Calculate Heading From Magnetometer And Accelerometer

Correct raw sensor readings before finding reliable direction. Add declination and review calibrated output vectors. Export results later for reports, logs, maps, and dashboards.

Calculator

Example Data Table

Case Mx My Mz Ax Ay Az Declination Use
Phone board 23.40 -4.80 41.60 0.12 -0.05 0.99 2.40 General field check
Tilted robot 18.20 11.70 35.10 -0.32 0.18 0.93 -1.10 Mobile platform
Logger sample -7.50 29.40 38.80 0.04 0.21 0.98 5.70 Outdoor record

Formula Used

Calibrate each magnetic axis first:

Mxc = (Mx - Ox) × Sx, Myc = (My - Oy) × Sy, Mzc = (Mz - Oz) × Sz

Normalize acceleration and estimate tilt:

|A| = √(Ax² + Ay² + Az²), roll = atan2(Ay, Az), pitch = atan2(-Ax, √(Ay² + Az²))

Compensate the magnetic vector:

Xh = Mxc cos(pitch) + Mzc sin(pitch)

Yh = Mxc sin(roll) sin(pitch) + Myc cos(roll) - Mzc sin(roll) cos(pitch)

Find heading, apply declination, and wrap it:

heading = atan2(-Yh, Xh), true heading = wrap360(heading + declination)

How to Use This Calculator

  1. Enter raw magnetometer values for X, Y, and Z.
  2. Enter accelerometer values in g units.
  3. Add hard iron offsets from your calibration process.
  4. Add soft iron scale factors for each magnetic axis.
  5. Enter local magnetic declination for true heading.
  6. Select the axis convention used by your device.
  7. Press Calculate and read the result above the form.
  8. Download CSV or PDF when a record is needed.

Tilt Compensated Heading Guide

Why This Calculation Matters

A tilt compensated heading calculator helps turn raw sensor data into a useful direction. A magnetometer senses the Earth field. An accelerometer estimates gravity. Together, they can describe the device attitude and the magnetic north direction. This page adjusts both sensor groups before the final angle is shown.

Calibration Inputs

Raw readings often contain bias. A case magnet, battery, screw, or nearby wire can shift every magnetic axis. These shifts are called hard iron offsets. Scale errors also appear when one axis responds more strongly than another. Soft iron scale inputs help correct those changes. The calculator subtracts offsets, then multiplies by scale factors.

Tilt And Declination

The accelerometer is used to estimate roll and pitch. These angles show how the device is tilted. A level compass can use only horizontal magnetic values. A tilted device needs compensation. The formulas rotate the magnetic vector back toward the horizontal plane. Then the arctangent function gives a heading angle.

Declination is another important option. Magnetic north and true north are not always the same. Local declination adds or subtracts that difference. Positive values move the result east. Negative values move it west. You can enter zero when magnetic heading is enough.

Reading The Output

The tool also reports intermediate values. It shows calibrated magnetic axes, normalized acceleration, roll, pitch, heading, quadrant, and cardinal direction. These details make testing easier. They also help compare results with embedded code, phone sensors, or field measurements.

Accuracy Tips

Use stable samples for better accuracy. Keep the sensor away from motors and large metal objects. Rotate the device slowly during calibration. Check that acceleration is close to one g when the device is still. Very high acceleration means the tilt estimate may be unreliable.

This calculator is useful for robotics, mapping, drones, phones, and outdoor instruments. It is not a replacement for sensor fusion filters. Gyroscope data can improve dynamic motion. Still, these equations give a clear reference. They are excellent for learning, debugging, and simple navigation tasks.

Save the result when you need records. The CSV export works well for spreadsheets. The PDF export is useful for reports. Example values are included, so you can test the form before using your own device data. Repeat measurements at different orientations to reveal wiring mistakes and axis swaps.

FAQs

What does tilt compensation mean?

It means the magnetic vector is corrected for device roll and pitch. This helps find heading when the sensor is not level.

Why is an accelerometer required?

The accelerometer estimates gravity direction. Gravity gives roll and pitch, which are needed to rotate magnetic readings onto the horizontal plane.

What are hard iron offsets?

They are constant magnetic shifts caused by nearby magnets, current paths, screws, batteries, or enclosures. Subtracting them improves heading accuracy.

What are soft iron scale factors?

They correct unequal magnetic response across axes. Values usually come from calibration software or an ellipsoid fitting process.

Should I use magnetic or true heading?

Use magnetic heading for raw compass comparison. Use true heading when maps, navigation bearings, or geographic directions need declination correction.

Why does the calculator show warnings?

Warnings appear when acceleration is far from one g or the horizontal magnetic field is weak. Both cases can reduce heading quality.

Which axis convention should I choose?

Start with compass style. If your device heading is mirrored or rotated, try the other conventions and compare with known directions.

Can this replace a full sensor fusion filter?

No. It is a static reference method. A fusion filter with gyroscope data performs better during fast movement and vibration.

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