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Date: 2024-11-08 12:42:17
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In the code you shared, the initial position uncertainties have a standard deviation of about 45 meters (=sqrt(2*10^3)). The process noise at each step is the same order of magnitude. So the filter's uncertainty in its position just from the model is on the order of tens or low hundreds of meters.

The measurement noise that you are adding has a standard deviation of 2.5 degrees in latitude and longitude. Let's do some quick math on that. The radius of the ISS orbit is about 6778000 meters. We can find the uncertainty in meters using the arc length formula: s = r * theta = (6778000) * (2.5 * pi / 180) = 295746. So the uncertainty in each measurement is on the order of hundreds of thousands of meters.

What will the filter do when it knows the position of the spacecraft accurate to tens of meters and then gets a measurement that's only accurate to hundreds of thousands of meters? It will, correctly, almost completely ignore the measurement. If you want the filter to pay attention to the measurements, then I would suggest turning the measurement noise way down. For example, if you wanted the measurements to have an uncertainty of 100 meters, a noise standard deviation of 0.0008 degrees is about what you would want.

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Posted by: Dawson Beatty