How many satellites required for an LPV approach?

[simon]

I can't find this answer anywhere. I thought 5 or 6.

[SJFedor]

I think it's 4 or 5. Don't quote me though.

[simon]

Hmmm. I thought I read that 5 or 6 were required to detect satellite failure in the remaining required 4.

[Eclipse]

I thought three satellites were the minimum required to establish a "3D" location (one which includes altitude).

[SJFedor]

I thought three satellites were the minimum required to establish a "3D" location (one which includes altitude).

True, but then there's a 4th one thrown in for signal integrity checks.

[simon]

Sort of. Three to four.

The way it works is this: Each GPS satellite knows its position and the current time. Periodically it broadcasts this information.

A receiver picks up the information. Using the time the signal was received and the time the signal was transmitted (Contained in the signal), the receiver can calculate the distance from the satellite. Note that the time difference is small as the signal travels at the speed of light. Using the position of the satellite (Also in the signal), the receiver would then know that it is a fixed distance on a sphere around the satellite.

Using signals from three satellites, the receiver can then use triangulation to pinpont the exact position in space of the receiver.

The problem is, how does the receiver know the current time? It needs to know it with atomic clock accuracy because it is using measuring signals traveling at the speed of light. It can't get the current time from the satellites because it is that very time that it is measuring to get the position in the first place.

However, it is possible to determine the location of a receiver with only three satellites, but only roughly and effectively not accurately enough for navigation or use in most GPS applications. Even if a receiver doesn't know the current time, it does know the approximate distance to all the satellites - between 2000km when directly overhead and 14000km when on the opposite side of the earth. This is not a great distance for the speed of light and it is only going to be receiving signals from closer satellites, so between the three times received, the transmitter can figure out a range of possible locations.

To improve accuracy, a fourth satellite is used. With a fourth signal, the current time can be computed with atomic clock accuracy. There can only be one location for the receiver that matches the four times received. The current time is calculated and from that, the triangulation can be computed with accuracy.

Interestingly, the four times do not actually match precisely due to things like atmospheric conditions. This is where WAAS comes in. I won't get into an explanation for WAAS but the satellites receive the correction information and add it to the information packet that goes to the receiver. If the receiver can handle the WAAS information, it makes the correction. However, what I don't know is if 1 or 2 additional satellites are required for this accuracy to be ensured.

[SABRE17]

and it all happens before you can blink !

[PHall]

All of the aircraft GPS units that I have used so far needed to "see" four satellites before they would give a navigation solution.
So basically, if it's giving you a navigation solution, then you have enough.

[Mustang]

Five, I would think.  Four for the position solution, one WAAS bird for differential correction.