Estimation of the measurement noise - adaptive Kalman filter

[ChristopherRabotin]

High level description

Issue #326 will support estimation of the ground station biases. Although important, it's possible that one may increase the measurement noise quite high in order to accommodate for unmodeled dynamics as a temporary solution, and manually tune the filter.

The purpose of this ticket is to implement a measurement noise variance estimator using any N consecutive measurements from a given OD participant. Equation 2.13 in this paper shows that the measurement noise should have a mean of zero, and therefore it is possible to use any number of previous estimates to compute a more appropriate measurement noise.

Requirements

• Add a function to the ODP to estimate the measurement noise.

Test plans

• Define a station with a noise level R1 and set it to a level of R2 in the ODP such that R1<R2. Ensure that the estimator can compute a more appropriate noise model.
• Repeat with R1>R2, ensuring that the estimator returns an estimate not too far from the one used in the simulated tracking data. This will likely require disabling automatic residual rejection.
• Add a small finite burn in a test scenario, analyzing the behavior to guide the documentation of this functionality.

Design

The simplest approach here is probably to run this estimator post facto and recommend that the OD analyst use the results for tuning the filter for the next pass. In the best of all worlds, the function would return not just the optimal noise level for each measurement, but also a supported set up of the model for each ground station, e.g. by defining the whole Gauss Markov process that best matches the data.