All About IMUs - Pressure Sensors

You’ll find a common theme with any positioning system is utilizing other sensors to increase navigation reliability and resiliency. In our previous post, we saw how magnetometers are used to increase reliability in IMUs by utilizing the Earth’s magnetic field to determine the direction of True North. For height estimation, you’ll often find atmospheric pressure sensors integrated with GNSS and IMUs to increase accuracy. But why? As we’ve done before in this series for other aspects, let’s delve into the challenges of height determination in navigation systems, and how pressure sensors can be integrated to create a more robust solution.

Inaccuracy with GNSS Height

As discussed in our GPS and GNSS Overview, ionospheric delay and multipath effects can increase the time for a signal to reach a receiver, leading the receiver to perceive it’s further away from the satellite, resulting in positional error. In this case, let’s solely consider height - Any delays or additional travel time for the signal will result in an estimated height lower than the true height. Since these sources of error are a consequence of the environment or the available satellites overhead, it’s difficult to eliminate them.

Additionally, jamming, spoofing, obstruction, and weak signals can all impair GNSS availability and accuracy. There are receiver configuration options to overcome these challenges, but independently verifying the estimation is invaluable.

Estimating Height from Barometric Pressure

We know that atmospheric pressure drops as elevation increases. For small changes in elevation, this behavior can be approximated as linear quite accurately. So by sampling ambient pressure at two points in time and using static pressure formulas (e.g. hydostatic pressure formula $h = \frac{P_1 - P_2}{\rho*g}$ for simplicity) we can determine any change in elevation. Keep in mind that for larger changes in altitude, the linear approximation is prone to error and changes temperature must be compensated.

Approximation of Atmospheric Pressure Variation with Altitude

It’s important to note that comparing pressures in this way only yields the change in height, not the absolute height (above sea level). To obtain that, we simply need to perform the same process from a reference point where the exact height is already known. This can be as simple as taking a sample at a known location (e.g. landmark) or pulling up the latest weather data for pressure at sea level. Once we have this reference value, we can determine the elevation change of all future readings from this location.

Improving GNSS Accuracy with Accurate Height

Beyond improving our height estimation accuracy, using atmospheric pressure to determine height can also improve our GNSS accuracy. As outlined in our GPS and GNSS Overview, GNSS requires tracking of four satellites to determine position and time. If more than four satellites are available, we can use the more accurate height estimation (derived from the pressure sensor) to select the best combination of satellites. Let’s illustrate this with an example:

Assume our GNSS receiver is tracking 6 satellites overhead. That presents 15 possible combinations of 4 satellites to use for position and timing. After selecting to minimize dilution of precision and avoiding small horizon inclination (to minimize ionospheric delays), we can compare the estimated height from the remaining satellite combinations against our height estimation from the pressure sensor. Any GNSS heights estimated below our pressure sensor height we can accurately assume are affected by errors such as multipathing. The satellite combination that gives us the lowest error to our pressure sensor height is the most accurate, and the one we’ll select. Meaning that, not only is the GNSS height now more accurate, but the timing and horizontal position are also the most accurate of all satellite combinations.

Pressure Sensor Height Determination Errors

Daily Pressure Variance

Anyone who’s seen a weather report knows that the local pressure is not static. In fact, the local pressure changes continuously throughout the day. As a result, while you can calibrate your pressure sensor height determination at a known location, this calibration will lose its accuracy over time. That’s why it’s important to recalibrate the pressure sensor height determination every so often to minimize errors. One can follow the same process during initial calibration to recalibrate (e.g. use landmarks or GNSS if neeeded).

Pressure Variations and Wind

Relying on instantaneous pressure measurements increases the liklihood of capturing erroneous pressure changes due to wind and other pressure varying events (e.g. a closed door inside). Digital pressure sensors typically include sampling configurations to average readings to minimize and remove these errors.

Temperature Variations

Since pressure sensor height determinations rely on the change in the density of air, any change in ambient temperature will also change the ambient pressure (dust off that Ideal Gas Law Knowledge). Many pressure sensors include temperature sensors in package so that temperature variations can be compensated in the height determination.

Conclusion

Pressure sensors form another important pillar of reliability in our navigation sensor stack. When integrated with GNSS and inertial measurements, they allow for more accurate height determination which can sometimes lead to more accurate position estimation from GNSS. With care taken to account for weather, temperature, and local pressure variations, pressure sensors are a cheap addition that pay dividends for any navigation solution.