Kalman Filter and Unscented Kalman Filter Comparison

[bcazabonne]

Hi @Echulion

Please find below some answers.

@Echulion

So in my Kalman Filter and UKF code everything is same except I use KalmanEstimatorBuilder() in the first one and UnscentedKalmanEstimatorBuilder() in the second one

That’s right. My dream is to have a single Builder class common to all Kalman filters. The user could choose the type based on a KalmanFilterType enumerate. Unfortunately, that’s not implemented yet and user shall use the Builder corresponding to the Kalman he/she wants to use.

@Echulion

I would expect the results of Kalman Filter OD and UKF OD to differ from each another substantially, but they come out to be same. I wonder if there is something I am missing here.

UKF is maily used for problems with big uncertainties (e.g. high eccentric orbits, undetermined maneuver, stochastic parameters, etc.). I think that Starlink orbits contain in OEM files are smooth and don’t contain particular uncertainty. Therefore, it is normal that UKF and EKF give same results. In other words, you will see differences in case of estimation problems with big uncertainties.

@Echulion

And the diagonal elements of the covariance matrix initP should be square of these sigmaPos and sigmaVel values. However, calculation with this way gives really big numbers and I am just not sure about it.

sigma parameters represent the uncertainty of your data. For instance, if you use position data with 10 meters of uncertainty, you can set sigmaPos equals to 10. However, I don’t know the uncertainty of position/velocity in Starlink OEM files…

@Echulion

In my UKF code I was using default values in MerweUnscentedTransform. Now I randomly assigned alpha, beta, and kappa in it. Now, Kalman Filter results and UKF results are different. So regarding my first question, the input parameters of MerweUnscentedTransform were the only things that create this difference between Kalman Filter and UKF?

Default values come from litterature and correspond to “optimal” values for flight dynamics problems. Because your problem doesn’t contain strong non-linearities, you can keep using default values.
For more information, you can look at the two papers available in the following post: Unscented filter with non-zero process noise - #13 by bcazabonne

@Echulion

If above formulation is not how we supposed to calculate some of those parameters, is there a generic way that is accepted in the literature that you know of?

Accuracy of ephemeris files strongly depend on the orbit type and the provider. Having default values is difficult for this type of data.
For instance, you can look at the following paper which present the accuracy of CPF files (CPF is also a format of satellite ephemeris).
Therefore, I recommend you to look at spacetrack website to see if this information is available somewhere for Starlink OEM.

Best regards,
Bryan