelBodyRecovered(:,2)) title('Y-axis') ylabel('Angular Velocity (rad/s)')```

```figure(3) plot(time,angVelBody(:,3), ... time,gyroReadingsBody(:,3), ... time,angVelBodyRecovered(:,3)) title('Z-axis') ylabel('Angular Velocity (rad/s)') xlabel('Time (s)')```