Decreased vertical precision is an artefact of measurement geometry more than e.g. number of frequencies.
Horizontal position has the benefit of having satellites at almost all azimuths. But the vertical position estimate only gets satellites from at most half of possible elevations (above the horizon).
There is a lot of talk of military uses here, but this technique is also used for environmental monitoring.
GNSS interferometric reflectometry (GNSS-IR) uses navigation satellites as the transmitter for a bi-static radar. The measurement device is any GNSS receiver (even your phone).
The technique can estimate environmental parameters like sea level, soil moisture, snow depth, and vegetation water content from systematic changes in the the multi-path around the antenna.
I'm a postgraduate researcher working on GNSS interferometric reflectometry (GNSS-IR), a related but slightly different technique.
I'll shout out this awesome open source project, where you can use GNSS-IR and your own RINEX files to measure tides or soil moisture around your antenna: https://gnssrefl.readthedocs.io/en/latest/
(Your antenna needs to be near the sea or bare soil, respectively)
You've got exactly the right idea, except "cross compare" is underselling it :)
Here's a previous thread on this topic[0].
For each (receiver, satellite) pair, you can calculate the TEC along the signal propagation path by comparing the time of flight of two carrier waves (e.g. L1 and L2)[1].
By fusing the data from each line of sight together you can get a rough, real time, 3D (4D) model of the ionosphere. Then, you have a separate problem of identifying ionospheric anomalies in the model and relating them to phenomena like earthquakes.
Aerial survey LiDAR can process multiple returns from a single laser pulse. So, some energy might be reflected back from a leaf, but some energy will pass through (or around) the leaf, hit the ground, then reflect back to the sensor. Some systems can record 5+ points from a single laser pulse.
With this information, you can filter the point cloud to only include points from the final return, which is likely to be the ground/a solid surface unless the vegetation is very dense.
A raw point cloud is run through a series of processing steps to label each point with a class, e.g. "Ground", "Low/Medium/High Vegetation", "Building", "Transmission Tower", etc.
There will be a different algorithm for each feature class. For example, points that are part of a building might be identified by finding groups of points that form a very flat surface. ML models can also do this based on training data.
The final digital elevation model (DEM) is then just taking the "Ground" class from the classified point cloud and using them to triangulate a surface. This differs from a digital surface model (DSM), which will triangulate a surface based on ground+building+vegetation points.
It's a bit pricer but very capable and well documented. There is a physical switch to enable power input for the modem over a separate USB to the data connection, so the power for transmission can bypass the Pi electronics.
I noticed during testing that the 4G connection would sometimes drop and require manual intervention to reset... So I added a systemd timer to test the connection and bring the interface down/up again whenever it disconnects. No problems since then, now with two months of uptime with ~200MB upload per day :)
I'm running a Raspberry Pi based GNSS receiver from a 26 Ah SLA battery and an 80W panel. Just passed 2 weeks of uptime in a cloudy period of southern hemisphere autumn.
A monte carlo simulation using historical conditions said it had a ~95% chance of no downtime over 3 winter months. A slightly larger battery would bring that up to 99%.
The Pi (3b+), GNSS reciever (u-blox ZED F9P), and Waveshare 7600G 4G modem average about 3.5W idle. The GNSS reciever is about 0.1 - 0.2 W of that. Wifi would be more energy efficient, I imagine.
Horizontal position has the benefit of having satellites at almost all azimuths. But the vertical position estimate only gets satellites from at most half of possible elevations (above the horizon).
See "Vertical Dilution of Precision":
https://en.wikipedia.org/wiki/Dilution_of_precision