Still don't know their height

The BBC has an article by Chris Baraniuk about still-unknown mountains:

The British mapping service Ordnance Survey has just confirmed the height of Ben Nevis (photo) is one meter taller than we thought. But there are many other mountains around the world whose heights remain very uncertain.
On all the current maps, Ben Nevis, Britain’s highest peak, is listed as 1,344 meters. But it’s actually 1,345 meters. That was the discovery of Ordnance Survey geodetic consultant Mark Greaves, who made a new, highly accurate GPS measurement in the autumn of 2015.
In fact, the actual difference in result was not a whole meter, but enough for the height to be rounded up from 1,344.527 to 1,345.
Greaves explains that two hours of tracking a total of twelve navigation satellites was needed to make the measurement. In that time, half a million bits of information from the satellites were received and recorded by a GPS device on top of Ben Nevis. This info contained time data and data on the wavelength of the signals but even, though those signals travel at the speed of light, it took a few microseconds to get from the satellites to Earth. “Because the code from the satellite has to travel twenty thousand kilometers, it’s delayed in time,” explains Greaves. “So the receiver has a code which is offset.”
By observing the offset, it's possible to work out exactly how far away the receiver is from the satellites’ position in space. Data from three or more satellites is used to work out the 3D position of the receiver. And that’s the first interesting quirk of the process— you start by measuring the distance from a satellite, not the height of the peak itself.
By combining that information with data from other, more permanent Ordnance Survey receivers nearby, it’s possible to work out what the most accurate reading must be and, indeed, the height above sea level, which gives the final result.
Not every mountain is measured as accurately as this. In Britain, many peaks are surveyed from the air using a technique called photogrammetry. This involves flying over a hill or mountain and taking a series of photographs which can then be analysed to produce a 3D model. Because the model will be perfectly to scale, the height can be reasonably well estimated, but it’s not as accurate as GPS.
Around the world there are many peaks which, either because of their obscurity or their treacherousness, have never been accurately measured with GPS. In September of 2015, National Geographic reported about one effort to measure the height of Hkakabo Razi (pronounced ka-kuh-bo rah-zee) in Myanmar (formerly known as Burma). The expedition was faced with such harsh conditions and setbacks that the climbers were unable to complete their task. The exact height of Hkakabo Razi remains the subject of debate.
There are the many South American peaks of the Andes which, as this online guide book points out, have never been conclusively measured. Take a given mountain like Cerro Paradones as an example. It’s listed here and there at heights ranging from around forty-nine hundred meters to just over five thousand meters.
The new Ben Nevis measurement differs only slightly from a 1949 estimate. But Ulugh Muztagh, a peak in the Kun-Lun Mountains in Asia, had its height revised down from 7,723 meters to 6,973 meters in 1985, following a Chinese-American expedition.
Then there are the mountains that no one has climbed. Labuche Kang III East, likely the second highest unclimbed peak in the world, is a good example. It lies on the edge of the Himalayas in Tibet. As Wikipedia notes: “The height is unknown, but is listed at over 7,200 meters on both Chinese and Russian maps of the area.”
Even Everest has been the subject of dispute. In 2011, Nepal sought to challenge the official measurement of Everest at 8,848 meters with its own study. There was debate over the height, because Nepal argued that the snow on top of the peak should be included in the measurement; it appears that China disagreed, suggesting a four meter reduction in the measurement would be more accurate.
Strangely, this disagreement followed consensus that had just been reached the previous year. To date, the results of a new GPS survey by Nepal have not been widely reported.
The world’s highest mountains are challenging places to carry out any kind of measurement. It’s humbling to think how their magnitude still dwarfs us to the extent that we do not really know, for sure, just how tall many of these mighty peaks really are.

Rico says you'd think satellites and GPS would've solved this, but there are peaks in Antartica that haven't been measured, either...