Beidou (or .. how to do sat. nav. with just 3 sats)

Gegroet,


Some time ago, I came across a webpage concering the launch of the 3th
Beidou satelllite (the Chinese satellite-navigation system using
geostationairy satellites).

I don't know if there are plans to add a 4th satellite, but the Beidou-
system current only has 3 satellites. And, from what I know of the GPS/
Glonass/Galileo)link systems), I've always been told that you need 4
satellites to get a basic "fix".

Does this mean that Beidou is currently not operational yet, or is it
possible to do satellite navigation using just 3 satellites?



Cheerio! Kr. Bonne.

Kristoff Bonne wrote:

Yes.

One satellite gives you a circle of position, that is, your location is
somewhere on that circle.

A second satellite gives you two possible points, which are where two
circles of position intersect.

A third satellite will confirm one of those two possible points as the
correct one.

A fourth satellite provides altitude determination.

--
St. John

St. John Smythe wrote:

No. 1 sat defines a sphere in space where you are standing.

2 sats define a circle where the two spheres intersect.

3 sats define 2 circles which have two points in common.

4 sats define which of the 2 points is your location.

There is no "altitude" in space.

Stubby wrote:

Of course. Please consider my remarks as having been prefaced with "on
the earth's surface."

--
St. John

Stubby wrote:

Of course, the preceding assumes that you are carrying a clock with the
same accuracy as the clocks on the satellite. As this is a highly
improbable assumption, the correct (IMHO) analysis is:

2 Sats place you on an hyperboloid of revolution;

3 Sats place you on the line where two hyperboloids of revoluton
intersect;

another hyperboloid of revolution.

A four satellite solution gives x, y, z, and local clock correction:
four equations and four unknowns.

The four satellite solution is also not, in general, unique... The GPSR
has logic that (usually) allows it to discard the irrelevant
solution(s) from the set of correct ones.