NavList:

This is a short follow-up on my previous long posting.

Let's say we have two LOPs:

LOP1: Parameter P
Lat = Lat1(P)
Lon = Lon1(P)

LOP2: Parameter R:
Lat = Lat2(R)
Lon = Lon2(R)

where the four functions on the right are known directly from the two GP's and Ho's.

In order to get the intersection of the LOP's we solve:

Lat1(P) = Lat2(R)
Lon1(P) = Lon2(R)

So we have two equations for two unknowns P and R.  In principle we can use one equation to eliminate one parameter, say:

P = Lon1_inverse[ Lon2(R) ]

and construct a single equation for one unknown = the other parameter:

Lat1( Lon1_inverse[ Lon2(R) ] ) = Lat2(R)

The LOP's are circles, therefore this equation is quadratic in nature yielding up to two distinct solutions.  The Van Allen's, John Karl's, Andres Ruiz's vector solutions are all equivalent to the above formal procedure.

Thus you can find your fix "directly" without any AP.


Peter Hakel