Would you like to incorporate an electronic compass in a consumer product you’re designing or a personal device you’re constructing? If so, you’ll do well to understand as much as possible about the differences between various sensors and how certain forms of interference can affect their accuracies.
Whenever a new high-volume consumer electronics market develops, the semiconductor companies are never far behind, providing excellent components at surprisingly low prices. The market for sensors in consumer products is a recent example. It all started with an accelerometer used to select between portrait and landscape display orientations and then, with the addition of a magnetometer, evolved into the electronic compass (eCompass) used to align street maps to the smartphone’s geographic heading or to enable augmented reality overlays. As a result, high-volume pricing for smartphone accelerometer and magnetometer sensors is now less than $1 each.
A magnetometer sensor alone cannot provide an accurate compass heading for two reasons. First, the magnetic field measured at the magnetometer varies significantly with tilt angle. Second, the magnetometer requires calibrating not only for its own offset but also against spurious magnetic fields resulting from any nearby ferromagnetic components on the circuit board. This article describes how the accelerometer is used to compensate the magnetometer for tilt and includes a simple technique for calibrating the magnetometer.
SENSOR SELECTION
The accelerometer should be three axis and capable of operating in the ±2-g range with a minimum of 10 bits of resolution. The output of a 10-bit accelerometer operating in the ±2-g range will change by 512 counts as the accelerometer is rotated 180° from pointing downward to upward, giving an average sensitivity of one count per 0.35° change in tilt. This is more than adequate for tilt-compensation purposes.
It is important to check the accelerometer datasheet for the “0-g offset accuracy” which is the output when the accelerometer is in 0-g freefall. Since this value is a constant additive error on each accelerometer channel, it adds a bias in the calculated tilt angles, so look for accelerometers where this parameter does not exceed 50 mg.
The magnitude of the earth’s geomagnetic field is typically about 50 µT with a horizontal component that varies over the earth’s surface, from a maximum of about 40 µT down to 0 at the geomagnetic poles. If an eCompass is required to operate in horizontal geomagnetic fields down to 10 µT (in arctic Canada, for example) with a noise jitter of ±3°, then a back-of-the-envelope calculation indicates that a magnetometer with a maximum noise level of 0.5 µT is needed.
Most of my projects have used Freescale’s MMA8451Q Xtrinsic three-axis, 14-bit accelerometer and MAG3110 three-axis magnetometer. The MMA8451Q is supplied in a 3-mm × 3-mm × 1-mm, 16-pin QFN package and provides a 14-bit data output with ±30-mg, 0-g offset accuracy. The MAG3110 magnetometer is supplied in a 2-mm × 2-mm × 0.85 mm, 10-pin DFN package and provides a measurement range of ±1,000 µT with 0.1-µT resolution and a noise level down to 0.25 µT. Both parts operate with a supply voltage between 1.95 V and 3.6 V.
Similar sensors are supplied by Asahi Kasei (AKM), Kionix, STMicroelectronics, and other manufacturers. Your best strategy is to go to the manufacturers’ websites and make a list of those that provide samples in single units or low-volume packs of up to five devices. With a bit of luck, you may be able to get both the accelerometer and magnetometer sensors for free. Add a handful of decoupling capacitors and pull-up resistors and you should be well within the $5 component cost.
Each reader has a preferred microcontroller to read the raw data from the two sensors and implement the eCompass. This article assumes the microcontroller provides an I2C bus to interface to the sensors, supports floating-point operations whether natively or through software emulation libraries, and has a few spare bytes of program and data memory…
LAYOUT & BOARD BRING-UP
Once you’ve selected your sensors, the next step is to design the accelerometer and magnetometer daughterboard with I2C bus connection to the microcontroller. Reference schematics for the MMA8451Q and MAG3110 are provided in the sensor datasheets and reproduced in Figure 1.
Figure 1: Schematics for (a) MMA8451Q and (b) MAG3110 sensors (Source: M. Pedley, Circuit Cellar 265)
Don’t waste any time rotating the accelerometer or magnetometer packages to align their x-, y-, and z-sensing directions to each other since this will be fixed later in software. But do ensure the sensor board will not be mounted in the immediate vicinity of any ferromagnetic materials since these will produce a constant additive magnetic field termed the “hard-iron field.” The most common ferromagnetic materials are iron, steel, ferrite, nickel, and cobalt. Non-ferromagnetic materials are all safe to use (e.g., aluminum, copper, brass, tin, silver, and gold).
The calibration process described later enables the estimation and software subtraction of any hard-iron field, but it’s good practice to minimize hard iron interference at the design stage. Remember, a current trace will create a cylindrical magnetic field that falls off relatively slowly with the inverse of distance, so place the magnetometer as far away from high current traces as possible. A 0.1-A current trace at 10-mm distance will produce a 2-µT magnetic field, four times our 0.5-µT error budget, only reducing to 0.5 µT at a 40-mm distance. More detailed layout guidance is provided in Freescale Semiconductor’s application note AN4247: “Layout Recommendations for PCBs Using a Magnetometer Sensor.”
You’ll be surprised at the number of features implemented in the latest consumer sensors (i.e., freefall detection, high- and low-pass filtering options, automatic portrait and landscape detection, etc.), but disable all these since you simply want the raw accelerometer and magnetometer data. Configure the accelerometer into a 2-g range and check that you can read the x, y, and z accelerometer and magnetometer data (in units of bit counts) from the sensors’ internal registers at a sampling rate of between 10 Hz and 50 Hz. Smartphones commonly use IDH3 to minimize power consumption while anything above 50 Hz is overkill. Check the accelerometer datasheet for the conversion factor between counts and g (4,096 counts per g for the MMA8451Q in ±2-g mode) and use this to scale the x, y, z accelerometer readings into units of g. Do the same for the x, y, z magnetometer data again taking the conversion factor from the magnetometer datasheet (10 counts per µT for the MAG3110).
COORDINATE SYSTEM
The equations and C software in Listing 1 use the “aerospace,” or “x-North y-East z-Down,” coordinate system depicted in Photo 1.
Listing 1: C source code for the tilt-compensated eCompass (Source: M. Pedley, Circuit Cellar 265)
This defines the initial eCompass orientation to be where the x-axis points north, the y-axis points east, and the z-axis points downwards. The three orientation angles, roll (ϕ), pitch (θ), and compass heading, or yaw (ψ)—are defined as clockwise rotations about the positive x, y, and z axes— respectively. Photo 1 also shows the earth’s gravitational vector which points downward with magnitude of 1 g or 9.81 ms-2 and the earth’s geomagnetic field vector, which points downward from horizontal (in the northern hemisphere) by the inclination angle δ to give a horizontal component B0cosδ and a downward component B0sinδ.
Photo 1: The aerospace noth-east-down coordinate system (Source: M. Pedley, Circuit Cellar 265)
Based on how your eCompass housing will be held, you should be able to assign the compass-pointing direction or x-axis, the downward or z-axis, and the y-axis, which should point to the right to complete a right-handed coordinate system.
AXIS ALIGNMENT & MAGNETIC CALIBRATION
You now need to align the sensor data to the aerospace coordinate system. As with all work with magnetometers, this should be performed on a wooden table well away from any laboratory power supplies or steel furniture. Place the eCompass flat and upright so the z-axis points downward and is aligned with gravity. Check that the accelerometer z-axis reads approximately 1 g and the x- and y-axes are near 0. Invert the eCompass so its z-axis points upward and check that the z-axis now reads approximately –1 g. Repeat with the x- and y-axes pointing downward and then upward and check that the x- and y-axis accelerometer readings are near 1 g and –1 g, respectively. It’s not important if the accelerometer readings are a few tens of mg away from the required reading since all you’re doing here is correcting for gross rotations of the sensor packages and the sensor daughterboard in multiples of 90°. Any needed correction will be unique for your board layout and mounting orientation but will be no more complicated than “swap the x- and y-accelerometer channels and negate the z-channel reading.” Code this accelerometer axis mapping into your software and don’t touch it again.
Figure 2 may help explain this visually. The accelerometer sensor measures both gravity and linear acceleration and, in the absence of any linear acceleration (as is the case when sitting on a desk), the magnitude of the accelerometer reading will always equal 1 g, and therefore, lie on the surface of a 1-g sphere, irrespective of the orientation.
Figure 2: Accelerometer axis alignment points (Source: M. Pedley, Circuit Cellar 265)
The six measurements lie on the vertices of an octahedron inscribed within the 1-g sphere and the axis mapping simply rotates and reflects the octahedron as needed until the accelerometer channels are correctly aligned.
The magnetometer axis alignment is similar to that of the accelerometer, but makes use of the geomagnetic field vector. Place the eCompass flat, upright, and pointing northward and then rotate in yaw angle by 270° to the east, south, and finally west. The x-channel magnetometer reading should be a maximum when the eCompass is pointed north and a minimum when pointed south. The y-channel magnetometer reading should be a minimum when the eCompass is pointed east and a maximum when pointed west. The z-channel reading should be approximately constant since the vertical component of the geomagnetic field is constant irrespective of rotation in yaw.
Then invert the eCompass on the desk and repeat the process. As before, the magnetometer x-axis reading should be a maximum when the eCompass is pointed north and a minimum when pointed south. But now, because of the inverted position, the magnetometer y-axis should be a maximum when the eCompass is pointed east and a minimum when pointed west. The magnetometer z-axis reading should still be constant but, in the northern hemisphere, lower than the previous upright readings since the magnetometer z-axis is now aligned against the downward component of the geomagnetic field vector.
Figure 3 shows upright and inverted magnetometer measurements taken in the northern hemisphere with a 270o compass rotation.
Figure 3: The upright (a) and inverted (b) magnetometer measurements (Source: M. Pedley, Circuit Cellar 265)
The maximum and minimum of the x- and y-axis magnetometer measurements occur at the expected angles and the z-axis measurement is less when inverted than when upright. These magnetometer axes are therefore correctly aligned but, as with the accelerometer correction, swap and negate the measurements from your three magnetometer channels as needed until correctly aligned and then lock down this part of your code.
A lot can be learned by closely looking at the measurements in Figure 3. The x- and y-magnetometer measurements lie on a circle with radius of approximately 25 µT enabling us to deduce that the horizontal geomagnetic field is approximately 25 µT. But the measurements are offset from zero by the magnetic “hard iron” interfering field, which results from both permanently magnetized ferromagnetic materials on the circuit board and from a zero-field offset in the magnetometer sensor itself. Consumer sensor manufacturers long ago realized it was pointless to accurately calibrate their magnetometers when their target market is smartphones, each with a different hard-iron interfering field. The magnetometer sensor offset is, therefore, calibrated together with the circuit board hard-iron magnetic field. For now, simply note that the x and y components of the hard iron offset have values of approximately 215 µT and 185 µT. A simple method to determine all three hard-iron components is described later.
