NavList:

Dear Paul,

A good didactical explanation of the method.

This remember me my end of career project where to solve the kinematics and dynamics of a complex mechanism, each component contribute with his own equation F, and the solution, like in the FEM method, is obtained from a set of n equations like:

∆F = ∂F/∂t ∆t + ∂F/∂B ∆B + ∂F/∂L ∆L

In your example F is the altitude or the lunar distance.

A generalization could be used if n observations are obtained, using the method of least squares.

At the university I used this method in heat transfer, in deformation and stress calculations for a structure, in thermodynamics, … And I have use it only once in my job when I worked in robotics, for calculate a space manipulator. For hobby and passion: navigation, I have used this method (1)(2) in my program CelestialFix.exe solving for latitude B, longitude L, course R and speed V.

Severance (3) was the first who published a solution using this method in “Overdetermined celestial fix by iteration“, and Kaplan (4) generalize it for use in the STELLA program.

Regards,

(1)     http://fer3.com/arc/m2.aspx?i=112117&y=201003

(2)     Position and motion from celestial observations

(3)     http://www.ion.org/search/view_abstract.cfm?jp=j&idno=298

(4)     http://www.usno.navy.mil/USNO/astronomical-applications/publications/sel-tech-rep

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Andrés Ruiz

Navigational Algorithms

http://sites.google.com/site/navigationalalgorithms/