[time-nuts] A novel use of GPS multipath

jimlux jimlux at earthlink.net
Sat Dec 17 08:44:20 EST 2016

On 12/16/16 9:54 PM, Mark Sims wrote:
> http://clasp-research.engin.umich.edu/missions/cygnss/docs/CYGNSS_FactSheet_October2014.pdf
> I wonder what the return signal strength of the reflected signals is?

There's quite a few of these bistatic radar using GPS as illuminator 
things over the years, airborne and space borne.

You get a fairly big signal: if you're in LEO, the signal has already 
gone 20,000 km from GPS satellite to surface of earth,reflects and goes 
400-1000 km more.  The entire earth is illuminated, and the antenna on 
the spacecraft sees pretty much everything within a thousand km 
(depending on the height.

The reflectivity of ocean water is quite high, and even soil is pretty 
good.  The number is usually worked as sigma0 (pronounced sigma naught), 
which is the normalized radar cross section - RCS in square meters per 
square meter of surface.

Typical numbers for L-band range from -20 to +10 dB - depending on the 
material and whether there are features (waves, furrows) that result in 
bragg scattering in a preferred direction (this is how you measure the 
wind speed with a radar from space)

The trick on this kind of measurement is not detecting the signal in the 
first place, it's getting some kind of spatial resolution - the signal 
from thousands of square km is big, the signal from any little square is 

GPS is useful because you can build a fairly simple receiver, record the 
raw bits, and then, on the ground, post process to extract the direct 
signals (which gives you the satellite position and time very 
accurately) and get the reflections..  By combining the data from 
multiple satellites (made much easier because you know the time and 
position of each recording), you can get measurements for discrete areas 
on the surface of the Earth.  It's a sort of multilateration process, 
and solving a big set of linear equations - much like any form of 
tomography.  Each GNSS satellite/observer pair gives you a "reflected 
power vs delay" curve, a given delay maps into a sort of egg shaped 
ellipse on the surface of the earth. You can form a linear equation for 
each egg/slice/ellipse, and then iteratively solve the system (since the 
measurements are noisy, etc.)

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