Modified recursive maximum likelihood adaptive filter for nonlinear aircraft flight-path reconstruction

Abstract

Nonlinear aircraft flight-path reconstruction is basically a state estimation problem that can be solved with adaptive filtering techniques, as it involves the estimation of flight trajectories and unknown parameters such as biases, scale factors, and noise statistical uncertainties of flight instrumentation systems. Among many algorithms, the recursive maximum likelihood (RML) method is a popular scheme in adaptive filtering for nonlinear state-parameter estimation problems. However, the RML algorithm is sensitive to initialization errors of system parameters. Divergence may occur at large values of these errors. The objective of the present study is to develop a modified recursive maximum likelihood (MRML) adaptive filter that is less sensitive to the effects of initialization errors. The new algorithm revises the conventional RML adaptive filter by including the effect of the parameter estimator in the prediction error vector computation. Numerical results are presented for a nonlinear aircraft model. System states and a variety of parameters including measurement noise standard deviations were estimated with the conventional RML adaptive filter and compared with corresponding estimates of the new MRML adaptive filter. Numerical simulations were carried out with different a priori estimates of parameters and system state vector elements. The results indicate that the MRML adaptive filter, as developed here, produces estimates that are both more accurate and less sensitive to parameter initialization errors than those obtained with the conventional RML adaptive filter.