Statistical Dependence Analyses of Operational Flight Data Used for Landing Reconstruction Enhancement

Abstract

The RTS smoother is widely used for state estimation and it is utilized here to increase the data quality with respect to physical coherence and to increase resolution. The purpose of this paper is to enhance the performance of the RTS smoother to reconstruct an aircraft landing using on board recorded data only. Thereby, errors and uncertainties of operational flight data (e.g. altitude, attitude, position, speed) recorded during flights of civil aircraft are minimized. These data can be used for subsequent analyses in terms of flight safety or efficiency, which is commonly referred to as Flight Data Monitoring (FDM). Statistical assumptions of the smoother theory are not always verified during application but (consciously or not) assumed to be fulfilled. These assumptions can hardly be verified prior to the smoother application, however, they can be verified using the results of an initial smoother iteration and modifications of specific smoother characteristics can be suggested. This project specifically verifies assumptions on the measurement noise characteristics. Variance and covariance of the measurement noise can be checked after the initial smoother application. It is discovered that these characteristics change over time and should be accounted for with a time varying covariance matrix. This sequence of matrices is estimated by kernel smoothing and replaces an initially assumed fixed and diagonal covariance matrix used for the first smoother run. The results of this second smoother iteration are mostly improved compared to the initial iteration, i.e. the errors are significantly reduced. Subsequently, the remaining dependence structures of the residuals of the second smoother iteration can be captured by copula models. Their interpretation is useful for a revision of the physical model utilized by the RTS smoother.