Hi everyone!

I have a question about the understanding of the covariance matrix.

I’m computing orbits with BatchSLE from RA/DEC measurements, and sometimes with range measurements.

Until now, I considered the covariance matrix of the estimated solution to represent the precision of the solution, as if the diagonal terms were the position/velocity probability distribution.

But since the covariance matrix values are proportional to the measurement sigma given in input, I can get these values to be as small as I want even with significant residuals.

For instance, I can get the position STD values in LVLH (I take the square root of the diagonal terms) to be 10^-30 m with 10^-3° residuals for a 1500 km orbit.

Does the covariance matrix give the precision of the solution, or just its uniqueness regarding the measurements?

If my measurements’ sigma are perfectly estimated, can I consider the covariance to represent a position/velocity probabilistic distribution?

Is there a better estimation of the precision of my solution?

Thanks in advance,

Théophile