Kalman Filter and Unscented Kalman Filter Comparison

[bcazabonne]

Hi @Echulion

Your 2 questions address 2 difficult subjects of the orbit determination for which there is no perfect answers with perfect values since they depend on the measurement provider and the prediction model

@Echulion

In the case where I provide my own dataset, how can I possibly know the uncertainty in the position and velocity? I mean I could have a rough guess on it, but it would probably give me results with reduced accuracy, no?

Because in the long term you plan to use optical measurements, the uncertainty will be related to your optical measurements. It is difficult to know the uncertainty because it is related to the sensor. Good sensors have a small sigma value and bad sensors have a big one. I know that calibration campaign using ephemeris based orbit detemination of GNSS satellites can be used to calibrate the sigma value of optical sensors. Unfortunately, I’m not an expert of that method. The best is to ask the sensor costumer or main users about the uncertainty of the measurements it provides.

At the end I think the estimated orbit will be close between a rough guess and a perfect guess of the sigma. The main difference will be on the estimated covariance matrix.

@Echulion

For this specific Starlink example, covariance matrix is already provided. So using diagonal elements of this matrix, we can find sigmaPos and sigmaVel at every step of the iteration. Determining this parameters for another satellite might be difficult as you said. But, do you know how to find the initial process noise matrix (initQ) or its calculation is also not straight forward?

initQ is the dark side of the Kalman Filter
initQ represents the expected error of your prediction model. Therefore, it depends on the prediction model you will use. With an accurate prediction model, you shall set small values.
It is really difficult to intialize this matrix. Personally, I’m a bit scared of this matrix because it has a significant impact on the estimated solution and we don’t know what to put inside.
To give you an example, there is an Orekit tutorial for which we perform accurate orbit determination of Lageos 2 satellite with an initQ of [1.e-9, 1.e-9, 1.e-9, 1.e-12, 1.e-12, 1.e-12]

Best regards,
Bryan