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It is clear that a barometer is more accurate in measuring altitude than GPS. However is it true that the barometer improves GPS position accuracy?

Would be a GPS device and a GPS+barometer device equally accurate if we didn't look at the altitude?

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    $\begingroup$ "It is clear..."? You seem to have both a particularly low quality GPS device and a particularly magic barometer. What devices are you using, and what numbers do you have for their errors in altitude? GPS should be accurate to meters, barometers can be off by hundreds of meters. $\endgroup$ – user10851 Jun 7 '16 at 9:10
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    $\begingroup$ That is just not so. You can buy GPS devices that have cm or even mm accuracy. The designers of your cell phone just didn't care about that. $\endgroup$ – CuriousOne Jun 7 '16 at 14:16
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    $\begingroup$ @ChrisWhite Barometers have terrible absolute accuracy (because air pressure varies, obviously), but they can have rather good differential accuracy. So if air pressure isn't varying much and you have a good zero point, barometers can be very good. $\endgroup$ – tfb Jun 7 '16 at 14:19
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    $\begingroup$ @Farcher Airplanes use barometers because they don't care about height above ground. The only thing that matters is the pressure at which they are flying. That reading is often converted to feet based on a standard atmosphere, but this is just tradition and that is certainly not an accurate measure of the number of feet between the plane and the ground. The only way to make a barometer accurate is to calibrate it (within the last couple hours, and not very far from where you are using it). That calibration is done with a GPS! $\endgroup$ – user10851 Jun 7 '16 at 17:16
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    $\begingroup$ To get ~ cm's of accuracy from GPS you are talking about differential gps. This requires a local base station that's surveyed-in to cm's of accuracy, and permissions to communicate with it. $\endgroup$ – docscience Jun 7 '16 at 22:50
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The science of sensor fusion provides, by the combination of multiple, seemingly redundant measurements, a reduction of variance in the combined measurement. Basically speaking, for independent, identically distributed noise processes, the signal to noise of combined $n$ measurements is increased by the factor of $\sqrt{n}$.

And in fact, commercial INS (Inertial Navigation Systems) include among the accelerometers, GPS recievers, and gyro sensors, an aneroid barometer, all of which feed into a Kalman filter resulting in a very accurate estimate of position, velocity and three axis attitude.

Examples include the LN100 fom Litton and Honeywell's EGI (Embedded GPS in INS) systems

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  • $\begingroup$ A barometric altimeter doesn't measure the altitude. If you follow the altimeter, you follow an isobaric surface, and the actual altitude may vary a lot. In cruise the altimeter is set to a standard reference pressure of 1013.25 hPa on the ground, which is likely wrong all the time, but the same for all aircraft which can use different isobaric surfaces (named flight levels) to prevent collision. There is no barometric altimeter in the INS. GPS is way more accurate than inertial systems, INS is used because it's not relying on any external equipment. $\endgroup$ – mins Jun 10 '16 at 5:51
  • $\begingroup$ @mins it may be that with your particular experience with GPS-INS systems there was no barometer involved, but I know from my own experience and the Honeywell model we used there was a barometer in the instrument as part of the sensor fusion algorithm. Also if you just google a combination of 'GPS INS Barometer' you will find many articles that discuss the use. I don't know the exact details in the KF but suspect the barometer reading is loosely coupled; doesn't have significant weighting. $\endgroup$ – docscience Dec 1 '16 at 1:06
  • $\begingroup$ These units combine 3 instruments: INS, GPS and barometer to get the best of 3 worlds: GPS for accuracy, INS and barometer for better rates of measure. But neither INS or barometer increase GPS accuracy. This is used when high rates of measure are needed (e.g. missile guidance), which cannot be achieved with GPS alone. So between two actual GPS measures, the position variation is estimated using the other quicker instruments, the result has likely a lower accuracy than the GPS alone. If you have another information, please post a link. $\endgroup$ – mins Dec 1 '16 at 6:27

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