IMU Accelerometer + Gyroscope Complementary Filter Calculator

ANA›Life Services Authority›National Calculator Authority›IMU Accelerometer + Gyroscope Complementary Filter Calculator

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IMU Accelerometer + Gyroscope Complementary Filter Calculator

Calculates the fused angle estimate using a complementary filter that combines high-frequency gyroscope integration with low-frequency accelerometer angle measurement. The filter balances gyroscope drift correction against accelerometer noise.

### Accelerometer Inputs

Accelerometer X (m/s²)

Accelerometer Y (m/s²)

Accelerometer Z (m/s²)

### Gyroscope Inputs

Gyroscope Rate (°/s)

Time Step Δt (s)

Previous Angle θ_prev (°)

### Filter Parameter

Filter Coefficient α (0–1)

α close to 1 → trust gyroscope more; α close to 0 → trust accelerometer more

Axis for Accelerometer Angle

Roll (X-axis, using Y and Z) Pitch (Y-axis, using X and Z)

Calculate

Results will appear here.

function imuCalc() { const ax = parseFloat(document.getElementById('imu-accel-x').value); const ay = parseFloat(document.getElementById('imu-accel-y').value); const az = parseFloat(document.getElementById('imu-accel-z').value); const gyroRate = parseFloat(document.getElementById('imu-gyro-rate').value); const dt = parseFloat(document.getElementById('imu-dt').value); const prevAngle = parseFloat(document.getElementById('imu-prev-angle').value); const alpha = parseFloat(document.getElementById('imu-alpha').value); const axis = document.getElementById('imu-axis').value;

const resultDiv = document.getElementById('imu-result');

// --- Validation --- if (isNaN(ax) || isNaN(ay) || isNaN(az)) { resultDiv.innerHTML = '⚠ Please enter valid accelerometer X, Y, Z values.'; return; } if (isNaN(gyroRate)) { resultDiv.innerHTML = '⚠ Please enter a valid gyroscope rate.'; return; } if (isNaN(dt) || dt ⚠ Time step Δt must be a positive number.'; return; } if (isNaN(prevAngle)) { resultDiv.innerHTML = '⚠ Please enter a valid previous angle.'; return; } if (isNaN(alpha) || alpha 1) { resultDiv.innerHTML = '⚠ Filter coefficient α must be between 0 and 1.'; return; }

const accelMag = Math.sqrt(axax + ayay + az*az); if (accelMag ⚠ Accelerometer magnitude is near zero — check your inputs.'; return; }

// --- Accelerometer angle (degrees) --- // Roll: atan2(ay, az) // Pitch: atan2(-ax, sqrt(ay² + az²)) let accelAngleDeg; let accelAngleFormula; if (axis === 'roll') { accelAngleDeg = Math.atan2(ay, az) * (180 / Math.PI); accelAngleFormula = 'θ_accel = atan2(ay, az)'; } else { accelAngleDeg = Math.atan2(-ax, Math.sqrt(ayay + azaz)) * (180 / Math.PI); accelAngleFormula = 'θ_accel = atan2(−ax, √(ay² + az²))'; }

// --- Gyroscope integrated angle --- const gyroAngleDeg = prevAngle + gyroRate * dt;

// --- Complementary filter --- // θ_fused = α × (θ_prev + ω × Δt) + (1 − α) × θ_accel const fusedAngle = alpha * gyroAngleDeg + (1 - alpha) * accelAngleDeg;

// --- Time constant equivalent --- // τ = α × Δt / (1 − α) const tau = (alpha * dt) / (1 - alpha + 1e-15);

// --- Cutoff frequency --- // f_c = 1 / (2π × τ) const fc = 1 / (2 * Math.PI * tau);

resultDiv.innerHTML = '### Results ' + '' + 'ParameterValue' + 'Accelerometer Angle (θ_accel)' + accelAngleDeg.toFixed(4) + ' °' + 'Gyroscope Integrated Angle (θ_gyro)' + gyroAngleDeg.toFixed(4) + ' °' + 'Complementary Filter Output (θ_fused)' + fusedAngle.toFixed(4) + ' °' + 'Accelerometer Magnitude |a|' + accelMag.toFixed(4) + ' m/s²' + 'Filter Time Constant (τ)' + tau.toFixed(4) + ' s' + 'Equivalent Cutoff Frequency (f_c)' + fc.toFixed(4) + ' Hz' + 'Gyroscope Weight (α)' + (alpha * 100).toFixed(1) + ' %' + 'Accelerometer Weight (1−α)' + ((1 - alpha) * 100).toFixed(1) + ' %' + '' + 'Axis: ' + (axis === 'roll' ? 'Roll' : 'Pitch') + ' | ' + 'Accel angle formula: ' + accelAngleFormula + '

'; }

#### Formulas Used

1. Accelerometer Angle

Roll:   θ_accel = atan2(ay, az) Pitch: θ_accel = atan2(−ax, √(ay² + az²))

2. Gyroscope Integration

θ_gyro = θ_prev + ω · Δt

where ω is the gyroscope angular rate (°/s) and Δt is the time step (s).

3. Complementary Filter

θ_fused = α · θ_gyro + (1 − α) · θ_accel

α = filter coefficient (0 ≤ α ≤ 1) High α → trusts gyroscope (good for fast dynamics, prone to drift) Low α → trusts accelerometer (good for slow dynamics, noisy for vibration)

4. Equivalent Time Constant & Cutoff Frequency

τ = α · Δt / (1 − α) fc = 1 / (2π · τ)

The filter acts as a high-pass filter on the gyroscope and a low-pass filter on the accelerometer, with crossover at fc.

#### Assumptions & References

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References

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