Real-Time Frequency Response Estimation from Flight Data

Abstract

A nonparametric method for estimating frequency responses in realtime using a method based on recursive least squares in the time domain was developed and studied. The proposed method uses sinusoidal functions at selected frequencies known to be contained in the input in conjunction with recursive least squares to rapidly estimate Fourier series coefficients for input and output time series, and thereby estimate frequency responses. Practical problems that arise when applying the discrete Fourier transform in recursive form were identified using simple examples. A general expression for accurate realtime calculation of the covariance matrix for recursive least squares parameter estimation was developed and used to calculate valid uncertainty bounds for realtime frequency response estimates. Simulation data generated with optimized multisine inputs were used to investigate the accuracy of the proposed method for realtime frequency response estimation, and to validate the calculated error bounds. The approach was also applied in realtime to flight data from a subscale jet transp ort aircraft. Comparisons of realtime frequency response estimates and error bounds with results from conventional postflight batch analysis showed that results from the realti me method were in statistical agreement with postflight batch estimates, with valid error bounds that properly indicated the quality of the realtime frequency response estimates.