A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2010 Nov 17, 09:49 +0100
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.