A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-2: real data studies

In part-1 of this paper an adaptive filtering based on a reference recursive recipe (RRR) was developed and tested on a simulated dynamics of a spring, mass and damper with a weak nonlinear spring. In this paper the above recipe is applied to a more involved case of three sets of airplane data that have a larger number of state, measurements and unknown parameters. The flight tests cannot always be conducted in an ideal situation of the process noise and the measurement noises being white Gaussian as is generally assumed in the Kalman filter. The measurements may not be available with respect to the center of gravity and possess scale and bias factors, which will have to be modelled and estimated as well. The coupling between the longitudinal and lateral motion brings in added difficulty but makes the problem more interesting. It turns out that even a parameter that strongly affects the airplane dynamics is estimated which vary widely among the approaches. The RRR has been shown to be better than the earlier approaches in estimating the unknowns. The generalized cost functions that are introduced in the present work help identify definitive results from deceptive results.