RAIM probably would detect it.
That statements deserves an explanation. So here we go:
For determining the position, the GPS receiver needs to receive signals from four GPS satellites. These four signals constitute four equations which are solved to find four unknowns. These are 3D position of the receiver (x,y,z or lat,lon, h) and receiver clock bias.
When there are more than four satellite in view, these are added to the list of equations. The total problem is now overbounded (e.g. seven equations and four unknowns), and solved by a least square estimate. The solution is most likely not an exact solution to all equations, but gives the best fit.
The reason that there is not an exact fit is due to small errors in the measurement. These are due to various causes such as: ionospheric disturbances, ephemeris errors, receiver errors and others.
With the clock bias estimated, it is possible to determine the difference in time between transmission and the reception of a satellite signal. When you multiply the time difference with the speed of light, you obtain the measured distance to the satellite called pseudorange.
When there are four satellites in view, the pseudorange is always equal to the distance between the measured position and the reported position of the satellite.
If there are more than four satellites that is usually not the case.
RAIM compares the pseudorange to the distance between the satellite (known, transmitted from the satellite) and the receiver reported position. The difference is called pseudorange error. Normally, the pseudorange errors are small in the order of a few meters. As long as the range error is within certain bounds, RAIM assumes that it is due to standard measurement noise. Only if the range error grows over a certain threshold it is unlikely that the error is due to normal uncertainty in the measurements. In that case RAIM triggers an alert.
When only one satellite fails (drifts away from its reported orbit, clock failure) while other satellites are doing fine it is possible to determine how big the position error can grow before RAIM kicks in. This is called the HPL or horizontal protection limit. When multiple satellites fail, it is not sure when RAIM sounds the alarm. However, it is very unlikely that the solution of the overbounded problem will deviate far from the true position while at the same time all the pseudoranges errors stay within the limits.
Of course for RAIM it is always necessary to receive signals from at least five satellites. And in general the more satellites the better.
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