Covariance for SLR-based OD

Hi folks,

I’ve got a question about SLR-based OD and the resulting covariance matrix. Essentially, the values I get in the matrix are much smaller than I would have expected and I am trying to figure out if that is something that I have done in my configuration, if this is a limitation of covariance estimation in general, or perhaps some inadequacy in the data I’ve provided.

I am using SLR data from the ILRS for Ajisai and I take three orbits worth of observations: 6 observations in this period and about 70 data points in total. Each data point is a “normal point” with a specified uncertainty sigma value ranging from about 5mm up to 5cm. If I do an estimated minus observered comparison after using BLS to perform an OD and then plot the residuals I find that they are about ± 6m which I am happy with for the time being. I would expect the trace of the sqrts of the covariance to be of the same order as the residuals but this isn’t what I find. Instead, the value is on the order of 1mm. Is there something I am not considering in this approach or anything that I need to be aware of when using these algorithms?


Hi @Paul1

I think the accuracy of the obtained covariance is correlated with the uncertainty of your measurements. Therefore, I’m not surprised to see a covariance close to the standard deviation of your measurements.


Hi Bryan,

Thanks for getting back to me so quickly. That makes sense, although that does make the covariance somewhat less useful than I thought it was for purposes such as collision probability calculation. I thought that the covariance contained information about the orbit fit (which can be bad even with good measurement data, e.g. if perturbations are excluded for the dynamical model) rather than just being related to the variances of the measurements themselves and was therefore useful as a positional uncertainty. I will have to go an have a bit more of a read up on quite what it represents.

Thanks again,