[Update] This is for an on-board autonomous navigation system (3-dimensions, interplanetary) using a Kalman Filter. There is no target trajectory. I have the position and velocity measurement models with noise working correctly and process noise from an onboard clock. At this time, I'm only considering constant velocity during a long cruise segment such as New Horizons.
I will try matlab code from page 41 for the 2D case.
1) Are integrators such as Runge-kutta integrating acceleration and velocity without gravitational contributions?
2) Would it be appropriate to use Cowell's method for interplanetary orbit propagation?
3) If this were performed in real-time implementation, would past JPL ephemerides of the bodies be used?
4) What is the most common (practical) orbit propagator for interplanetary case?
Folks, I've reached my limit with understanding n-body problem for orbit propagation, in particular the state transition matrix (STM). If I can't solve this, I believe I will not graduate this June and will quit my engineering PhD effort. I've researched for weeks and only found examples for 2-body and 3-body problems around earth, but mine is interplanetary.
Assuming the state vector is [Rx Ry Rz Vx Vy Vz]T, I cannot analytically determine the state transition matrix for n-bodies (Sun, Earth, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Neptune, Uranus, Pluto). Considering that the STM is 6x6, the upper left and lower right quadrant are zeros, whereas the upper right quadrant is a diagonal one, but I cannot determine the lower left quadrant of gravitational forces (pertubations not necessary).
It appears the guide should be between pages 7-9 of this pdf, but there is no example. https://pdfs.semanticscholar.org/3341/f68082eb45509dcbacc5b4146d5b96acc89d.pdf
Please, I am begging as a Mechanical Engineering PhD candidate. My professor is the type that expects me to solve this on my own, but I think this is the end for me.