Kalman filter

This sandbox illustrates how observation and forcast error affect the tracking performance of an analytic Kalman filter for a satellite in orbit. The model predicts a perfect geo-synchronous orbit, whereas the true trajectory wobbles a fair bit. A data assimilation algorithm like the Kalman filter can recursively improve the model's predictions with the help of position measurements. Experiment with the following elements:

The orange horizontal line in the top right subplot represents the average log density of the true state evaluated at the filter's position estimate. In most real system's, this quantity cannot be calculated, as the true state is unknown. For this synthetic experiment, however, it allows us to quantify the filter performance. Try to find a combination of observation and forecast errors that maximizes this log density and remains stable over extended periods of time.