A Heuristic Reference Recursive Recipe for the Menacing Problem of Adaptively Tuning the Kalman Filter Statistics. Part-2. Real Data Studies (1505.07208v1)

Abstract: In the previous paper an adaptive filtering based on a reference recursive recipe 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 which have a larger number of state, measurements, and unknown parameters. Further the flight tests cannot always be conducted in an ideal situation of the process noise and the measurement noises being white and Gaussian as is generally assumed in the Kalman filter. The measurements are not available in general with respect to the center of gravity, 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. At times the noisy measurements from the longitudinal and lateral motion are input into the longitudinal states. This leads to the resulting equations becoming linear with the measurement noise forming the process noise input. At times it turns out that even a parameter that strongly affects the airplane dynamics is estimated which vary widely among the approaches. This requires a careful look at the estimates. We also recommend a closer look at the correlation coefficients (that is generally ignored in such studies) of the estimated parameters which provide an insight into their subsequent uses. The present recipe has been shown to be better than the earlier approaches in estimating the unknowns. In particular the generalized cost functions that are introduced in the present work help to identify definitive results from deceptive results.