Consider Covariance?greenspun.com : LUSENET : CU Statistical Orbit Determination : One Thread
I am computing the consider covariance transition matrix and having trouble. I have computed B = [0 0; 0 -theta/l] theta being the state theta not the matrix I am computing. SO thetadot = A*theta + B. Now this theta is the consider covariance transition transition theta. When I am integrating this I find that one index is a function of another and theta (from the state). How do I solve this considering that theta from the state is a function of time? Do you see my dilema here man? I am reaching out to all of you in Cyberland..
-- Star Man (firstname.lastname@example.org), February 28, 2000
The easiest way to calculate THETA is by using the formula
THETA = dX(t)/dC(t0) = [ dTHETA/dx0 dTHETA/dg ] [ dTHETAdot/dx0 dTHETAdot/dg ]
THETA = THETA0 * cos(kt) + THETAdot0 * sin(kt)/k THETAdot = -THETA0*k*sin(kt) + THETAdot0 * cos(kt)
-- David Goldstein (email@example.com), February 28, 2000.
By solving the differencial equation:
thetaDoubleDot = -g/l * theta (this is the linearized equation of motion)
-- David Goldstein (firstname.lastname@example.org), February 29, 2000.
Where did you get your expresions for THETA and THETAdot (i.e. the state variables)?
-- Jason Stauch (email@example.com), February 29, 2000.